There was St. Hildegard if Bingem who is quickly developing a cult following in the music world. Gorgeous stuff. Also a genius. She was able to help create polyphonic music styles, and it's definitely music for women to sing as created by a woman. She's also (so I've heard) the first composer in thr western world whose name we actually know.

Clara Schumann was the wife of composer Robert Schumann, and she was a composer and pianist in her own right. She actually was the main breadwinner when Robert's crippling depression prevented him from working.

Ethel Smyth, in addition to being a great composer in late nineteenth/early twentieth centuries, was one hell of a woman. I'd love to get a time machine and have a beer with her. My favorite story is how she was jailed for her involvement in a protest for women's rights, then conducted a protest performance of her suffrage anthem "The March of the Women" with her toothbrush while leaning out of the jailhouse window.

I'd recommend listening to one of her operas "The Wreckers" and her Mass. Funny story about the Mass - it's speculated she wrote it more as a gift to a Catholic friend she had a crush on (to whom she dedicated the work) and decided that the composition should end with the Gloria (usually the second movement) because ending in the traditional Agnus Dei was too low key for her.

Alma Mahler was a fledgling composer when she married Gustav, but he forced her to forgo her art as a condition for marriage. After she cheated on him with Walter Gropius, Gustav realized he was a sexist asshole and helped her publish a few songs. Not exactly "prominent", but interesting. Who knows what could have been if Gustav hadn't been such a jerk?

Sorry Wiley, this one's quickly becoming a total trivia dump, so I'm removing it. I've got like half an interesting answer written for you though, could you submit a new one more along the lines of "Why weren't there more women composers in the age of Beethoven, Mozart, etc?"

Regarding a side question you pose - here are some ways to understand the broad strokes of genre throughout history.

This is a pretty good image that illustrates the broad strokes of classical music genres: https://laymanclassics.files.wordpress.com/2011/04/classical_music.gif

Here are some sample styles from key composers. I have not included early music here and won't go too much into the more recent genres that have emerged.

Baroque - Characterized by intricate mathematical interactions between instruments, rigid flow of time, and a single emotional message in each movement. They are more examinations than explorations

Bach: https://www.youtube.com/watch?v=Kpqm1hxgH-w

Handel: https://www.youtube.com/watch?v=Kuw8YjSbKd4

Classical - Fluctuations in time, broader emotional expressions, less rigid interactions between melody and supporting voices, exploration of ideas within pieces. Still adhering to "traditional" forms.

Mozart - https://www.youtube.com/watch?v=JTc1mDieQI8

Beethoven - https://www.youtube.com/watch?v=BVL7gLwzct0

Romantic - Much more individual expression, aesthetic exploration, departure from forms, much less rigid in time, explorations of non-traditional harmonic structures. Less adherence to "rules", alluding to later post-modern sensibility.

Chopin - https://www.youtube.com/watch?v=YGRO05WcNDk

Wagner - https://www.youtube.com/watch?v=SRmCEGHt-Qk

20th Century - Rules and systems more optional, impressionistic compositions, expression through gross dissonance and disturbance of norms, departure from forms, incorporation of non-traditional tonal structures/time-signatures and ethnic influence,

Stravinsky - https://www.youtube.com/watch?v=aGFRwKQqbk4 (worth noting that this debut literally caused a riot)

Copland - https://www.youtube.com/watch?v=t4E1JYP5Tgc

It's important to note that prior to Beethoven (or roughly around that time), composers weren't really seen as "Rock stars" or artistic geniuses. Hildegard would have been seen as a hard worker who was inspired by divinity and had plied her service as a musician. While the music that she created was made for women, this was not a feminist effort as we might think of it today - this was simply a reflection of the tools at her disposal as she lived and worked in a monastery.

The idea of musicians as creative and expressive geniuses who commanded followings really didn't come around until the late 18th century. Music often served more of a functional role in peoples' lives than a purely emotional one compared to today. Music was more often seen as clever or well crafted than moving, significant, or deeply personal.

As a result, some of the most important and influential composers in history were not recognized for their genius until well after their death.