Maihueniopsis conoidea (F.Ritter ex Backeb.) F.Ritter, Kakteen Südamerika 3: 873. 1980 sec. Hunt 2016
- ≡Opuntia conoidea (F.Ritter ex Backeb.) G.D.Rowley in Natl. Cact. Succ. J. 13: 25. 1958 syn. sec. Hunt 2016
- –Tephrocactus conoideus F.Ritter ex Backeb., Cactaceae 1: 286. 1958, nom. inval., syn. sec. Hunt 2006
- =? Opuntia tarapacana Phil. in Anales Mus. Nac. Santiago de Chile 1: 27. 1891 syn. sec. Hunt 2016
- ≡Tephrocactus tarapacanus (Phil.) Backeb., Kaktus-ABC: 114. 1936 ["1935"] syn. sec. Hunt 2016
- ≡? Maihueniopsis tarapacana (Phil.) F.Ritter, Kakteen Südamerika 3: 874. 1980 syn. sec. Hunt 2016
- =Tephrocactus parvisetus Backeb., Descr. Cact. Nov. 3: 15. 1963 syn. sec. Kew WCVP (2019)