$H,H'$ normal in $G,G'$ respectively and $G \cong G' $ and $H \cong H' $ $\implies$ $G/H \cong G'/H'$ ?
126098
Isomorphism of factor groups
27436
Does $G\cong G/H$ imply that $H$ is trivial?
45580
Intersection of conjugate subgroups is normal
62879
Question about the proof of $GCH$ holds in $\mathbf L$
77361
How to prove $|H|[K:K \cap (g^{-1}Hg)]=|K|[H:H \cap (gKg^{-1})]$?
55350
H is a subgroup of G and G' is a subgroup of H. Prove H is normal in G.
34724
For $G$ a group and $H\unlhd G$, then $G$ is solvable iff $H$ and $G/H$ are solvable?
155054
$G$ be a group and $H$ be a normal subgroup of index $p$ ( a prime ) ; suppose $K$ is a subgroup of $G$ not contained in $H$ , then $G=HK$?
58033
$G\times H\cong G$ with $H$ non-trivial
58205
$ N $ normal in a finite group $ G $, $ |N| = 5 $ and $ |G| $ odd. Why is $ N \subseteq Z(G) $?
44934
Show that every normal subgroup can be written as an intersection of $\ker \chi$'s for $\chi \in \operatorname{Irr}(G).$
85508
Prove that $G$ is an abelian group if $\{(g, g):g\in G\}$ is a normal subgroup.
54911
The preimage of a normal subgroup under a group homomorphism is normal
30676
$G'$ and the product of all the elements in an odd order group
79367
Understanding the difference between two theorems related to $|G\,:\,K|=|H\,:\,K|\cdot|G\,:\,H|$.
111886
Let $(G,•)$ be a group in which $(a•b)^3 = a^3•b^3$. Prove that $H=\{x^3 : x \in G\}$ is a normal subgroup of $G$.
43645
Show that $G/H\cong S_3$