Phylum [Vertebrata] Lamarck, 1801 see Infraphylum Vertebrata Lamarck, 1801
   Class Agnatha Cope, 1889
     Subclass †Pteraspidomorphi Goodrich, 1909 see Class Pteraspidomorphi Goodrich, 1909
       1 Order †Heterostraci Lankester, 1868 - heterostracans see Subclass Heterostraci Lankester, 1868
       2 Order †Thelodontida see Order Thelodonti Jaekel, 1911