Would $Z_{40}$ be an example, or the dihedral group $D_{2n}=D_{40}$ work? And how do we obtain the subgroups of $D_{40}$?
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1Cyclic groups have only one subgroup of a given order – J. W. Tanner Nov 13 '20 at 04:19
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What about $D_{40}$? – chickenwing72 Nov 13 '20 at 04:42
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Have you seen that subgroup of $S_5$ that has order $20$ and $5$ subgroups of order $4$? – Jyrki Lahtonen Nov 13 '20 at 05:04
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Also, I recommend that you take a look at our guide for new askers. Your question falls a bit short of what is expected. It is a bit difficult to compile an answer that would help you. I can post a 1-line answer, one likely to collect a few upvotes even, but it is uncertain that you would find it helpful. Also, I haven't verified that the question has not been handled already :-( – Jyrki Lahtonen Nov 13 '20 at 05:10
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The dihedral group of order $40$ works also. – Jyrki Lahtonen Nov 13 '20 at 05:16
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Initially I had in mind the group $C_2\times(C_5\rtimes C_4)$ with abelian Sylow $2$-subgroups, but it was easy to find a previous thread answering your question also. – Jyrki Lahtonen Nov 13 '20 at 05:18