How to prove the following: Groups of order less than 60, are solvable?
I tried to do this by showing that groups of order $p^n$, $p q$, $p^2 q$, $p q r$ for primes $p$, $q$, $r$ are solvable. In this way, almost every group of order less than 60 is eliminated. Precisely, it only remains to show that groups of order 24, 40, 48, 54, 56 are solvable. It seems to me that this is too complicated way of solving, so I would like to know is there any other more elegant (and shorter) solution to the problem.
Thanks in advance.