[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
           Subclass Holocephali Bonaparte, 1832
             01 Family †Gregoriidae Lund & Grogan, 2004, incertae sedis
             02 Family †Harpacanthidae Lund & Grogan, 2004, incertae sedis
             03 Family †Lagarodontidae Lebedev, 2008, incertae sedis
             04 Order †Iniopterygiformes Zangerl & Case, 1973
             05 Order †Orodontiformes Zangerl, 1981
             06 Order †Eugeneodontiformes Zangerl, 1981
             07 Order †Petalodontiformes Zangerl, 1981
             08 Order †Debeeriiformes Grogan & Lund, 2000 [monotypic]
             09 Order †Helodontiformes Patterson, 1965 [monotypic]
             09 Superorder Holocephalimorpha Lund, 1986