Show that there is just one subgroup $H \subset S_4$ such that $[S_4:H] = 2$
1996
$A_n$ is the only subgroup of $S_n$ of index $2$.
52105
Prove that $HK$ is a subgroup iff $HK=KH$.
87766
Using Cayley's Theorem to find an isomorphic subgroup.
141379
All groups where underlying set has at most 4 elements
89659
$H_1 ,H_2 \unlhd \, G$ with $H_1 \cap H_2 = \{1_G\} $. Prove every two elements in $H_1, H_2$ commute
146969
Proving that every group of order $4$ is isomorphic to $\Bbb Z_4$ or $\Bbb Z^*_8$
156319
Show that a group with $|G| = 33$ contains an element of order $3$
35800
If $K \leq H \leq G$, show that $[G:K] = [G:H][H:K]$.
103829
Find the subgroups of A4
151130
When is the product of $n$ subgroups a subgroup?
56245
Let H be a subgroup of a group G. Prove that the following statements are equivalent.
130455
If $H,K⊲G$ and $H∩K = \{1_G\}$, then all elements in $H$ commute with all elements in $K$
7575
Show the commutator subgroup of $S_{n}$ is $A_{n}$ for $n \geq 5$
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...
138297
Let $G = GL_2\mathbb (R)$. Show that $T$ is a subgroup of $G$
22477
If H is a subgroup of a group G and K is a normal subgroup of G the show that K is a normal subgroup of HK.
64408
Subgroup of $\mathbb{Q}$ with finite index