Subgroups of index 3 are normal
109060
Group containing no subgroup of index 2
61373
A normal subgroup that is not a characteristic
74970
Subsubgroups are subgroups of subgroups / Multiplicative Property of the Index
103423
Normal subgroup where G has order prime
78580
Is $SL_n(\mathbb{R})$ a normal subgroup in $GL_n(\mathbb{R})$?
89508
Existence of normal subgroups for a group of order $36$
38095
The Commutator Subgroup is Normal.
109236
Subgroups containing kernel of group morphism to an abelian group are normal.
15630
Normal subgroup of prime order is characteristic
11043
A normal subgroup is the union of conjugacy classes.
37971
Prove that the center of a group is a normal subgroup
151727
If $|G/H|=4$ then $G$ is union of three proper subgroups
46121
Does the intersection of two finite index subgroups have finite index?
99999
A question on identifying normal subgroups of $S_4$
85677
Is there a free subgroup of rank 3 in $SO_3$?
155502
Index of a maximal subgroup in a finite group
11731
Normal subgroups of $S_4$