The Sylow Theorems · Medium problem

$D_{40}$, the symmetries of a regular $40$-gon, has order $80$. Its Sylow $2$-subgroups have order $16$, generated by the rotations through multiples of $11.25^\circ$ ($40/8$ of a full turn) together with the reflections through those same axes. How many Sylow $2$-subgroups does $D_{40}$ have?