Hazuki is the girls' mother, manager and songwriter.

When the Japanese government puts civilian organizations in charge of the country's air force, some of these companies decide to put their aspiring idol singers behind the controls of their fighter planes. Among these groups of idol singers is Hummingbird, a five-woman team consisting of the Toreishi sisters: Satsuki, Uzuki, Yayoi, Kanna and Miina. During a taping session, video director Kudo sees some potential in these girls and jumps in to help them reach the top of the charts by directing their debut video.
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(Source: Anime News Network)

One day in the near future, the Japanese Self-Defense Force decides to transfer the command (and financing) of their air force to private companies and investors. Most reject the idea as a joke, but some show business-oriented companies catch up on the idea, spawning the birth of a new type of idol: the so-called "Idol Pilots", celebrity combat pilots.
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The five Toreishi sisters, Kanna, Yayoi, Satsuki, Uzuki, and Mina, are teenage idol singers who are collectively known as The Hummingbirds. They are also one of the ace fighter pilot squadrons in the Japanese military. When they aren't saving the world from major overseas threats, they are on stage in frilly dresses, pursuing their idol career. This is the story of how they came to be Japan's most successful idol group and their first line of defense.

Hazuki Toreishi