plants Haeckel (1866) - plants
   Division Charophyta Migula (1889) - charophyte algae and embryophytes see charophytes
     Subdivision [Streptophytina] see [unranked] Streptophytina Lewis & McCourt (2004)
       Class Equisetopsida C.Agardh (1825) - horsetails see Subclass Equisetidae Warm. (1883)
         Vascular Plants see Phylum Tracheophyta Sinnott ex Caval.-Sm. (1998)
           [Ferns]
             Subclass Polypodiidae Cronquist, Takht. & Zimmerm. (1966)
               Order Polypodiales Link (1833) - cathetogyrates
                 Family Pteridaceae E.D.M.Kirchn. (1831) - pteroids
                   I Subfamily Cryptogrammoideae S. Linds. (2009)
                   II Subfamily Ceratopteridoideae R.M.Tryon (1987) see Subfamily Parkerioideae Burnett (1835)
                   III Subfamily Pteridoideae Link (1841)
                   IV Subfamily Cheilanthoideae Horvat (1927)
                   V Subfamily Vittarioideae Link (1841)