Division Bacillariophyta Engl. & Gilg (1919) see Phylum Bacillariophyta Engl. & Gilg (1919)
   Class Coscinodiscophyceae Round & R.M. Crawford (1990) - radial centrics
     Subclass Biddulphiophycidae Round & R.M. Crawford (1990) see Class Mediophyceae Medlin & Kaczmarska (2004)
       Order Hemiaulales Round & R.M. Crawford (1990)
         Family Hemiaulaceae Heib. (1863)
           01 Genus Hemiaulus Heib. (1863)
           02 Genus Eucampia Ehrenb. (1839)
           03 Genus Climacodium Grunow (1868)
           04 Genus Cerataulina H. Perag. ex F. Schütt (1896)
           05 Genus Trinacria Heib. (1863)
           06 Genus Abas R. Ross & P.A. Sims (1980)
           07 Genus Briggera R. Ross & P.A. Sims (1985)
           08 Genus Pseudorutilaria Grove & Sturt (1886)
           09 Genus Keratophora Pant. (1889)
           10 Genus Kittonia E. Grove & G. Sturt (1887)
           11 Genus Strelnikovia R. Ross & P.A. Sims (1985)
           12 Genus Riedelia Jousé & Shesh.-Por. (1971), nom. illeg.
           13 Genus Baxteriopsis G. Karst. (1928)
           14 Genus Sphynctolethus Hanna (1927)
           15 Genus Ailuretta P.A. Sims (1986)