For finite group $G$ of order $n$ such that there exists a unique subgroup of order equal to each positive divisor of $n$. Is it necessarily cyclic?
117899
At most one subgroup of every order dividing $\lvert G\rvert$ implies $G$ cyclic
157841
Existence of a non-abelian group of order $p^n$.
103423
Normal subgroup where G has order prime
64269
Finding the minimal $n$ such that a given finite group $G$ is a subgroup of $S_n$
45770
Does the order, lattice of subgroups, and lattice of factor groups, uniquely determine a group up to isomorphism?
150760
Are there any distinct finite simple groups with the same order?
109053
Show that a finite cyclic group of order $n$ has exactly one subgroup of order $d$ dividing $n$ and these are all the subgroups it has
2304
What is the quotient of a cyclic group of order $n$ by a cyclic subgroup of order $m$?
84823
When is the group of units in $\mathbb{Z}_n$ cyclic?
83654
Order of an element in a finite cyclic group
114187
In a finite cyclic group, the generator has the order of the group
59533
If $\gcd(m,n)=1$, then $\mathbb{Z}_n \times \mathbb{Z}_m$ is cyclic.
39976
If a group G has only the trivial group and G itself as its subgroup, can we be sure that G has prime order?
41231
Subgroups of (Z,+) of order n
76446
Why are cyclic groups of order $p$ (prime) unique up to isomorphism?
101596
Determine group G as cyclic
95534
If $|G|=p^nq$, then $G$ contains a unique normal subgroup of index $q$