Some of these factions may be part of each other, or allied, or otherwise closely linked. Some are definitely distinct.
Principal Johnstone is the principal of Galileo High. He also seems to know a lot about stars - he keeps detailed files (H So S 47, Hso S 48?) including surveillance photos (taken by Maia - H So S 55), on many (most?) of the stars attending Galileo.
Johnstone employs (or at least, uses) Maia as a spy/informant/agent (H So S 55 etc.). Maia has claimed that she works for Johnstone due to something related to her mother, who is apparently not dead as everyone else thinks (H So S 36).
Johnstone had a son whom Algol was friends with, who died. (H So S 71) The relevance of this to the conspiracy stuff, if any, is unclear.
A "weird place out in the hills", The Academy is a private school rumoured to be involved with the paranormal. Rumoured attendees include a girl with two heads (or two girls with one body, rather.) (H So S 14)
Johnstone appears to view the Academy as an enemy, or at least disapproves of its methods. (H So S 21)
Antares attended the Academy, for some (all?) between the Trudeau Bridge incident (five years ago (cf. H So S 22)? Certainly later than 6th Grade (cf. H So S 64)) and the last month or so (H So S 14).
A military school.
Ras Alhague attended Jessup for the last few years. While there, he was trained by and experimented upon by Sergeant Parks, who desires to somehow "become" a star (H So S 59).
Sergeant Parks was involved in initially bringing Ras to the school, and also targeted Yed as a potential student there (H So S 28). It seems likely both were targeted because they were stars.
Ras has stated that Jessup is government run and is supposed to be "protection" from places like the Academy and Station Cassiopeia (H So S 59).
Not Cassie herself, but the people who had her imprisoned and lashed up to the computer/radio station thing. They were situated somewhere remote (H So S 60) which was reachable by a journey taken at least partly by bus from the local area, with a return trip being possible within one day (H So S 29).
According to Maia, Cassiopeia was kidnapped (a fake boating accident used to cover her absence, with the Coast Guard complicit in some sense) (H So S 62).
They had Cassie lashed up to computers and were apparently using her to transmit... something, such that she showed up on mobile phones in the local area, although whether that was a side effect or the intention is unclear. Jake, Alan and Debbie all worked (and perhaps continue to work) there, although it is unknown how important they were to the overall organisation.
A suspiciously high concentration of stars have attended the camp. Known attendees include Yed, Zavijava and Merope, who were all, at some juncture, placed in a "special group" while there... (H So S 48)
They kidnapped Furud and Antares over the weekend. Their motives remain mysterious, but:
According to Maia, Mr. Henley was interested in her ability (i.e. the invisibility/glamour thing), and told Johnstone about it (H So S 36) As a result, Principal Johnstone applied pressure on Maia to accuse Mr. Henley of molestation, thereby getting him fired (H So S 25). Mr. Henley has subsequently committed suicide (or at least, so it seems.) (H So S 29, H So S 31)
Miss Heather Rose
This florally-named teacher has something mysterious about her. Furud claims that she hadn't taught before coming to Galileo High - indeed, that on paper she seemed not to exist at all (H So S 18). She taught at the Academy before she cam to Galileo (H So S 24, H So S 36).
Miss Rose seems to have some form of relationship with Ras beyond merely teacher/pupil: they're on first name terms with each other (H So S 5).