1. G a Group of order 60, G simple, prove G isomorphic to A5 2. Familiar with Sylow's Theorems, theorems leading up to Sylow. 3. We make the assumption that G is not isomorphic to A5 Then "given G cannot have a subgroup of index 2, 3, 4, 5," I can get the result. My problem is I don't know why the quoted statement is true. Clear for 2 alright, given G simple, but 3, 4, 5? Is this a fairly obvious result (if so, a hint please), or is it difficult to prove and should i move on until I know more about groups?