# Sylow's theorem5

Exhibit two Sylow 2-subgroups of Symmetric group $S_5$
Exhibit all of the Sylow 2-subgroups of Symmetric group $S_4$
Compute all Sylow subgroups of Dihedral group $D_{12}$ and $S_3\times S_3$
Use Sylow’s Theorem to prove Cauchy’s Theorem
The Sylow numbers of a direct product are products of the Sylow numbers