If there's an Inferno Cop character thrown in I will put forward that all Imaishi shows are in the same continuity: Panty and Stocking failed to help the Real God stop the Southern Cross from turning Inferno Cop into a Real God. As the peak of human evolution, Inferno Cop's ascension drew the attention of the Anti-Spirals. The Anti-Spirals fail their first attempt to destroy humanity, which a young Lord Genome witnesses. All of Earth begins developing into a militaristic, Spiral society, hence the spiral towers from the start of Gurren Hen, and also the Spiral nature of the city in Kill la Kill. Eventually, Satsuki and her kind manage to lift a successful number of humans to the status of Spiral Warriors, including a student at one of the academies, one Lordgenome. He rises to the rank of greatest Spiral Warrior, has his mind blown by the Anti-Spiral Life Form, and ends the Spiral resistance. His memories of Satsuki's rhetoric concerning humans being pigs in men's clothing leads to his creation of Beastmen, and the stage is set for one Simon the Digger to start clawing his way up.
YES. IT IS ALL CLEAR TO ME NOW.