Conclude the number of elements in $H$ divides the number of elements in $G$.
123560
Intuition behind why order of a subgroup divides order of a group.
17077
Prove or disprove: If $H$ and $G/H$ are cyclic, then $G$ is cyclic.
107010
How many elements of order $k$ are in $S_n$?
18881
Number of elements of order $7$ in a group
94571
How can we prove that $N_G(H)=H$ implies $N_{f(G)}(f(H))=f(H)$
11003
Proving that $G/N$ is an abelian group
15276
$G \times H \cong G \times K$ , then $ K \cong H$
151727
If $|G/H|=4$ then $G$ is union of three proper subgroups
106927
How do I prove $[G:H\cap K]\leq [G:H][G:K]$?
80273
Prove the centralizer of an element in group $G$ is a subgroup of $G$
35800
If $K \leq H \leq G$, show that $[G:K] = [G:H][H:K]$.
37596
If $\gcd(a,b)= 1$ and $a$ divides $bc$ then $a$ divides $c\ $ [Euclid's Lemma]
120642
Let $g : \Bbb N \times \Bbb N \to\Bbb N \times \Bbb N$ defined as $g(m,n) = (m + n,m - n)$
67554
In a group, the number of non-self-inverse elements is even
94507
Given $G$ group and $H \le G$ such that $|G:H|=2$, how does $x^2 \in H$ for every $x \in G$?
41237
$H$ is normal subgroup of $G$ iff $gHg^{-1}=H$ for every $g$ of $G$
122581
Prove or disprove that $G_1/H_1 \cong G_2/H_2$