If $k$ divides $n$ then there's only one subgroup of $G$ of order $k$
39938
Subgroups of a cyclic group and their order.
123796
Order of automorphism group of a $p$-group is divisible by $p$.
3439
Other proofs that subgroups of $A_5$ have order at most 12
2761
If $S$ is a nonempty subset of group $G$, then $S^{|G|}$ is a subgroup of $G$.
74218
Show that $S_n$ has no subgroup of index $t$ for $2 < t < n$
48393
Abelian groups of order n.
122125
Order of group element divides order of finite group
68201
Cyclic group of order $n$
99205
Group of order $p^k q$ where $p$ and $q$ are distinct primes - how to prove this property?
7324
Let $H$ be a subgroup of $G$ with $[G:H]=n$. Let $N$ be the kernel of the left-multiplication action on the cosets of $H$. Show $[G:N]$ divides $n!$
123560
Intuition behind why order of a subgroup divides order of a group.
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)
104549
When $d \mid n$, the number of elements of order $d$ in a cyclic subgroup of order $n$ is $\phi (d)$
11825
Let $H$ be a subgroup of $G$. Let $K = \{x \in G: xax^{-1} \in H \iff a \in H\}$. Prove that $K$ is a subgroup of $G$.
12667
How many subgroups of order $n$ does $D_n$ have?
89508
Existence of normal subgroups for a group of order $36$
7967
Prove that the order of the cyclic subgroup $\langle g^k\rangle $ is $n/{\operatorname{gcd}(n,k)}$