proof $S_n$ has no subgroup of order $ \frac {n!}{4}$
74218
Show that $S_n$ has no subgroup of index $t$ for $2 < t < n$
50762
If $S_n$ has cyclic subgroups of these orders or not?
46904
Let $G$ be a non-trivial group with no non-trivial proper subgroup. Prove that $G$ cannot be infinite group.
47179
Prove that $[N, G']=1$ when $N$ is a nilpotent subgroup of a group $G$?
99694
Number of subgroups of $S_4$
41688
An elementary problem in Group Theory: the unique noncyclic group of order 4
99999
A question on identifying normal subgroups of $S_4$
89508
Existence of normal subgroups for a group of order $36$
119808
Proving that $n$-cycle has order $n$
104112
Number of finite simple groups of given order is at most $2$ - is a classification-free proof possible?
125498
Check whether subgroup is normal in $ S_4$
34972
order of non abelian group can't be what?
101602
consider the group $G=\mathbb Q/\mathbb Z$. For $n>0$, is there a cyclic subgroup of order n
131594
Can the symmetric group $S_n$ be imbedded as a subgroup in $A_{n+1}$?
8841
A $p$-group of order $p^n$ has a normal subgroup of order $p^k$ for each $0\le k \le n$
115746
Find the order of a subgroup of $S_5$ generated by two elements
132342
Suppose $H$ is a subgroup of $S_n$ but $H$ is not a subgroup of $A_n$. Prove that |$H$ ∩ $A_n$| = $\frac{1}{2}|H|$?