Kingdom Chlorobiota C.Jeffrey ex Doweld (2001) - plants see Subkingdom Viridiplantae Caval.-Sm. (1981)
   Subkingdom Lycopodiobiotina Doweld (2001)
     Division Lycopodiophyta D.H.Scott (1900) see Phylum Lycopodiophyta D.H.Scott (1900)
       Class Isoëtopsida Rolle (1884)
         Order Isoëtales Prantl (1874)
           1 Family †Chaloneriaceae Pigg & G.W.Rothwell (1983)
           2 Family †Nathorstianaceae Němejc [monotypic]
           3 Family †Suavitasaceae J.Rice, G.W.Rothwell, G.Mapes & R.Mapes (1996) [monotypic]
           4 Family Isoëtaceae Rchb. (1828) [monotypic]