1. The problem statement, all variables and given/known data Let G be a group with |G|= mp where p is prime and 1<m<p. Prove that G is not simple 2. Relevant equations 3. The attempt at a solution I have proven the existence of a subgroup H that has order p(via Cauchy's Theorem), but I don't know how to use the representation of G on cosets of H or another method to somehow deduce that H is a normal subgroup of G thus forcing G to be not simple.