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
         Order Achnanthales P.C.Silva (1962)
           1 Family Achnanthacae see Family Achnanthaceae Kütz. (1844)
           2 Family Achnanthidiaceae D.G.Mann (1990)
           3 Family Cocconeidaceae Kütz. (1844)