If two groups are isomorphic to subgroups of each other, are they isomorphic themselves?
100149
If there are injective homomorphisms between two groups in both directions, are they isomorphic?
43832
Which groups are derived subgroups?
108830
Let $G$ be a group of order $2p$ , where $p$ is a prime greater than $2$. Then, G is isomorphic to $\mathbb{Z}_{2p}$ or $D_p$
125244
Equivalent definitions of normal subgroups
47617
Are groups with all the same Hom sets already isomorphic?
120155
How to show that this group presentation is isomorphic to dihedral group?
128300
Prove that a group with exactly two proper nontrivial subgroups is isomorphic to $\mathbb{Z}_{pq}$ or $\mathbb{Z}_{p^3}$.
2254
Finite group with isomorphic normal subgroups and non-isomorphic quotients?
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)
25439
f(a) = inverse of a is an isomorphism iff a group G is Abelian
157145
Subgroup of $S_8$ isomorphic to $G$
115849
Are the Groups having all subgroups of same order conjugate classified?
67374
Is it true that $\mathbb{R}$ and $\mathbb{R}^2$ are isomorphic as abelian groups?
112993
Is every quotient of a finite abelian group $G$ isomorphic to some subgroup of $G$?
56245
Let H be a subgroup of a group G. Prove that the following statements are equivalent.
46116
Proof of the First Isomorphism Theorem for Groups