For $n\geq 1$, let $S_{n}$ denote the group of all permutations on $n$ symbols. Which of the following statements is true?
- $S_{3}$ has an element of order $4$
- $S_{4}$ has an element of order $6$
- $S_{4}$ has an element of order $5$
- $S_{5}$ has an element of order $6$.