It is true that every group that has a finite number of subgroups is finite?
96614
Finite number of subgroups $\Rightarrow$  finite group
126426
Does every infinite finitely generated group contains an element of infinite period?
3439
Other proofs that subgroups of $A_5$ have order at most 12
155219
Prove or Disprove: If every nontrivial subgroup of a group $G$ is cyclic, then $G$ is cyclic.
145563
In an abelian group, the elements of finite order form a subgroup.
106660
Every subgroup of the integers has finite index
42449
Is there any efficient algorithm for finding subgroups of a given finite group?
47539
Find an abelian infinite group such that every proper subgroup is finite
50762
If $S_n$ has cyclic subgroups of these orders or not?
10816
Infinitely generated subgroup of a finitely one (weird)
13059
If a group is the union of two subgroups, is one subgroup the group itself?
151130
When is the product of $n$ subgroups a subgroup?
91874
Existence of finite indexed normal subgroup for a given finite indexed subgroup.
118849
If a cyclic group has an element of infinite order, how many elements of finite order does it have?
21673
If $|G| = p^n$ then $G$ has a subgroup of order $p^m$ for all $0\le m <n.$
144218
Does every finite nilpotent group occur as a Frattini subgroup?
151862
Is any subgroup of a direct product isomorphic to a direct product of subgroups?