Kingdom Protoctista Hogg, 1860
   Phylum Bacillariophyta Engl. & Gilg (1919) - diatoms see [unranked] Diatomea Kütz. (1844)
     Class Coscinodiscophyceae Round & R.M. Crawford (1990) - radial centrics
       Subclass Thalassiosirophycidae Round & R.M. Crawford (1990) see Class Mediophyceae Medlin & Kaczmarska (2004)
         Order Thalassiosirales Glezer & I.V. Makarova (1986)
           1 Family Thalassiosiraceae M. Lebour (1930), nom. cons.
           2 Family Sceletonemataceae Lebour (1930) see Family Skeletonemataceae M. Lebour (1930)
           3 Family Cyclotellaceae see Family Stephanodiscaceae Glezer & Makarova (1986)
           4 Family Lauderiaceae (Schütt) Lemmerm. (1899)