A system of taxonomy of the cryptogams, the Smith system was published in:
Smith, G.M. (1938). Cryptogamic Botany, vol. 1. Algae and fungi. McGraw-Hill, New York. Smith, G.M. (1955). Cryptogamic Botany, vol. 2. Bryophytes and pteridophytes. 2nd ed. McGraw-Hill, New York.
Division Chlorophyta
Class 1. Chlorophyceae Order 1. Volvocales Family 1. Chlamydomonadaceae Family 2. Volvocaceae Order 2. Tetrasporales Order 3. Ulotrichales Family 1. Ulotrichaceae Family 2. Microsporaceae Family 3. Cylindrocapsaceae Family 4. Chaetophoraceae Family 5. Protococcaceae Family 6. Coleochaetaceae Family 7. Trentepohliaceae Order 4. Ulvales Family 1. Ulvaceae Family 2 Schizomeridaceae Order 5. Schizogoniales Family Schizogoniaceae Order 6. Cladophorales Family 1. Cladophoraceae Family 2. Sphaeropleaceae Order 7. Oedogoniales Family Oedogoniaceae Order 8. Zygnematales Family 1. Zygnemataceae Family 2. Mesotaeniaceae Family 3. Desmidiaceae Order 9. Chlorococcales Family 1. Chlorococcaceae Family 2. Endosphaeraceae Family 3. Characiaceae Family 4. Protosiphonaceae Family 5. Hydrodictyaceae Family 6. Oöcystaceae Family 7. Scenedesmaceae Order 10. Siphonales Family 1. Bryopsidaceae Family 2. Caulerpaceae Family 3. Halicystaceae Family 4. Codiaceae Family 5. Derbesiaceae Family 6. Vaucheriaceae Family 7. Phyllosiphonaceae Order 11. Siphonocladiales Family 1. Valoniaceae Family 2. Dasycladaceae Class 2. Charophyceae Order Charales Family Characeae
Division Euglenophyta
Order 1. Euglenales Order 2. Colaciales (Euglenocapsales)
Division Pyrrophyta
Class 1. Cryptophyceae Class 2. Desmokontae Class 3. Dinophyceae Order 1. Gymnodiniales Order 2. Peridiniales Order 3. Dinophysidales Order 4. Rhyzodiniales Order 5. Dinocapsales Order 6. Dinotrichales Order 7. Dinococcales
Division Chrysophyta
Class 1. Xanthophyceae (Heterokontae) Order 1. Heterochloridales Order 2. Rhizochloridales Order 3. Heterocapsales Order 4. Heterotrichales Order 5. Heterococcales Order 6. Heterosiphonales Class 2. Chrysophyceae Order 1. Chrysomonadales Suborder 1. Cromulinae Suborder 2. Isochrysidineae Suborder 3. Ochromonadineae Order 2. Rhizochrysidales Order 3. Chrysocapsales Order 4. Chrysotrichales Order 5. Chrysosphaerales Class 3. Bacillariophyceae Order 1. Centrales Order 2. Pennales
Division Phaeophyta
Class 1. Isogeneratae Order 1. Ectocarpales Order 2. Sphacelariales Order 3. Tilopteridales Order 4. Cutleriales Order 5. Dictyotales Class 2. Heterogeneratae Subclass 1. Haplostichineae Order 1. Chordariales Order 2. Sporochnales Order 3. Desmarestiales Subclass 2. Polystichineae Order 1. Punctariales Order 2. Dictyosiphonales Order 3. Laminariales Class 3. Cyclosporeae Order Fucales
Division Cyanophyta
Class Myxophyceae (Cyanophyceae) Order 1. Chroococcales Order 2. Chamaesiphonales Order 3. Hormogonales
Division Rhodophyta
Class Rhodophyceae Subclass 1. Bangioideae Order Bangiales Subclass 2. Florideae Order 1. Nemalionales Order 2. Gelidiales Order 3. Cryptonemiales Order 4. Gigartinales Order 5. Rhodymeniales Order 6. Ceramiales
Division Myxothallophyta Class 1. Myxomycetae Subclass 1. Endosporeae Subclass 2. Exosporeae Class 2. Phytomyxinae Class 3. Acrasieae
Division Eumycetae Class 1. Phycomycetae Order 1. Chytridiales Family 1. Rhizidiaceae Family 2. Olpidiaceae Family 3. Synchytriaceae Family 4. Cladochytriaceae Family 5. Woroninaceae Order 2. Blastocladiales Order 3. Monoblepharidales Order 4. Ancylistales Order 5. Saprolegniales Family 1. Saprolegniaceae Family 2. Leptomitaceae Family 3. Pythiaceae Order 6. Peronosporales Order 7. Mucorales Order 8. Entomophthorales Class 2. Ascomycetae Subclass 1. Protoascomycetae Subclass 2. Euascomycetae Order 1. Aspergillales Order 2. Erysiphales Order 3. Hysteriales Order 4. Phacidiales Order 5. Pezizales Order 6. Tuberales Order 7. Helvellales Order 8. Exoascales Order 9. Hypocreales Order 10. Sphaeriales Order 11. Dothidiales Order 12. Laboulbeniales Class 3. Basidiomycetae Subclass 1. Eubasidii Order 1. Agaricales (Hymenomyceatae) Order 2. Lycoperdales (Gasteromycetae) Order 3. Dacryomycetales Order 4. Tremellales Order 5. Auriculariales Subclass 2. Hemibasidii Order 1. Urediniales Order 2. Ustilaginales Family 1. Ustilaginaceae Family 2. Tilletiaceae Class 4. Fungi imperfecti Lichens Subclass 1. Ascholichenes Subclass 2. Basidiolichenes
Division Bryophyta
Class 1. Hepaticae (liverworts) Order 1. Sphaerocarpales Family 1. Sphaerocarpaceae Family 2. Riellaceae Order 2. Marchantiales Family 1. Ricciaceae Family 2. Corsiniaceae Family 3. Targioniaceae Family 4. Monocleaceae Family 5. Marchantiaceae Order 3. Jungermanniales Suborder 1. Metzgerineae Suborder 2. Jungermannineae Order 4. Calobryales Class 2. Anthocerotae (hornworts) Order 1. Anthocerotales Class 3. Musci (mosses) Subclass 1. Sphagnobrya Subclass 2. Andreaeobrya Subclass 3. Eubrya
Division Psilophyta
Class 1. Psilophytinae (psilophytes) Order 1. Psilophytales Family 1. Rhyniaceae Family 2. Psilophytaceae Family 3. Pseudosporochnaceae Family 4. Zosterophyllaceae Family 5. Asteroxylaceae Order 2. Psilotales
Division Lepidophyta Class 1. Lycopodinae (lycopods) Order 1. Lycopodiales Family 1. Protolepidodendraceae Family 2. Lycopodiaceae Order 2. Selaginellales Family 1. Selaginellaceae Family 2. Miadesmiaceae Order 3. Lepidodendrales Family 1. Lepidodendraceae Family 2. Lepidocarpaceae Family 3. Bothrodendraceae Family 4. Sigillariaceae Order 4. Isoetales Family 1. Pleuromeiaceae Family 2. Isoetaceae
Division Calamophyta
Class 1. Equisetinae (horsetails) Order 1. Hyeniales Order 2. Sphenophyllales Order 3. Equisetales Family 1. Calamitaceae Family 2. Equisetaceae
Division Pterophyta
Class 1. Filicinae (ferns) Subclass 1. Primofilices (or Inversicatenales, Coenopterideae, Palaeopteridales) Order 1. Protopteridales Family 1. Protopteridaceae Family 2. Cladoxylaceae Order 2. Coenopteridales Family 1. Zygopteridaceae Family 2. Botryopteridaceae Family 3. Anachoropteridaceae Order 3. Archaeopteridales Subclass 2. Eusporangitae Order 1. Ophioglossales Order 2. Marattiales Subclass 3. Leptosporangiatae Order 1. Filicales Family 1. Osmundaceae Family 2. Schizaeaceae Family 3. Gleicheniaceae Family 4. Matoniaceae Family 5. Dipteridaceae Family 6. Hymenophyllaceae Family 7. Cyatheaceae Family 8. Dicksoniaceae Family 9. Polypodiaceae Family 10. Parkeriaceae Order 2. Marsileales Order 3. Salviniales
