Division Bacillariophyta Engl. & Gilg (1919) see Phylum Bacillariophyta Engl. & Gilg (1919)
   Class Coscinodiscophyceae Round & R.M. Crawford (1990) - radial centrics
     Subclass Rhizosoleniophycidae Round & R.M. Crawford (1990)
       Order Rhizosoleniales P.C.Silva (1962)
         Family Pyxillaceae (Schütt) Simonsen (1972)
           1 Genus Pyxilla Grev. (1865)
           2 Genus Gladius Forti & Schulz (1932)
           3 Genus Gyrodiscus Witt (1886)
           4 Genus Mastogonia Ehrenb. (1844)
           5 Genus Pyrgupyxis Hendey (1969)