Normal subgroups of infinite groups
41085
Conjugate subgroup strictly contained in the initial subgroup?
39938
Subgroups of a cyclic group and their order.
23941
Normal Subgroups that Intersect Trivially
99999
A question on identifying normal subgroups of $S_4$
12589
Show that every subgroup of the quaternion group Q is a normal subgroup of Q
58694
Which non-abelian finite groups have the property that every subgroup is normal?
44942
A group $G$ with a subgroup $H$ of index $n$ has a normal subgroup $K\subset H$ whose index in $G$ divides $n!$
42582
Infinite group with only two conjugacy classes
47731
Intersection of all $p$-Sylow subgroups is normal
9232
Group with proper subgroups infinite cyclic
131204
A non-trivial normal subgroup N of a finite group G or order $p^n$ is such that $N\cap Z(G)\neq \{ 1\}$
3104
Prove that a group is infinite and nonabelian.
22444
Normal subgroups of dihedral groups
37971
Prove that the center of a group is a normal subgroup
45727
If $G$ contains a normal subgroup $H \cong \mathbb{Z_2}$ such that $G/H$ is infinite cyclic, then $G \cong \mathbb{Z} \times \mathbb{Z_2}$
44165
the image of normal subgroups
2254
Finite group with isomorphic normal subgroups and non-isomorphic quotients?