Class Chondrichthyes Huxley, 1880 - cartilaginous fishes
   Subclass Elasmobranchii Bonaparte, 1838 - shark-like fishes
     Cohort Euselachii Hay, 1902 - spined sharks and relatives see Infraclass Euselachii Hay, 1902
       Subcohort Neoselachii Compagno, 1977 - modern sharks and rays see Cohort Neoselachii Compagno, 1977
         Superorder Squalomorphii (Compagno, 1973) see Division Squalea (Shirai, 1996)
           Order Hexanchiformes Compagno, 1973 - six-gill sharks
             Family Chlamydoselachidae Garman, 1884 - frill sharks