Why can't $A_4$ has a subgroup of order $6$?
76943
Existence of subgroup of order six in $A_4$
28181
Sylow subgroups of $S_3$ and $S_4$
131594
Can the symmetric group $S_n$ be imbedded as a subgroup in $A_{n+1}$?
8694
$A_4$ is not isomorphic to $D_6$
146969
Proving that every group of order $4$ is isomorphic to $\Bbb Z_4$ or $\Bbb Z^*_8$
53207
Let $p$ be a prime. If a group has more than $p − 1$ elements of order $p$, why can’t the group be cyclic?
46904
Let $G$ be a non-trivial group with no non-trivial proper subgroup. Prove that $G$ cannot be infinite group.
50762
If $S_n$ has cyclic subgroups of these orders or not?
14890
Let $G=\langle a\rangle$ be a cyclic group of order $n$. Show that, for every divisor $d$ of $n$, there exists a subgroup of $G$ whose order is $d$.
134376
Let $G$ be a nonabelian group. Let $a \in G$ have order $4$ and let $b \in G$ have order $3$. Then the order of the element $ab$ in $G$
149578
Subgroups of $(\mathbb Z_n,+)$
49257
How to show that Klein four-group is a normal subgroup of the alternating group $A_4$
104080
Group with order $pq$ has subgroups of order $p$ and $q$
15526
Question on groups of order $pq$
74586
Prove that every group of order $4$ is abelian
51861
$S_4$ is not isomorphic to $D_{12}$
89508
Existence of normal subgroups for a group of order $36$