Kingdom Protoctista Hogg, 1860
   Phylum Bacillariophyta Engl. & Gilg (1919) - diatoms see [unranked] Diatomea Kütz. (1844)
     Class Fragilariophyceae Round (1990) - araphid, pennate diatoms see Class Bacillariophyceae Haeckel (1878)
       Subclass Fragilariophycidae Round (1990) - core araphid diatoms
         01 Order Fragilariales P.C.Silva (1962)
         02 Order Rhaphoneidales Round (1990)
         03 Order Ardissoniales see Order Ardissoneales Round (1990)
         04 Order Toxariales Round (1990)
         05 Order Thalassionematales Round (1990)
         06 Order Rhabdonematales Round & R.M. Crawford (1990)
         07 Order Climacospheniales Round (1990)
         08 Order Entopylales see Order Cyclophorales Round & R.M. Crawford (1990)
         09 Order Plagiogrammales Round & R.M. Crawford (1990) see Order Plagiogrammales Gogorev & Stepanova (2015)
         10 Order Pseudohimantidiales see Order Protoraphidales Round (1990)