Let $G$ be a group s.t. $|G|=pqr$ where $p,q,r$ are primes that need not be distinct. Prove that $G$ is soluble.
So, I don't know whether I should handle this case by case and try to get the Sylow theorems involved or if there is an easier way to do this, a slick trick I am not seeing perhaps. Does anyone have any insights?