Supergirl was the leader of a gang?
A criminal gang no less!! And she and Batgirl do some hand-to-hand judo style combat in that issue too. This is Supergirl's first appearance in Adventure Comics without being a cameo in a someone else's story. And it is (I think) the first time the Maid of Might ever had the prime spot in any DC comic (rather than being a support strip) and had a story that occupied the whole of an issue from cover to cover.
From memory, let me see if I can fill in some of the details behind just a few of the more interesting covers posted thus far...
Adventure Comics #385: the woman in purple was pretending to be Kara's long lost sister, also sent to Earth in a rocket when Argo City was doomed. In reality she turned out to be a human con artist using various tricks and scams to fake super powers; the idea was to hoax the Maid of Might into demonstrating her own powers by crushing coal into diamonds, then sell the diamonds for a fortune.
Adventure Comics #386: Supergirl saves some random monster in a carnival sideshow and he takes a shine to her. He tracks her down even though she's switched into Linda Danvers, then he pulls off her dress right in front of everyone to turn her back into Supergirl. Yikes! Bang goes the secret id!
Adventure Comics #387: The kid in the picture is Lex Luthor's nephew. Luthor secretly had a kid sister called Lena Thorul who was best friends with Linda Lee Danvers. She was also a telepath. Anyway, eventually Lena got married and had a son who had even more powerful PSI powers than his mom, and the son breaks Uncle Lex out of prison, so Uncle Lex decides to use his nephew's powers to commit crime.
Adventure Comics #386: Braniac creates a Casanova-style robot to woo Supergirl as part of a trap. When the robot turns up on Earth it first goes after Supergirl's best friend Linda Danvers, unaware that Linda is really Supergirl.
Btw, I have a real interesting pic of my own lined up for tomorrow (80 days!) It's not a cover, but it's an obscure Supergirl appearance related very firmly to the number 80. I'm wondering how many fans will be able to tell where it's from(..?)
R5