If $G=H\times K$ then can we view $G/K$ as $H$?
66863
How is the quotient group related to the direct product group?
94507
Given $G$ group and $H \le G$ such that $|G:H|=2$, how does $x^2 \in H$ for every $x \in G$?
85129
If $H_1, H_2\leq G$ are such that $H_1\cong H_2$ then $G/H_1\cong G/H_2$?
135808
Show that there is a positive integer $n$ such that $G \cong \ker(\phi^{n}) \times \phi^{n}(G)$
120495
Does this correctly interpret the "$\cong$" between groups as "$=$" between sets?
114221
A Group $G$ is soluble $\iff G^{(k)}=\{e\}$ for some $k$
45727
If $G$ contains a normal subgroup $H \cong \mathbb{Z_2}$ such that $G/H$ is infinite cyclic, then $G \cong \mathbb{Z} \times \mathbb{Z_2}$
2235
Showing $\text{Aut}_\mathsf{Grp}(\mathbb{Z}/2\mathbb{Z} \times \mathbb{Z}/2\mathbb{Z}) \cong S_3$
146760
Prove that H is a subgroup of G
117538
What is the interpretation of $a \equiv b$ mod $H$ in group theory?
67772
How to find $k$ such that $(\mathbb{Z} \times \mathbb{Z})/ \langle (m,n)\rangle \cong \mathbb{Z} \times \mathbb{Z}_k$
34724
For $G$ a group and $H\unlhd G$, then $G$ is solvable iff $H$ and $G/H$ are solvable?
41237
$H$ is normal subgroup of $G$ iff $gHg^{-1}=H$ for every $g$ of $G$
98739
If $H$ is a subgroup of $G$ and $K$ is a subgroup of $H$, then $$|G:K|=|G:H||H:K|$$
140962
Counterexamples for $G \times H$ isomorphic to $G$ implies $H$ trivial.
151727
If $|G/H|=4$ then $G$ is union of three proper subgroups
70861
$\mathbb P^n\times \mathbb P^m\not\cong \mathbb P^{m+n}$