Phylum Chordata Bateson, 1885 - chordates
   Subphylum Vertebrata Cuvier, 1812 - vertebrates
     Pisces
       1 Class †Pituriaspida Young, 1991 see Order Pituriaspida Young, 1991
       2 Class Mixini see Class Myxini (Jaekel, 1911)
       3 Class †Pteraspidomorphi Goodrich, 1909
       4 Class Cephalaspidomorphi Moy-Thomas & Mile, 1971
       5 Class †Placodermi McCoy, 1848
       6 Class Chondrichthyes Huxley, 1880 - cartilaginous fishes
       7 Class †Acanthodii Owen, 1846
       8 Class Actinopterygii Woodward, 1891 - ray-finned fishes
       9 Class Sarcopterygii Romer, 1955 - lobe-finned fishes and tetrapods see Clade Sarcopterygii Romer, 1955