Is it true that every cyclic group of order $n$ contains exactly the same number of subgroups as the number of divisors of $n$?
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
110708
On proving that a finitely generated group has a finite number of subgroups with index $n$.
101345
Suppose $n$ is an even positive integer and $H$ is a subgroup of $\mathbb Z/n \mathbb Z$. Prove that either every element of $H$ is...
21673
If $|G| = p^n$ then $G$ has a subgroup of order $p^m$ for all $0\le m <n.$
76446
Why are cyclic groups of order $p$ (prime) unique up to isomorphism?
73211
Cyclic subgroups dealing with prime numbers Question
151862
Is any subgroup of a direct product isomorphic to a direct product of subgroups?
9232
Group with proper subgroups infinite cyclic
22783
Is the set $Z_n = \{ 0, 1, . . . , n-1 \}$ for $n ≥ 1$ is a group under addition modulo n?
7575
Show the commutator subgroup of $S_{n}$ is $A_{n}$ for $n \geq 5$
90453
How can I find cyclic subgroups of $S_3$?
42389
If $(G, \oplus)$ has order $2n$, prove that every proper subgroup of $(G, \oplus)$
141890
$G$ is a Group of order $pq$, if $G$ has exactly one subgroup of order $p$ and another with order $q$, then $G$ is cyclic ($p,q$ are prime)
59811
Finite Abelian groups with the same number of elements for all orders are isomorphic
47478
Show that any cyclic group of even order has exactly one element of order $2$
127306
Is the group of units of a finite ring cyclic?
99694
Number of subgroups of $S_4$