MONOCYATHIDA, Okulitch, 1935: Cup one walled, solitary or low modular; pelta may be present.
AJACICYATHIDA, R. Bedford & J. Bedford, 1939: Cup two walled, solitary or low modular; inner wall of centripetal type of development; intervallum with septa, with or without plate tabulae
PUTAPACYATHIDA, Vologdin, 1961: Intervallum with plate tabulae; redimiculi may be present on intervallum side of either or both walls
CAPSULOCYATHIDA, Zhuravleva, 1964: Thalamid cup, single- or multichambered; inner wall of invaginal type of development; septa and/or plate tabulae may be present in intervallum of multichambered cups
ARCHAEOCYATHIDA, Okulitch, 1935: Cup two walled, of solitary or low- to high-modular organization, with septal type of development; inner wall of centripetal type; intervallum with taeniae, pseudosepta, pseudotaenial network, dictyonal network, calicles, or syringes; segmented or independent (membrane and plate) tabulae may be present
KAZACHSTANICYATHIDA, Konyushkov, 1967: Cup multichambered, solitary or modular, with massive modular types by individualization of modules around new central cavities; development of thalamid type, with stromatoporoid growth pattern; chambers of subspherical to mattresslike shape, with pillars
Orders | |_ Famillies inside the Monocyathida {Ajacicyathida , Putapacyathida , Capsulocyathida , Archaeocyathida , Kazachstanicyathida} | |_ Suborders inside the Ajacicyathida {Monocyathida , Putapacyathida , Capsulocyathida , Archaeocyathida , Kazachstanicyathida} | |_ Superfamillies inside the Putapacyathida {Monocyathida , Ajacicyathida , Capsulocyathida , Archaeocyathida , Kazachstanicyathida} | |_ Famillies inside the Putapacyathida {Monocyathida , Ajacicyathida , Capsulocyathida , Archaeocyathida , Kazachstanicyathida} | |_ Suborders inside the Capsulocyathida {Monocyathida , Ajacicyathida , Putapacyathida , Archaeocyathida , Kazachstanicyathida} | |_ Suborders inside the Archaeocyathida {Monocyathida , Ajacicyathida , Putapacyathida , Capsulocyathida , Kazachstanicyathida} | |_ Suborders inside the Kazachstanicyathida {Monocyathida , Ajacicyathida , Putapacyathida , Capsulocyathida , Archaeocyathida}