Does $G$ always have a subgroup isomorphic to $G/N$?
63162
Is there a characterization of groups with the property $\forall N\unlhd G,\:\exists H\leq G\text{ s.t. }H\cong G/N$?
107687
How to prove that $U_{2^n}$ is isomorphic as group to $\mathbb Z_2 \times \mathbb Z_{2^{n-2}}$ for $n \ge 3$?
86336
For $G$ group and $H$ subgroup of finite index, prove that $N \subset H$ normal subgroup of $G$ of finite index exists
149578
Subgroups of $(\mathbb Z_n,+)$
151130
When is the product of $n$ subgroups a subgroup?
151699
Group of inner automorphisms of a group $G$
51145
Is it possible to prove $g^{|G|}=e$ in all finite groups without talking about cosets?
157040
For groups $A,B,C$, if $A\times B$ and $A\times C$ are isomorphic do we have $B$ isomorphic to $C$?
123860
When are two direct products of groups isomorphic?
137949
If the quotient group $G/N$ be isomorphic to $G_2$, is $G$ isomorphic to $G_1\times G_2$ where $N$ is isomorphic to $G_1$?
111375
Normality of subgroups and Sylow groups under homomorphisms...
87882
If $N \lhd G$ is abelian and $G/N$ is abelian then $G$ is abelian
35353
Isomorphic quotient groups $\frac{G}{H} \cong \frac{G}{K}$ imply $H \cong K$?
121034
Follow-up to question: Aut(G) for G = Klein 4-group is isomorphic to $S_3$
90616
When is mapping $g$ to $g^{-1}$ a group homomorphism?
78553
A simple finite group $G$ with $n$ p-Sylows is isomorphic to a subgroup of $\mathbb A_n$
5812
Is there an isomorphism between factor groups and subgroups of symmetric groups?