Subgroups of Symmetric Group Isomorphic to Product of Subgroups

Theorem
Let $S_n$ denote the symmetric group on $n$ letters.

Let $K \in \closedint 1 n$.

Then there are $\dbinom n k$ subgroups of $S_n$ which are isomorphic to $S_k \times S_{n - k}$, where $\dbinom n k$ denotes the binomial coefficient.

All of these $\dbinom n k$ subgroups are conjugate.