Algebra trick question: quotient/factor group isomorphic to a subgroup of $S_n$ where $[G:H]=n$
5812
Is there an isomorphism between factor groups and subgroups of symmetric groups?
58033
$G\times H\cong G$ with $H$ non-trivial
151130
When is the product of $n$ subgroups a subgroup?
41231
Subgroups of (Z,+) of order n
11957
G is the product of its Sylow subgroups
59561
Suppose that G is a group and N < G a normal subgroup. Prove G/N is simple
61526
An exercise about nilpotent quotient groups
29996
Prove that if a normal subgroup $H$ of $ G$ has index $n$, then $g^n \in H$ for all $g \in G$
108213
$N_1,N_2,N_3 \unlhd G, N_i\cap N_j =\{e\}, G = N_iN_j$. Want to show that $G$ is abelian, $N_i$ are isomorphic.
23579
If $G$ is isomorphic to $H$, then ${\rm Aut}(G)$ is isomorphic to ${\rm Aut}(H)$
2304
What is the quotient of a cyclic group of order $n$ by a cyclic subgroup of order $m$?
933
How many groups exist with order $n$ (two isomorphic groups are treated as the same group)
131516
Subgroup generated by n-th powers of elements
70904
Subgroups of $U(n)$ isomorphic to a direct sum of cyclic groups
140471
Is $ G \cong G/N \times N$?
46260
Prove that a group generated by two elements of order $2$, $x$ and $y$, is isomorphic to $D_{2n}$, where $n = |xy|.$
7575
Show the commutator subgroup of $S_{n}$ is $A_{n}$ for $n \geq 5$