Harumi is Mitsuko younger sister. Mitsuko does care for her and wants what's best for her. Unfortunately, because of her cold personality, Harumi keeps her distance, which does bother her. She does truly care about her sister and wants her to be happy and grow up her own way.
As seen on volume 5's extras, Maruta and Mitsuko have a good relationship, which Maruta being seemingly the only person not afraid of Mitsuko. Maruta constantly teased Mitsuko due to her true childish self compared to her mature persona, and due to her love for her little sister, as Harumi feared Mitsuko's personality, She also nicknamed Mitsuko "Micchan". They maintain being friends after Mitsuko had graduated she even invited her along for Summer trip.
Mitsuko is very harsh to Mei, as seen when she scolded her for not keeping the students in line. She does respect her and left the school to her in full confidence and was very pleased with her how she chose to run the school.
Himiko seem to be afraid of her and due to that fear was worried about Yuzu and how things would turn out.
Apon first meeting one another Yuzu was defending Nene from Her and she didn't seem to like her but after her speach was pleased to see her speaking her mind and standing up forherself and other students.