$G/N\cong G/N'$ implies $N\cong N'$ for the normal subgroups?
2254
Finite group with isomorphic normal subgroups and non-isomorphic quotients?
8841
A $p$-group of order $p^n$ has a normal subgroup of order $p^k$ for each $0\le k \le n$
27703
an example of a non-abelian group $G$ containing a proper normal subgroup $N$ such that $G/N$ is abelian.
91874
Existence of finite indexed normal subgroup for a given finite indexed subgroup.
157840
Is it true that $(R\times S)[G]\cong R[G]\times S[G]$?
2174
Proving that HK is a subgroup when K is normal
58033
$G\times H\cong G$ with $H$ non-trivial
142413
Normal Subgroups of $SU(n)$
55350
H is a subgroup of G and G' is a subgroup of H. Prove H is normal in G.
27436
Does $G\cong G/H$ imply that $H$ is trivial?
45727
If $G$ contains a normal subgroup $H \cong \mathbb{Z_2}$ such that $G/H$ is infinite cyclic, then $G \cong \mathbb{Z} \times \mathbb{Z_2}$
63162
Is there a characterization of groups with the property $\forall N\unlhd G,\:\exists H\leq G\text{ s.t. }H\cong G/N$?
141043
$H$ normal in $G$. Need $G$ contain a subgroup isomorphic to $G/H$
94239
Proof that if group $G/Z(G)$ is cyclic, then $G$ is commutative
123610
How to show that the commutator subgroup is a normal subgroup
23533
All subgroups normal $\implies$ abelian group
87882
If $N \lhd G$ is abelian and $G/N$ is abelian then $G$ is abelian