Freshwater Algae of North America
   Class Zygnematophyceae C.Hoek, D.G.Mann & H.M. Jahns (1995), nom. inval. - conjugating green algae see Class Zygnematophyceae Round ex Guiry (2013)
     Order Desmidiales - placoderm desmids
       1 Family Closteriaceae A. Pritch. (1872)
       2 Family Desmidiaceae Kützing ex Ralfs (1845)
       3 Family Gonatozygaceae
       4 Family Peniaceae Haeckel (1894) [paraphyletic]