Subgroup half as big as its group is normal.
75568
Subgroup of index $2$ is Normal
80381
Groups with "few" subgroups
58694
Which non-abelian finite groups have the property that every subgroup is normal?
104460
When a group is cyclic
55350
H is a subgroup of G and G' is a subgroup of H. Prove H is normal in G.
25832
Let $K$ be a normal subgroup of order 2 in group $G$, show that $K$ lies in the centre of $G$
23533
All subgroups normal $\implies$ abelian group
103002
Group equals union of two subgroups
139611
Can a normal subgroup of a finite nonabelian group be nonabelian?
54911
The preimage of a normal subgroup under a group homomorphism is normal
67554
In a group, the number of non-self-inverse elements is even
22444
Normal subgroups of dihedral groups
116125
A group $G$ with $G'$ abelian and every abelian normal subgroup finite
11043
A normal subgroup is the union of conjugacy classes.
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.
156463
The complement of a proper subgroup generates the whole group
49122
Why commutator subgroup is normal to G?