TITLE: Are there some list of the finite subgroups of the mapping class groups of low genus surfaces?
QUESTION [6 upvotes]: We already know the bound of the order of the finite subgroups of the $Mod(S_g)$. If we take a further step, to find all the finite subgroups, then what is the result for low genus cases? For example, are there some list of all types of the finite subgroups of $Mod(S_g)$ for $g \leq 10$?

REPLY [4 votes]: As pointed out in the preceding answer, what you are looking for are all possible automorphisms of a compact Riemann surface of genus $g$. You'll find some answers at this question.