Riemann surfaces with automorphism groups admitting partitions

A finite group Go, is said to admit a partition il there is a set of subgroups Gi, i = l, 2, ■ • ■ , s, 5^2, so that (1) G0 = UJ=i G¿ and (2) if tVj and i, j>0, then GiC = (e) where e is the identity in Go.