On January 12, 1820 the Astronomical Society of London was founded. (It changed its name to the Royal Astronomical Society when it was granted a royal charter in 1831.) John Herschel was active in its founding and development. His father William Herschel was its first President, though because of ill health he wasn't really active.
William's sister Caroline was awarded the society's Gold Medal for her work in astronomy, and in 1835 was made an honorary fellow. However women couldn't become full members of the society until 1915. (Shame.)
You can read
more about the Herschels here.