Finite index subgroups of mapping class groups

Let g >= 3 and n >= 0, and let M-g,M- n be the mapping class group of a surface of genus g with n boundary components. We prove that M-g,M- n contains a unique subgroup of index 2(g-1)(2(g)-1) up to conjugation, a unique subgroup of index 2(g-1)(2(g)+1) up to conjugation, and the other proper subgroups of M-g,M- n are of index greater than 2(g-1)(2(g)+1). In particular, the minimum index for a proper subgroup of M-g,M- n is 2(g-1)(2(g)-1).