An Interesting Problem in Algebra

[Nootropic]

There's rarely any interesting threads in pure mathematics and lately I feel like threads such as "Pi" are getting far more attention than they actually deserve, so I thought I'd throw out an interesting problem in [abstract] algebra.

 

If G is group such that G has no nontrivial subgroups (subgroups other than itself and (e)), prove that G is finite of prime order.

 

Of course, you need at least a decent understanding of basic elementary group theory to answer this. Enjoy!