[Phylum] Chordata Bateson, 1885 - chordates
   Subphylum Craniata auct.
     Infraphylum Vertebrata Lamarck, 1801 - vertebrates
       Superclass Gnathostomata Gegenbaur, 1874 - jawed vertebrates
         Class Chondrichthyes Huxley, 1880 - cartilaginous fishes
           01 Family †Bandringidae Zangerl, 1969, incertae sedis
           02 Family †Kathemacanthidae Gagnier & Wilson, 1996, incertae sedis
           03 Family †Palaeospondylidae Gill, 1896, incertae sedis
           04 Family †Polysentoridae Zangerl, 1979, incertae sedis
           05 Family †Protodontidae Woodward, 1932, incertae sedis
           06 Family †Wellingtonellidae Märss, Wilson & Thorsteinsson, 2002, incertae sedis
           07 Order †Altholepidiformes Andreev, Coates, Shelton, Cooper, Smith & Sansom, 2015
           08 Order †Elegestolepidida Andreev, Coates, Karatajute-Talimaa, Shelton, Cooper & Sansom, 2017
           09 Order †Mongolepidiformes
           10 Order †Polymerolepidiformes [monotypic]
           11 Order †Omalodontiformes Turner, 1997
           12 Order †Antarctilamniformes Ginter et al., 2008
           13 Order †Phoebodontiformes Ginter, Hairapetian & Klug, 2002
           14 Superorder †Cladoselachimorpha
           15 Superorder †Ctenacanthimorpha
           16 Superorder †Xenacanthimorpha
           17 Subclass Holocephali Bonaparte, 1832
           18 Subclass Euselachii Hay, 1902 - sharks, rays, and related fossils