Let G be a group, let N be normal in G and let H be a subgroup of G. Assume that G/N and H are finite and that gcd(|G/N|,|H|)=1. Prove that H is a subgroup of N. I was thinking about using Lagrange Theorem. and maybe using the fact that G may act on the set of left cosets (G/N) by conjugation. and the find the kernel of that action and then maybe use the first isomorphism theorem. But I don't get very far with that.