1. The problem statement, all variables and given/known data Let H, K be subgroups of S_5, where H is generated by (1 2 3) and K is generated by (1 2 3 4 5). Is HK a subgroup of S_5? 2. Relevant equations HK is a subgroup iff HK = KH. 3. The attempt at a solution Is there an easy way of answering this question without computing HK and KH?