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### How to find cyclic subgroups of $S_4$ with certain numbers of elements [duplicate]

In the group $S_n$ consisting of the set of all bijections from $\{1,2,...,n\}$ to $\{1,2,...,n\}$ with a binary operation $◦$ denoting composition of functions. I am asked to find cyclic subgroups of ...
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### SubGroups of $S_4$ of order $8$ and $12$. Describe by hand
What's a "good" way of describing $S_4$ subgroups by hand? The following post gives a pretty detailed stategy but i can't figure out some tools that are used: How to enumerate subgroups of ...
### Find the number of conjugacy classes in $S_4$
So I know all the elements of $S_4=\{e,(12),(13),(14),(23),(24),(34),(12)(34),(13)(24),(12)(23),(123),(132),(124),(142),(134),(143),(234),(243),(1234),(1342),(1423),(1243),(1432),(1324)\}$ I also ...