subgroup of a finitely generated group not necessarily finitely generated (Hungerford exercise)
10816
Infinitely generated subgroup of a finitely one (weird)
122353
Status of the classification of non-finitely generated abelian groups.
131204
A non-trivial normal subgroup N of a finite group G or order $p^n$ is such that $N\cap Z(G)\neq \{ 1\}$
95240
Show that $({\mathbb{Q}},+)$ is not finitely generated using the Fundamental Theorem of Finitely Generated Abelian Groups.
71035
Non abelian subgroup of a abelian group.
157841
Existence of a non-abelian group of order $p^n$.
6115
Show that $GL_n(\mathbb{F})$ is a finite group iff $\mathbb{F}$ has a finite number of elements
89508
Existence of normal subgroups for a group of order $36$
102622
K is a subgroup of G. Show that K is not a normal subgroup
110708
On proving that a finitely generated group has a finite number of subgroups with index $n$.
111049
Groups with given automorphism groups
61550
Existence of elements of order $p^k$ in a finite group
115204
Show that SO(n) is a normal subgroup of O(n)
86336
For $G$ group and $H$ subgroup of finite index, prove that $N \subset H$ normal subgroup of $G$ of finite index exists
41231
Subgroups of (Z,+) of order n
145254
$G$ be a non-nilpotent and supersoluble finite group.
42449
Is there any efficient algorithm for finding subgroups of a given finite group?