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 edit
- 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
Division Euglenophyta edit
- Order 1. Euglenales
- Order 2. Colaciales (Euglenocapsales)
Division Pyrrophyta edit
- 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 edit
- 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
Division Phaeophyta edit
- 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 edit
- Class Myxophyceae (Cyanophyceae)
- Order 1. Chroococcales
- Order 2. Chamaesiphonales
- Order 3. Hormogonales
Division Rhodophyta edit
- 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 edit
- Class 1. Myxomycetae
- Subclass 1. Endosporeae
- Subclass 2. Exosporeae
- Class 2. Phytomyxinae
- Class 3. Acrasieae
Division Eumycetae edit
- 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 edit
- 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 edit
- 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 edit
- 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 edit
- Class 1. Equisetinae (horsetails)
- Order 1. Hyeniales
- Order 2. Sphenophyllales
- Order 3. Equisetales
- Family 1. Calamitaceae
- Family 2. Equisetaceae
Division Pterophyta edit
- 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