# Example of infinite group with infinitely many simple subgroups

What is an example of an infinite group with a composition series and infinitely many simple subgroups?

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Another (perhaps less cheat-y) one is the group of permutations of $\mathbb N$, which contains all the alternating groups $A_n$ as subgroups.
Why is the composition series in the second case finite? Also, to be clear, you mean all permuations of $\mathbb{N}$ or only the finitely supported ones? (Or does it matter?) –  Jason DeVito Nov 12 '12 at 20:35
I see - I think the part I was missing was that $A_{\text{finitary}}$ is also simple. –  Jason DeVito Nov 12 '12 at 21:15