Group isomorphic to all its proper quotients, and not simple
8066
Sort-of-simple non-Hopfian groups
7973
Groups of order $pq$ have a proper normal subgroup
37351
Group of Order $p^2$ Isomorphic to $\mathbb{Z}_{p^2}$ or $\mathbb{Z}_{p}$ $\times$ $\mathbb{Z}_{p}$
3907
Abelian quotient group
26321
How to describe the quotient group Z x Z /
61732
Prove any group with 3 elements is isomorphic to $\mathbb{Z}_3$
70904
Subgroups of $U(n)$ isomorphic to a direct sum of cyclic groups
23279
Group Theory Isomorphism
55393
Existence of a group isomorphism between $(\mathbb K,+)$ and $(\mathbb K^\times,\cdot)$
150207
Non isomorphic subgroups of cyclic groups
70658
Isomorphism between quotient modules
129452
Groups $G,H$ with surjective homomorphisms that are quotient of each other
59902
Example of $2$ non-isomorphic groups that have the same quotients
27670
Group homomorphisms $\mathbb{Q}\to\mathbb{R}$
86542
Group of positive rationals under multiplication not isomorphic to group of rationals
126930
Finding all group homomorphisms of $S_n\to\mathbb{C}^*$ and $A_n\to\mathbb{C}^*$
33455
Question on group homomorphisms involving the standard Z-basis