Classification of the family Trinucleidae
Fm. †Trinucleidae Hawle and Corda 1847
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G. †Anebolithus Huges and Wright 1970
G. †Auritolithus Holloway et al. 2022
G. †Bergamia Whittard 1955
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Invalid names: Bohemaspis Horbringer 1986 [synonym], Brandysops Horbringer 1986 [synonym], Cochliorrhoe Whittard 1966 [synonym]
G. †Botrioides Stetson 1927
G. †Costonia Whittard 1956
Subfm. †Cryptolithinae Angelin 1854
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G. †Broeggerolithus Lamont 1935
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†Broeggerolithus broeggeri Bancroft 1929
†Broeggerolithus broeggeri ulrichi Bancroft 1949
†Broeggerolithus discors Angelin 1854
†Broeggerolithus nicholsoni Reed 1910
Invalid names: Ulricholithus Bancroft 1949 [synonym]
G. †Cryptolithoides Whittington 1941
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†Cryptolithoides reticulatus Ross and Shaw 1972
†Cryptolithoides ulrichi Whittington 1941
G. †Cryptolithus Green 1832
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†Cryptolithus recurvus Ulrich 1919
†Cryptolithus tessellatus Green 1832
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Invalid names: Cryptolithus lorettensis Foerste 1924 [synonym], Trinucleus bellulus Ulrich 1879 [synonym]
G. †Deanaspis Hughes et al. 1975
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†Deanaspis bedinanensis Dean 1967
†Deanaspis goldfussii Barrande 1846
†Deanaspis goldfussii senftenbergii Hawle and Corda 1847
†Deanaspis seftenbergii Hawle and Corda 1847
G. †Decordinaspis Harper and Romano 1967
G. †Eirelithus Lamont 1941
G. †Furcalithus Fortey and Owens 1987
G. †Gymnostomix Fortey and Owens 1987
G. †Hanchungolithus Lu 1956
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†Hanchungolithus richthofeni Kayser 1883
Invalid names: Ichangolithus Lu 1963 [synonym]
G. †Incaia Whittard 1955
G. †Jianxilithus Zhang and Zhou 1876
G. †Lloydolithus Bancroft 1933
G. †Lordshillia Whittard 1966
G. †Marrolithoides Williams 1948
G. †Myinda Stubblefield and Bulman 1927
G. †Myindella Hutchison and Ingham 1962
G. †Myttonia Whittard 1955
G. †Novaspis Whittington 1941
G. †Paratretaspis Dean 1973
G. †Paratrinucleus Whittington 1941
G. †Parkesolithus Campbell and Durham 1970
G. †Reedolithus Bancroft 1929
G. †Reuscholithus Bancroft 1929
G. †Telaeomarrolithus Williams 1948
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Invalid names: Fimbriomarrolithus Williams 1948 [objective synonym]
Subfm. †Trinucleinae Hawle and Corda 1847
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G. †Tretaspis M'Coy 1849
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†Tretaspis anderssoni Stormer 1945
†Tretaspis askerensis Owen 1980
†Tretaspis ceriodes angelini Stormer 1930
†Tretaspis hadelandica hadelandica Stormer 1945
†Tretaspis hisingeri Owen 1980
†Tretaspis kiaeri Stormer 1930
†Tretaspis latilimba Linnarsson 1869
†Tretaspis latilimbus norvegicus Owen 1980
†Tretaspis moeldenensis Cave 1960
†Tretaspis reticulata Ruedemann 1901
†Tretaspis sagenosus Whittington 1959
†Tretaspis seticornis anderssoni Stormer 1945
†Tretaspis sortita Reed 1935
†Tretaspis sortita broeggeri Stormer 1945
G. †Trinucleus Murchison 1839
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†Trinucleus conollyi Fortey 2006
†Trinucleus seticornis Hisinger 1840
Invalid names: Edgellia Shaw 1950 [objective synonym]
G. †Whittardolithus Hughes and Addison 1975
G. †Xiushuilithus Zhou 1976
G. †Yinpanolithus Lu and Chang 1974
Invalid names: Hanchungolithinae Lu 1963 [empty], Marrolithinae Hughes 1971 [empty], Microdiscus [nomen vanum], Tretaspidinae Whittington 1941 [empty]