A subgroup of $S_n$ having index 2 is $A_n$.
1996
$A_n$ is the only subgroup of $S_n$ of index $2$.
33387
Proof that $n\Bbb Z \leq \Bbb Z$ and are the only subgroups of $\Bbb Z$
75568
Subgroup of index $2$ is Normal
94999
A subgroup with an index of 2 is normal to the group.
127996
$M_1$ and $M_2$ are subgroups and $M_1/N=M_2/N$. Is $M_1\cong M_2$?
46121
Does the intersection of two finite index subgroups have finite index?
74218
Show that $S_n$ has no subgroup of index $t$ for $2 < t < n$
70001
Any group of order $2p$ has a subgroup of order $p~$($p$ being a prime)
48369
discrete subgroups of euclidean space
132342
Suppose $H$ is a subgroup of $S_n$ but $H$ is not a subgroup of $A_n$. Prove that |$H$ ∩ $A_n$| = $\frac{1}{2}|H|$?
144582
Index of a subgroup in $SL_2(\mathbb{Z})$
140334
Let $G$ be a group and $H$ be a subgroup of $G$ of index $2$ .Then show that if $a,b\notin H$ then $ab\in H$.
137691
What are the self-normalizing subgroups of $S_n$?
75068
subgroups of $\mathbb Z / 2 \mathbb Z \times \mathbb Z / 2 \mathbb Z$
122335
Abelian $p$-group with unique subgroup of index $p$
72048
Finding Sylow 2-subgroups of the dihedral group $D_n$
11731
Normal subgroups of $S_4$