binary gender system
matriarchy
https://en.wikipedia.org/wiki/Matriarchy
https://homosaurus.org/terms/matriarchy
https://www.wikidata.org/wiki/Q185681
A social system in which women hold the primary power positions in roles of political leadership, moral authority, social privilege and control of property.
matriarchal
matriarchal system
The Wiley Blackwell Encyclopedia of Gender and Sexuality Studies