MONOCYATHIDAE R. Bedford & W. R. Bedford, 1934: Wall with simple pores.
PALAEOCONULARIIDAE Chudinova, 1959: Wall with attached microporous sheath.
TUMULIOLYNTHIDAE Rozanov, 1966: Wall with simple tumuli.
SAJANOLYNTHIDAE Rozanov, 1989: Wall with multiperforate tumuli.
GLOBOSOCYATHIDAE Okuneva, 1969: Wall with bracts or scales.
FAVILYNTHIDAE Debrenne, 1989: Wall with canals.