Is there a normal subgroup $H$ such that $S_6/H$ is isomorphic to $S_5$
91772
Proving that $A_n$ is the only proper nontrivial normal subgroup of $S_n$, $n\geq 5$
157853
$Q_8$ is isomorphic to a subgroup of $S_8$, but not isomorphic to a subgroup of $S_n$ for $n\leq 7$.
61373
A normal subgroup that is not a characteristic
11665
Show that $D_{12}$ is isomorphic to $D_6\times C_2$
145511
Suppose $H$ is the only subgroup of order $o(H)$ in the finite group $G$. Prove that $H$ is a normal subgroup of $G$.
154878
Prove that $H$ is a normal subgroup in the finite group $G=\langle S\rangle $ iff $sHs^{-1}$ $\subseteq H$ for all $s\in S$.
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 $G$
121034
Follow-up to question: Aut(G) for G = Klein 4-group is isomorphic to $S_3$
113357
Groups of order $pqr$ and their normal subgroups
97928
Normal subgroup of a normal subgroup
128300
Prove that a group with exactly two proper nontrivial subgroups is isomorphic to $\mathbb{Z}_{pq}$ or $\mathbb{Z}_{p^3}$.
27703
an example of a non-abelian group $G$ containing a proper normal subgroup $N$ such that $G/N$ is abelian.
124140
Quick way to find the number of the group homomorphisms $\phi:{\bf Z}_3\to{\bf Z}_6$?
23579
If $G$ is isomorphic to $H$, then ${\rm Aut}(G)$ is isomorphic to ${\rm Aut}(H)$
142413
Normal Subgroups of $SU(n)$
157145
Subgroup of $S_8$ isomorphic to $G$
150204
Isomorphisms between the groups $U(10), U(5)$ and $\mathbb{Z}/4\mathbb{Z}$