Normal subgroup of index a divisor of n!
44942
A group $G$ with a subgroup $H$ of index $n$ has a normal subgroup $K\subset H$ whose index in $G$ divides $n!$
57227
Maximal normal $\pi$-subgroups and torsion subgroups
7575
Show the commutator subgroup of $S_{n}$ is $A_{n}$ for $n \geq 5$
97928
Normal subgroup of a normal subgroup
6134
Some Subgroup of Dihedral Group is Normal
155502
Index of a maximal subgroup in a finite group
51747
Showing that the intersection of all subgroups of order $n$ is normal
99999
A question on identifying normal subgroups of $S_4$
63780
to show characteristic subgroup is normal in G
44165
the image of normal subgroups
113357
Groups of order $pqr$ and their normal subgroups
122335
Abelian $p$-group with unique subgroup of index $p$
23941
Normal Subgroups that Intersect Trivially
70373
Intersection of normal subgroups proof
133528
$\lvert K(\alpha_1,\dots,\alpha_n) : K \rvert$ is a divisor of $n!$
13742
Proving that a normal, abelian subgroup of G is in the center of G if |G/N| and |Aut(N)| are relatively prime.
16804
Prove whether or not a subgroup is normal in the dihedral group $D_4$