Kingdom Protoctista Hogg, 1860
   Phylum Bacillariophyta Engl. & Gilg (1919) - diatoms see [unranked] Diatomea Kütz. (1844)
     Class Bacillariophyceae Haeckel (1878) - pennates
       Subclass Bacillariophycidae D.G.Mann (1990) - raphid diatoms
         01 Order Lyrellales D.G.Mann (1990)
         02 Order Naviculales Bessey (1907)
         03 Order Mastogloiales D.G.Mann (1990)
         04 Order Dictyoneidales D.G.Mann (1990)
         05 Order Cymbellales D.G.Mann (1990)
         06 Order Achnanthales P.C.Silva (1962)
         07 Order Amphorales see Order Thalassiophysales D.G.Mann (1990)
         08 Order Bacillariales Hendey (1937)
         09 Order Epithemiales see Order Rhopalodiales D.G.Mann (1990)
         10 Order Surirellales D.G.Mann (1990)