Partition of a conjugacy class to conjugacy classes of a normal subgroup
68317
Conjugacy class of $G$ splitting as Conjugacy class of $H\unlhd G$
103423
Normal subgroup where G has order prime
117862
Number of partitions of an $n$-element set into $k$ classes
51747
Showing that the intersection of all subgroups of order $n$ is normal
86336
For $G$ group and $H$ subgroup of finite index, prove that $N \subset H$ normal subgroup of $G$ of finite index exists
49527
Prove that $a$ commutes with each of its conjugates in $G$ iff $a$ belongs to an abelian normal subgroup of $G$.
44934
Show that every normal subgroup can be written as an intersection of $\ker \chi$'s for $\chi \in \operatorname{Irr}(G).$
110018
Conjugacy classes in $A_n$.
142421
Conjugacy Classes in Finite Groups
2174
Proving that HK is a subgroup when K is normal
3456
Commutator of two normal subgroups with trivial intersections
21958
Splitting of conjugacy class in alternating group
41231
Subgroups of (Z,+) of order n
11731
Normal subgroups of $S_4$
29996
Prove that if a normal subgroup $H$ of $ G$ has index $n$, then $g^n \in H$ for all $g \in G$
2254
Finite group with isomorphic normal subgroups and non-isomorphic quotients?
93952
Show that $X$ can be represented as a union of disjoint equivalence classes