Looking at a late 50's Fifth Avenue Coach Lines map, it lists the following lines that were run by the NYCTA:
M1-Madison/Chambers Sts.
M3-49/50 Sts
M7-65/66 Sts
M11-York Av/57 St
M13-1st Av
M15-2nd Av
Fifth Av Coach Lines operated two divisions which were the FACO and the NYCO divisions in the borough of Manhattan. It doesn't list the meanings to the NYCO and FACO abbreviations. The same route numbers were used in both divisions on separate routes. For example:
6(FACO)-current M6 route
6(NYCO)-current M30 route
15(NYCO)-23 St Crosstown
15(FACO)-current Q32 route
The 20(FACO) was the 57th Street crosstown route operated by 5th Av Coach.
5 & 19 FACO operated along the current M5 route except the 5 operated via Broadway and the 19 operated via Riverside Drive between 135 St and 157 St.