Subgroup of the center that is not Characteristic subgroup
61373
A normal subgroup that is not a characteristic
124224
How many groups of order $n$ with center {e} exist?
23941
Normal Subgroups that Intersect Trivially
40846
When can a (finite) group be written as the quotient of some other group by its center?
27780
Subgroup which is generated by odd elements
7418
The Center of $\operatorname{GL}(n,k)$
158975
Isomorphism of centers of isomorphic groups
105139
Verification of Proof that a nonabelian group G of order pq where p and q are primes has a trivial center
81230
Difference between centralizer and center groups?
122266
equivalent definition of normal subgroup
33309
Subgroup of $\mathbb{R}$ either dense or has a least positive element?
151029
The number of non normal subgroups of a group cannot be $1$?
132704
If G is not commutative, then is there always a subgroup that is not a normal subgroup?
44165
the image of normal subgroups
99999
A question on identifying normal subgroups of $S_4$
32759
Open neighborhood of the identity with no proper subgroup.
92493
If $G$ is non-abelian, then $Inn(G)$ is not a normal subgroup of the group of all bijective mappings $G \to G$