Class Conjugatophyceae Engl. (1892) see Class Zygnematophyceae Round ex Guiry (2013)
   Order Desmidiales - placoderm desmids
     Family Desmidiaceae Kützing ex Ralfs (1845)
       01 Genus Actinotaenium (Nägeli) Schellenb. (1897)
       02 Genus Allorgeia L. Gauthier-Lièvre (1958)
       03 Genus Amscottia Groenblad (1954)
       04 Genus Bambusina Kütz. ex Kütz. (1849), nom. cons.
       05 Genus Bourrellyodesmus P. Compère (1977)
       06 Genus Brachytheca A.A. Gontcharov & M. Watanabe (1999)
       07 Genus Cosmarium Corda ex Ralfs (1848)
       08 Genus Cosmocladium Bréb. (1856)
       09 Genus Croasdalea C.E.M. Bicudo & C.T.J. Mercante (1993)
       10 Genus Cruciangulum D.B. Williamson (1999)
       11 Genus Desmidium C.Agardh ex Ralfs (1848)
       12 Genus Docidium Bréb. ex Ralfs (1848)
       13 Genus Euastridium W.West & G.S.West (1907)
       14 Genus Euastrum Ehrenb. ex Ralfs (1848)
       15 Genus Groenbladia Teiling (1952)
       16 Genus Haplotaenium Bando
       17 Genus Heimansia Coesel
       18 Genus Hyalotheca Ehrenb. ex Ralfs (1848)
       19 Genus Ichthyodontum A.M.Scott & G.W. Prescott (1956)
       20 Genus Ichtyocercus
       21 Genus Mateola Salisb.
       22 Genus Micrasterias C.Agardh ex Ralfs (1848)
       23 Genus Octacanthium (Hansgirg) Compère
       24 Genus Onychonema Wall. (1860) see Genus Sphaerozosma Ralfs (1848)
       25 Genus Oocardium Nägeli (1849)
       26 Genus Phymatodocis Nordst. (1877)
       27 Genus Pleurotaeniopsis
       28 Genus Prescottiella C.E.M. Bicudo (1976)
       29 Genus Raphidiastrum G.M. Palamar'-Mordvintseva (1976)
       30 Genus Sphaerozosma Ralfs (1848)
       31 Genus Spinocosmarium Prescott & A.M.Scott (1942)
       32 Genus Spondylosium Bréb. ex Kütz. (1849)
       33 Genus Staurastrum Meyen ex Ralfs (1848)
       34 Genus Staurodesmus Teiling (1948)
       35 Genus Streptonema Wall. (1860)
       36 Genus Teilingia Bourr. (1964)
       37 Genus Tetmemorus Ralfs (1848)
       38 Genus Triplastrum Iyengar & Ramanathan (1942)
       39 Genus Triploceras Bailey (1851)
       40 Genus Vincularia K. Fuciková & J. Kastovsky (2009)
       41 Genus Xanthidium Ehrenb. ex Ralfs (1848)