Cusps of a subgroup of the modular group (reviewed)

The cusps of a subgroup $\Gamma$ of the modular group are equivalence classes of points in $\mathbb{Q}\cup\infty$ under the action of $\Gamma$ by linear fractional transformation, where for \[ \gamma=\left(\begin{array}{ll}a&b\\c&d \end{array}\right)\in\Gamma, \] we define $\gamma\infty = \frac{a}{c}$ when $c\neq 0$, and $\gamma\infty = \infty$ when $c=0$.