Does A(adsbygoogle = window.adsbygoogle || []).push({}); _{5}(the alternating group of degree 5) contain a subgroup of order m for each factor m of 60?

My intuition says yes, but I can't seem to find a way to prove this, short of writing out example subgroups for each factor, which is really tedious. Although if I have subgroups of orders 2, 3, 4, and 5 would it be enough to look at products of these?

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# Subgroups of Alternating Group

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