Given a group $H\unlhd G$, is it natural/accurate to say that $G \cong H \oplus (G / H)?$
140471
Is $ G \cong G/N \times N$?
117538
What is the interpretation of $a \equiv b$ mod $H$ in group theory?
15276
$G \times H \cong G \times K$ , then $ K \cong H$
110390
Order of group $GL_{2}\left( \mathbb{F}_{p}\right) $
142375
Prove or disprove: If H is a normal subgroup of G such that H and G/H are abelian, then G is abelian.
39165
Suppose $G$ is a group and $H,K \trianglelefteq G$. If $H \cap K =1$ the $hk=kh$ for all $k \in K, h \in H$?
45727
If $G$ contains a normal subgroup $H \cong \mathbb{Z_2}$ such that $G/H$ is infinite cyclic, then $G \cong \mathbb{Z} \times \mathbb{Z_2}$
98739
If $H$ is a subgroup of $G$ and $K$ is a subgroup of $H$, then $$|G:K|=|G:H||H:K|$$
120495
Does this correctly interpret the "$\cong$" between groups as "$=$" between sets?
114221
A Group $G$ is soluble $\iff G^{(k)}=\{e\}$ for some $k$
27436
Does $G\cong G/H$ imply that $H$ is trivial?
106927
How do I prove $[G:H\cap K]\leq [G:H][G:K]$?
91287
Is $G/pG$ is a $p$-group?
85011
Prove that $\exists a,g,h\in G\colon h=aga^{-1}, g\neq h ,gh=hg$ in a finite non-abelian group $G$.
107935
If $G$ is a group, $H$ is a subgroup of $G$ and $g\in G$, is it possible that $gHg^{-1} \subset H$?
45310
If $H\leq Z (G)$ and $G/H$ is nilpotent, then $G$ is nilpotent.
37414
Question on Groups $G=\langle x,y|x^4=y^4=e,xyxy^{-1}=e\rangle$