According to Hachiman Hikigaya, Minami is a superficial person. Her relationships are only skin deep and she uses them to boost her own popularity.
Sobu High School
Minami's clique
None of the names of her current or first year clique members are made known to the audience. Almost all of her clique were shown to share certain personality traits of Sagami
Minami and her clique's antagonizing laughter at Yui Yuigahama
Minami is mentioned to be the leader of the second most influential clique, below Hayato's clique, in class 2-F. They are shown to be petty and mocking towards others. Minami would arrive late to the Cultural Festival committee because she was hanging out with them. Mostly Minami badmouths others to her clique. She gossips to her clique and insults Hachiman behind his back.
Minami ditching the meeting in order to gossip with her clique
It was also mentioned (in Volume 6.5 and Volume 7) that after the cultural festival, they had disgust and disdain for Hachiman. Together they would sneer/burst out laughing when their gaze met with Hachiman's. However, after the Kyoto trip, their gossiping about Hachiman slowly went away.
Haruka & Yukko
There is a possibility of Haruka being her clique members in first year, but now are in a different class. Sagami met Yukko for the first time in the planing committee who also happens to be a friend/acquaintance with Haruka, being in the same basket ball club. Yukko started to call Sagami on first name basis after their initial meeting and Sagami did the same. There are many traits they each share like lust for higher social standing, slacking off and their interest on Hayato.
Minami at the conference with Haruka and Yukko
In Episode 10 of season 1 (adapted from volume 6 of the light novel), her conference friends names were mentioned to be Yukko ( Voiced by :Megu Sakuragawa ) and Haruka ( Voiced by :Miki Inoue). They call each-other by their first names. Minami made sure that these two were considered equal to her in the Cultural Festival planning committee, as both of them sit together with Minami and Yukino in the conference room, even after Sagami becomes the chair person.
Hayato and Minami's friends stunned at Hachiman for scolding Minami
When Minami went into hiding during the Cultural Festival, they accompanied Hayato to the rooftop to coax her to return. Hachiman felt that they likely came because Hayato requested them to do so. Both of them seemed to console Minami, after she delivered her ending ceremony speech.
Aftermath of the Culture festival: Haruka, Yukko, and everyone else show sympathy for Minami just as Hachiman planned.
Hachiman believes that both Haruka and Yukko are friendly with Minami only on the surface, which was later shown to be true. They used Minami to appear cool and refused to help her work while on the Athletic Festival committee in Volume 6.5.
At the end of Volume 6.5, it seems that their friendship has deteriorated. Both of them refused to carry out Minami's plan during the Athletic Festival committee meeting. This shocked Minami greatly as she was hoping for them to stand up for her like they did during the Cultural Festival. However, they reveal they only did that before to gain a higher social status and to slack off. To Minami's shock, it turns out most of the committee's opposition and gossip about her originated from them. At the final meeting of the planning committee, when Minami introduced the harsh rule against the slackers, prohibiting them from taking part in the athletic festival, they verbally confronted her and slung insults at her. Ironically, their actions were no better than Hachiman's since they basically tried to break Minami's ego with harsh truth.
It is unknown if they have patched things up but it is unlikely, as Minami is only seen with her clique members after this.
Hayato Hayama
Hayato recommending Minami as the Culture Festival female representative
Like numerous other girls in her school, Minami seems to be interested in Hayato. She often tries to gain his approval. Hayato often acknowledges her but often hides his personal feelings. This is his habit of staying neutral and preserving his image.
Minami was recommended to be the class' female Cultural Festival representative by Hayato, but only so his clique would be left alone. He just agreed to Tobe's suggestion in class. It is mentioned later that he regrets it.
Hayato is able to see through Minami's facade, and can see her incompetence and irresponsibility. He dislikes Minami, but is friendly to her face. Only Hachiman is aware of his true feelings about her.
Minami has tried to be appealing to Hayato. In the light novel, Minami, along with her clique, invited Hayato to hangout as a pretense of inviting the remaining members in the conference room after a Cultural Festival meeting. Everyone in the vicinity turned down her offer and Hayato also followed their answer.
Hayato, Haruka, and Yukko attempting to comfort Minami into coming back to the school.
Hayato searched for her during the Culture Festival closing ceremony along with Haruka and Yukko. While Hayato and Minami's friends attempted to convince her to return to the festival, Hachiman plays the villain to get her to return. Hayato showed his violent side for the first time by grabbing the front of Hachiman's shirt and slammed him to the wall. He does this to defend Minami, along with his own personal reasons.
In Volume 10.5, Hachiman visualizes the benefits of putting Hayato in the school newspaper and imagined Sagami sneaking his picture.
Meguri Shiromeguri
Minami wanted to be on good terms with the student council president, so she volunteered for the Cultural Festival chairperson. At first, Meguri was excited to see Minami volunteer for the chairman but she soon showed her regret about the decision. As Minami slacks off in regards to leading and instead spends time with her class. Meguri was dumbfounded when Minami gave "power of attorney" to Yukino.
Meguri silent as Minami dumps her work on Yukino
Even though Meguri didn't say anything, it is obvious that she doesn't view Minami in a good light. She thought it would be a bad idea when Yukino suggested Minami as the Athletic Festival chairperson. Meguri also stated her concern of things ending like the Cultural Festival planning committee. However, Meguri went with Yukino and Yui to persuade her to be the chairperson for Athletic Festival.
In Volume 6.5, Meguri praised Minami for taking up the Athletic Festival chairman role properly, in comparison to herself.
Saki Kawasaki
Minami praising Saki's work
Although their interactions were very brief and barely shown on-screen together, Minami and Saki appear to have a decent relationship, especially compared to Minami's other relationships. While Hina Ebina is the one who assigned Saki as the costume designer for the Culture Festival, Minami complimented her work on the costumes.
Saki also suggested Minami's name as a suitable candidate for student council.
Yumiko Miura
Like most characters in the series, the anime rarely shows Yumiko and Minami interacting or even talking but they do interact very briefly in the light novel. Yumiko is the leader of the most popular clique in class, while Minami is in charge of the 2nd most popular group.
Minami appears to hold a great amount of enmity and jealousy towards Yumiko for her higher social position and her close relationship with Hayato. She doesn't show this outwardly, but Hayato and Hachiman were able to see through her facade to her real feelings. Yumiko isn't concerned about Minami at all, as she picks her friends based off their cuteness and doesn't bother with anyone lower on the social ladder than she is. Yumiko also puts a stop to Minami and her clique from damaging Yui's reputation, as Minami was spreading rumors and tried to brand Yui as Hachiman's girlfriend.
In Volume 6.5, Minami bowed and requested Yumiko's help with announcing for the Athletic Festival. Minami and Yumiko are finally able to tolerate each other.
Haruno Yukinoshita
Minami wanted the commendation by the so-called legendary Haruno. Minami put up her innocent façade in front of Haruno when they meet for the first time. Despite that they just met, even Minami felt the intense cold words from Haruno for being late and immediately knew she was outclassed, causing her to shiver.
Haruno used Minami to gain approval to participate in the cultural festival of Sobu High school (proving she sees Minami as nothing more than a pawn). Haruno is able to read through Minami's facade and purposely misleads Minami for Haruno's hidden intention, by telling Minami that she should be having fun instead of working hard, thus leading Minami to confidently slacking off from the planning committee room. When the planning committee comes back in full force, Haruno stated indirectly an harsh comment with sugar coat of how the planing committee should be. Hachiman notes this to be a point blank shot towards Sagami while others thought it to be a praise for the committee.
The Service Club
Yui Yuigahama
Yui and Minami appear on good terms at first
Yui tells Hachiman that both Minami and herself "almost get along", implying their difficulty to maintain a mutual friendship. Yui was a member of Minami's clique in their first year of high school and Minami was friendly to her back then. But now Minami holds a grudge towards Yui for joining the superior clique in second year, leaving a dent in their friendship that Yui tries to make up for. When Minami and Yui find each other at the fireworks festival, they appear to be close friends at first as Yui calls her by a cute nickname, "Sagamin". However, after Yui introduces Minami to the boy that she (Yui) is with (Hachiman), Minami behaves completely different than her earlier friendly exterior. Minami smirks at Hachiman and teases Yui. Even after Yui struggles to sustain a genuine smile and denied being in a romantic relationship with Hachiman, Minami clearly believes she is now better than Yui.
Yui's strained smile at Minami at the Fireworks festival
Hachiman noticed the bizarre difference in their attitudes towards each other. Whatever the case, Minami appears to maintain her relationship with Yui in face-value, but behind Yui's back Minami talks trash about Yui to her clique and tried to convince the whole class that Yui was Hachiman's girlfriend. Yui finally admit her hatred towards Sagami and analyses it to be rooted from Sagami trying to coax Yukino to do work for her.She also adds that she never liked Sagami before as well but tried her best to get along.
In Volume 6.5, Yui tried to console Sagami about the opposition from the volunteers and her friends Yukko and Haruka.
Yukino Yukinoshita
Minami tried to get help from Yukino during the Culture Festival after learning she is very talented, with an ulterior motive to gain the praise of success and to slack off while Yukino did all the grunt work. However, Minami grew jealous of Yukino for naturally taking up the spot light and makes her realize her inferiority, which puts a dent in Minami's ego. Minami finally took a stand over Yukino by including Haruno in the planing committee. Haruno praised Minami for her slacking off and thus restores Minami's ego, and making her no longer fear Yukino. However Hachiman's action turned the table back, giving Yukino a stand and Minami with bitterness of herself.
Yukino doesn't see Minami in good light, as she can see through her personality and intentions. Yukino might have lead the committee as a chairman but being recommended as Haruno's sister, got her down. When Minami came with the request, Yukino used it to show her skill as an Vice-chairperson. Even after the Cultural Festival Yukino still recommended Minami to become the athletic festival chairperson with the hope of fulfilling Sagami's request and to diffuse the situation in class f
They do not contact each-other after the festivals.
Hachiman Hikigaya
Minami's disdain towards Hachiman
Minami looks down on Hachiman when she first set her eyes on him at the fireworks festival. At first sight, Minami viewed Hachiman as a social outcast and a loser. Hachiman however, is fully aware of Minami's true personality but chooses to just not care about her, instead of hating her. Sagami's only attempt was to look down on Yui using Hachiman as a status symbol.
Hachiman draws attention to himself....
After their encounter at the fireworks festival, Hachiman tried to just ignore her, but was dragged into matters when they were chosen to be the male and female representatives for the Culture Festival planning committee. Hachiman is the first member of the entire committee to point out to everyone how much most of them (especially Minami) were irresponsibly using Hachiman and Yukino to slack off.
.......only to call her out on her incompetence.
Hachiman criticizes the way Minami is handling her responsibilities as chairperson of the Cultural Festival. He comes up with a mocking slogan, and openly complains to Hayato when he stops by.Hachiman only intended to lower the work load shuffled over Yukino due to Sagami's action and noting personal against Sagami.
Hachiman finally cracks Minami's ego.
Things became even worse when Minami ran away and hid during the Cultural Festival. When Hachiman managed to find her, she resented him for it as she was longing for someone more popular to do so. Realizing this, Hachiman finally had enough of her behavior and tells her off for her treatment to him. In his speech, he reveals true feelings by stating he knows she accepted her position simply because of the popularity she gets and wanted to be someone who can look down on others. While doing so, he vilifies himself as her friends and Hayato (who is aware of the real purpose) console the now speechless Sagami who realized how outspoken Hachiman was than she thought.
In the light novel, Minami would neither join nor stop her clique members from badmouthing Hachiman, but she wears a downcast expression every time his name is mentioned, as she is still unable to forget his harsh words.
In Volume 6.5, Yui notices Minami's disdain towards Hachiman, which Hachiman does not seem to mind and instead he appeared to feel proud of. A bit of his past treatment towards her is reflected in that of her supposed friends, as the two girls would admit they used Minami and would insult her after she turned against them.
This likely caused Minami to change her perspective of him as he wasn't the only person who broke her. It would seem this is the case as they started to work together, and its shown Sagami took Hachiman's advice to "bring the hammer down" on her opposition from the Athletic Festival.
After the Athletic Festival, Yui and Yukino feel that Sagami has changed, since she didn't give away the person (Hachiman) who broke the rules during the Botaish event and stated the foul in a round about manner. When Hachiman and Minami crossed paths in the hallway she only tells him to get out of her way. Hachiman notices their relationship is neutral and is okay with the result.