Template:Only two prime factors hence solvable

There are only two prime factors of this number. Order has only two prime factors implies solvable (by Burnside's $$p^aq^b$$-theorem) and hence all groups of this order are solvable groups (specifically, finite solvable groups). Another way of putting this is that the order is a solvability-forcing number. In particular, there is no simple non-abelian group of this order.