There is only one subgroup of order 4 in A4 (Alternating group of degree 4)(This subgroup is (1), (12)(34), (13)(24), (14)(23)). Why does this imply that this subgroup must be a normal subgroup in A4? Generalize to arbitrary finite groups.
I thought about using the fact that for some g that is an element of a group G, |gH^-1g^-1|=|H| (the order of the subgroup H equals each of its conjugates orders) in the whole group, I am not sure were to go from here. Can some help me on this one at all?