This name is a synonym of Mammillaria hahniana subsp. woodsii (R.T. Craig) D.R. Hunt.
The record derives from Tropicos
(data supplied on 2012-04-18)
which reports it as a synonym (record 50180809) with original publication details: Cact. Succ. J. (Los Angeles) 15: 33 1943.
Full publication details for this name can be found in IPNI: http://ipni.org/urn:lsid:ipni.org:names:151879-2.
This name was in version 1 of The Plant List, record tro-50180809, and has not been changed.