If $H$ is a subgroup of $S_n$ contains transpositions $(1,2), (1,3), ..., (1,n)$ then $H = S_n$
67926
$S_n$ is generated by elements of the form $(1k)$
72150
Union of the conjugates of a proper subgroup
44152
If $G$ has only one subgroup of order $n$, then that Subgroup is Normal
15276
$G \times H \cong G \times K$ , then $ K \cong H$
50762
If $S_n$ has cyclic subgroups of these orders or not?
154398
Show that H is a subgroup of G
148413
Proving $S_n$ is generated by the set $\{(1\text{ }2),(2\text{ }3),\cdots,(n-1\text{ }n)\}$ of $n-1$ transpositions.
71262
Subgroups of order $9$ isomorphic to $C_3 \times C_3$ in $S_6$
64269
Finding the minimal $n$ such that a given finite group $G$ is a subgroup of $S_n$
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 $G$.
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 $n!$
2761
If $S$ is a nonempty subset of group $G$, then $S^{|G|}$ is a subgroup of $G$.
103106
Proving that any permutation in $S_n$ can be written as a product of disjoint cycles
141043
$H$ normal in $G$. Need $G$ contain a subgroup isomorphic to $G/H$
117414
How would I prove what elements $S_3$ contains, and what its subgroups are?
96680
Generators of symmetric group $S_n$
120968
Isomorphism of stabilizer over $S_n$ to $S_{n-1}$