Abstract:
An account is given of the determination of all normal subgroups of index up to $1500$ in the modular group PSL$(2,Z) cong C_2 * C_3$, and all normal subgroups of index up to $500$ in the Hecke groups $H_q = C_2 * C_q$ for $4 le q le 12$, using an adaptation of the low index subgroups algorithm.