Finite non-abelian groups.
47239
For $p,q$ primes such that $q|p-1$, show there is only one non-abelian group of order $pq$, up to isomorphism
61373
A normal subgroup that is not a characteristic
122353
Status of the classification of non-finitely generated abelian groups.
111049
Groups with given automorphism groups
110018
Conjugacy classes in $A_n$.
150188
Construct a non-abelian group of order 75
152954
Extensions of finite cyclic groups
78553
A simple finite group $G$ with $n$ p-Sylows is isomorphic to a subgroup of $\mathbb A_n$
113936
Showing that a finite abelian group has a subgroup of order m for each divisor m of n
91874
Existence of finite indexed normal subgroup for a given finite indexed subgroup.
64582
Group covered by finitely many cosets
99538
Non-trivial groups pairwise non-isomorphic with isomorphic direct products
106123
Is there a finite abelian group $G$ such that $\textrm{Aut}(G)$ is abelian but $G$ is not cyclic?
85222
Direct sum of finitely-many non-abelian groups
35124
Can every non-simple group $G$ be written as a semidirect product?
35401
Examples of finite groups that are not a semidirect product
59902
Example of $2$ non-isomorphic groups that have the same quotients