Is there a group identity about what the maximum discrete subgroup of SU(N) is? How about all discrete subgroups of SU(N)? If not but a few particular cases are known, what about N<4? Its obvious that Z_N is a subgroup of SU(N) via the fundamental representation but beyond subgroups of Z_N I can't see any immediately obvious way of finding out other subgroups.
I've just realised what a stupid question this is, given U(1) is a subgroup of SU(N>1) and all Z_p are in U(1). The thing I've been thinking about in relation to Z_n and SU(N) doesn't actually construct the Z_n in terms of subgroups. Never mind!
