Vertebrata Cuvier, 1812 - vertebrates see Infraphylum Vertebrata Lamarck, 1801
   Gnathostomata
     Class Chondrichthyes Huxley, 1880 - cartilaginous fishes
       Subclass Holocephali Bonaparte, 1832
         1 Order †Chondrenchelyiformes Moy-Thomas, 1939 [monotypic]
         2 Order †Copodontiformes Obruchev, 1953 [monotypic]
         3 Order †Psammodontiformes Obruchev, 1953 [monotypic]
         4 Suborder †Cochliodontoidei [monotypic] see Order Cochliodontiformes Obruchev, 1953
         5 Suborder †Helodontoidei [monotypic] see Order Helodontiformes Patterson, 1965
         6 Suborder †Menaspoidei Patterson, 1965 [monotypic] see Order Menaspiformes Patterson, 1965
         7 Suborder †Squalorajoidei Patterson, 1965 [monotypic] see Order Squalorajiformes Patterson, 1965
         8 Suborder †Myriacanthoidei Patterson, 1965
         9 Order Chimaeriformes Obruchev, 1953 - chimaeras