Superphylum Deuterostomia Grobben, 1908 - deuterostomes see Infrakingdom Deuterostomia Grobben, 1908
   Phylum Chordata Bateson, 1885 - chordates
     Subphylum Craniata auct.
       Vertebrata Lamarck, 1801 - vertebrates see Infraphylum Vertebrata Lamarck, 1801
         Myopterygii Janvier, 1978 - myopterygians
           Superclass Gnathostomata Gegenbaur, 1874 - jawed vertebrates
             Grade Chondrichthiomorphi see Grade Chondrichthyomorphi
               Class Chondrichthyes Huxley, 1880 - cartilaginous fishes
                 Subclass Holocephali Bonaparte, 1832
                   Superorder Holocephalimorpha Lund, 1986
                     Cochliodontomorpha
                       Order †Chondrenchelyiformes Moy-Thomas, 1939 [monotypic]
                         Family †Chondrenchelyidae Jordan, 1923
                           1 Genus †Chondrenchelys Traquair, 1888
                           2 Genus †Harpagofututor Lund, 1982
                           3 Genus †Platyxystrodus Hay, 1899