Cosets and Lagrange's Theorem · Medium problem

In $U(40)$ (the units mod $40$), $\varphi(40)=16$. Compute the order of $3$ in $U(40)$ by checking divisors of $16$. It is given that $3^2 \equiv 9 \pmod{40}$ and $3^4 \equiv 1 \pmod{40}$. What is the index $[U(40):\langle 3\rangle]$?