A cyclic subgroup is normal?
34902
If $H$ is a cyclic subgroup of $G$ and $H$ is normal in $G$, then every subgoup of $H$ is normal in $G$.
118894
Cyclic subgroup of dihedral group
22477
If H is a subgroup of a group G and K is a normal subgroup of G the show that K is a normal subgroup of HK.
138406
If N and every subgroup of N is normal in G then G/N is abelian .
141265
Finding a normal and not normal subgroup of $S_3$
37971
Prove that the center of a group is a normal subgroup
102622
K is a subgroup of G. Show that K is not a normal subgroup
99788
Why does a multiplicative subgroup of a field have to be cyclic?
6134
Some Subgroup of Dihedral Group is Normal
16804
Prove whether or not a subgroup is normal in the dihedral group $D_4$
57227
Maximal normal $\pi$-subgroups and torsion subgroups
11731
Normal subgroups of $S_4$
142413
Normal Subgroups of $SU(n)$
44152
If $G$ has only one subgroup of order $n$, then that Subgroup is Normal
102146
If a group mod its commutator subgroup is cyclic, then the group is abelian?
55178
When there is a unique Sylow p-subgroup it is normal, does this mean that non-unique p-subgroups are not normal?
129485
A subgroup of a cyclic group is cyclic - Understanding Proof