1. Family Asyncorynidae Kramp, 1949
2. Family Cladocorynidae Allman, 1872
3. Family Cladonematidae Gegenbaur, 1857
4. Family Corynidae Johnston, 1836
5. Family Halimedusidae Arai & Brinckmann-Voss, 1980
6. Family Hydrocorynidae Rees, 1957
7. Family Milleporidae Fleming, 1828
8. Family Moerisiidae Poche, 1914
9. Family Pennariidae McCrady, 1859
10. Family Porpitidae Goldfuss, 1818
11. Family Pseudosolanderiidae Bouillon & Gravier-Bonnet, 2006
12. Family Pteronemidae Haeckel, 1979
13. Family Rosalindidae Bouillon, 1985
14. Family Solanderiidae Marshall, 1892
15. Family Sphaerocorynidae Prévot, 1959
16. Family Teissieridae Bouillon, 1978
17. Family Tricyclusidae Kramp, 1949
18. Family Zancleidae Russell, 1953
19. Family Zancleopsidae Bouillon, 1978
20. Family Ceratelladae Gray, 1868 accepted as Solanderiidae Marshall, 1892 (synonym)
21. Family Cladonemidae Gegenbaur, 1857 accepted as Cladonematidae Gegenbaur, 1857 (unaccepted > misspelling - incorrect original spelling)
22. Family Cladosarsiidae Bouillon, 1978 accepted as Corynidae Johnston, 1836 (unaccepted > junior subjective synonym)
23. Family Codonidae Haeckel, 1879 accepted as Corynidae Johnston, 1836 (unaccepted > junior subjective synonym)
24. Family Corynipteridae Weill, 1934 accepted as Zancleidae Russell, 1953 (invalid name, not based on genus)
25. Family Dendronemidae Haeckel, 1879 accepted as Cladonematidae Gegenbaur, 1857 (synonym)
26. Family Discalidae Haeckel, 1888 accepted as Porpitidae Goldfuss, 1818 (unaccepted > junior subjective synonym)
27. Family Eleutheriidae Russell, 1953 accepted as Cladonematidae Gegenbaur, 1857 (unaccepted > junior subjective synonym)
28. Family Halocordylidae Stechow, 1921 accepted as Pennariidae McCrady, 1859 (synonym)
29. Family Halocorynidae Picard, 1957 accepted as Zancleidae Russell, 1953 (unaccepted > junior subjective synonym)
30. Family Milleporadae Fleming, 1828 accepted as Milleporidae Fleming, 1828 (incorrect formation of family name)
31. Family Milleporina Ehrenberg, 1831 accepted as Milleporidae Fleming, 1828 (unaccepted > junior objective synonym)
32. Superfamily Moerisiida Poche, 1914 (invalid grouping (polyphyletic))
33. Family Orthocorynidae A. Agassiz, 1865 accepted as Zancleidae Russell, 1953 (invalid name, not based on genus name)
34. Family Polyorchidae A. Agassiz, 1862 accepted as Corynidae Johnston, 1836 (unaccepted > junior subjective synonym)
35. Family Porpalidae Haeckel, 1888 accepted as Porpitidae Goldfuss, 1818 (synonym)
36. Infraorder Porpitae accepted as Porpitidae Goldfuss, 1818 (incorrect family name formation, emended to Porpitidae by Guilding (1828))
37. Family Porpitellidae Haeckel, 1888 accepted as Porpitidae Goldfuss, 1818 (synonym)
38. Family Sarsiadae Forbes, 1848 accepted as Corynidae Johnston, 1836 (synonym and incorrect name formation)
39. Superfamily Sphaerocorynida Petersen, 1990 (unfounded grouping)
40. Family Spirocodonidae Uchida, 1927 accepted as Corynidae Johnston, 1836 (unaccepted > junior subjective synonym)
41. Family Syncorynidae Allman, 1872 accepted as Corynidae Johnston, 1836 (unaccepted > junior subjective synonym)
42. Family Velellidae Eschscholtz, 1829 accepted as Porpitidae Goldfuss, 1818 (unaccepted > junior subjective synonym, synonym)
43. Superfamily Zancleida Russell, 1953 (unfounded grouping)

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