If <I>G</I> is a finite group and <I>H</i> is a proper subgroup of <I>G</I> such that 
|<I>G</I>| 
 does not divide |<I>G</I>:<I>H</I>|! , then <I>H</I> contains a nontrivial normal subgroup of <I>G</I>.  In particular, <I>G</I> is not simple.