Are two groups isomorphic if each is isomorphic to a subgroup of the other?
43964
When can a pair of groups be embedded in each other?
933
How many groups exist with order $n$ (two isomorphic groups are treated as the same group)
151047
a non trivial example: $G/H$ is isomorphic to $G$
157145
Subgroup of $S_8$ isomorphic to $G$
152481
If order of group is $p^2$, where $p$ is prime, how can you deduce $G$ is isomorphic to $C_{p^2}$ or $C_p \times C_p$?
152603
Group isomorphic to its automorphism group
115849
Are the Groups having all subgroups of same order conjugate classified?
150207
Non isomorphic subgroups of cyclic groups
107511
If $G$ and $H$ are nonisomorphic group with same order then can we say that $Aut(G)$ is not isomorphic to $Aut(H)$?
46116
Proof of the First Isomorphism Theorem for Groups
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 $G_1$?
139835
Every Finite Group is Isomorphic to a Subgroup of $A_n$
94090
How to show that for any abelian group $G$, $\text{Hom}(\mathbb{Z},G)$ is isomorphic to $G$
40383
Is it true that $|g| = |\phi(g)|$ for all homomorphisms $\phi: G \to G$ and $g \in G$?
152904
Groups with Same Number Of Elements and Subgroups
13523
Are normal subgroups transitive?
99538
Non-trivial groups pairwise non-isomorphic with isomorphic direct products