Phylum [Tracheophyta] Sinnott ex Caval.-Sm. (1998) - vascular plants
   Subphylum Polypodiophytina Reveal (1996) [monotypic]
     Class Polypodiopsida Cronquist, Takht. & Zimmerm. (1966) - ferns
       Subclass Polypodiidae Cronquist, Takht. & Zimmerm. (1966)
         Order Polypodiales Link (1833) - cathetogyrates
           (eupolypods)
             Suborder Aspleniineae H.Schneid. & C.J.Rothf. (2016)
               32 Family Cystopteridaceae Shmakov (2001)
               33 Family Rhachidosoraceae X.C.Zhang (2011) [monotypic]
               34 Family Diplaziopsidaceae X.C.Zhang & Christenh. (2011)
               35 Family Desmophlebiaceae C.M. Mynssen, A. Vasco, L.S. Sylvestre, R.C.Moran & G. Rouhan (2016) [monotypic]
               36 Family Hemidictyaceae Christenh. & H.Schneid. (2011) [monotypic]
               37 Family Aspleniaceae Newman (1840) - spleenworts
               38 Family Woodsiaceae Herter (1949) [monotypic] - lady ferns
               39 Family Onocleaceae Pic.Serm. (1970) - onocleoids
               40 Family Blechnaceae Newman (1844) - blechnoids
               41 Family Athyriaceae Alston (1956)
               42 Family Thelypteridaceae Ching ex Pic.Serm. (1970) - thelypteroids