Determine if the cyclic group $\langle(1234)\rangle$ is normal in $S_4$
11731
Normal subgroups of $S_4$
6134
Some Subgroup of Dihedral Group is Normal
14003
$(\mathbb{Z}/2^n \mathbb{Z})^*$ is not cyclic Group for $n\geq 3$
44165
the image of normal subgroups
97928
Normal subgroup of a normal subgroup
142894
Showing that a group of order $pq$ is cyclic if it has normal subgroups of order $p$ and $q$
16804
Prove whether or not a subgroup is normal in the dihedral group $D_4$
104460
When a group is cyclic
78580
Is $SL_n(\mathbb{R})$ a normal subgroup in $GL_n(\mathbb{R})$?
146969
Proving that every group of order $4$ is isomorphic to $\Bbb Z_4$ or $\Bbb Z^*_8$
123610
How to show that the commutator subgroup is a normal subgroup
91622
Help with proof that $\mathbb Z[i]/\langle 1 - i \rangle$ is a field.
102871
$\langle r\rangle$ maximal $\iff r$ irreducible
49257
How to show that Klein four-group is a normal subgroup of the alternating group $A_4$
13682
Is $\langle a,b \mid a^2b^2=1 \rangle$ a semidirect product of $\mathbb{Z}^2$ and $\mathbb{Z}_2$?
119878
"Standard" ways of telling if an irreducible quartic polynomial has Galois group C_4?
91772
Proving that $A_n$ is the only proper nontrivial normal subgroup of $S_n$, $n\geq 5$