Let p denote a prime number. Let G be a finite group. Let P denote a p-sylow subgroup of G. Finally, let H be any subgroup of G that contains N_G(P). Prove that [G:H]≡1 mod p.
Well here is what I know right away: N is in H. This means that gPg . Since it is in H, this also means that N (P)=hPh^-1 So ghP(gh)^-1. This is about where I'm stuck.