### Subgroup proofs

Let G be a group, not necessarily finite, and let H be subgroup G. (a) Prove that U = intersection of all x in G xHx^-1 is the largest normal subgroup of G contained in H. (b) Show that no proper subgroup H of A_5 contains six distinct Sylow 5-subgroups. I need a detailed rigorous proof of this to study please.