Is the Frattini subgroup a normal subgroup?
65456
The Frattini subgroup is a characteristic subgroup.
112263
an example for $\pi$-quasinormal subgroup but is not normal
89508
Existence of normal subgroups for a group of order $36$
12589
Show that every subgroup of the quaternion group Q is a normal subgroup of Q
16804
Prove whether or not a subgroup is normal in the dihedral group $D_4$
19720
A normal subgroup intersects the center of the $p$-group nontrivially
7973
Groups of order $pq$ have a proper normal subgroup
57227
Maximal normal $\pi$-subgroups and torsion subgroups
111375
Normality of subgroups and Sylow groups under homomorphisms...
142413
Normal Subgroups of $SU(n)$
51359
Prove that every subgroup of an abelian group is a normal subgroup.
157819
Every group of order $56$ has a proper non - trivial normal subgroup?
113357
Groups of order $pqr$ and their normal subgroups
4883
Let $H$ be a subgroup of a group $G$ such that $x^2 \in H$ , $\forall x\in G$ . Prove that $H$ is a normal subgroup of $G$
22444
Normal subgroups of dihedral groups
139611
Can a normal subgroup of a finite nonabelian group be nonabelian?
45580
Intersection of conjugate subgroups is normal