Isomorphic to Subgroup of even permutations True or False 
Every finite group of odd order is isomorphic to a subgroup of $An$, the group of all even permutations.
The question was in entrance exam. I think there is counter example to this statement but i am not reaching that example. Can some one help?

One can embed $S_n$ can be embedded into$S_n\times S_n$ diagonally, i.e., $\sigma\mapsto (\sigma,\sigma)$ we see that $S_n$ embeds into $A_{2n}$ and so every finite group, order is odd or even, can be embedded into suitable alternating group.
(Compare it with similar statement any matrix group can be embedded into $SL(n)$ ) 
