The 1984 Löve classification [reference] was part of a taxonomic revision of the Tribe Triticeae. Following a broad interpretation of the biological species concept, Löve defined genera by their unique genome constitution, either as genera of diploids or polyploids. Thus, the genus Triticum was split into three genera, each corresponding to one of three ploidy levels in the genus.
| Genus Crithodium Link | [A genome] |
| Crithodium jerevani (Tumanian) Á.Löve (4x) | |
| Crithodium monococcum (L.) Á.Löve | |
| subsp. monococcum Boiss. | |
| subsp. aegilopoides (Link) Á.Löve | |
| Crithodium urartu (Tumanian ex Gandilyan) Á.Löve | |
| Genus Gigachilon Seidl | [BA genome] |
| Section Gigachilon | |
| Gigachilon aethiopicum (Jakubz.) Á.Löve | |
| Gigachilon polonicum (L.) Seidl | |
| subsp. polonicum | |
| subsp. carthlicum (Nevski in Kom.) Á.Löve | |
| subsp. dicoccoides (Körn. ex Asch. & Graebner) Á. Löve | |
| subsp. dicoccum (Schrank ex Schübler) Á.Löve | |
| subsp. durum (Desf.) Á.Löve | |
| subsp. palaeocolchicum (Menabde) Á.Löve & D.Löve | |
| subsp. turanicum (Jakubz.) Á.Löve | |
| subsp. turgidum (L.) Á.Löve | |
| Section Kiharae (Dorof. & Migush.) Á.Löve | |
| Gigachilon timopheevii (Zhuk.) Á.Löve | |
| subsp. timopheevii | |
| subsp. armeniacum (Jakubz.) Á.Löve | |
| Gigachilon zhukovskyi (Menabde & Ericzjan) Á.Löve | |
| Genus Triticum L. | [BAD genome] |
| Triticum aestivum L. | |
| subsp. aestivum | |
| subsp. compactum (Host) Thell. | |
| subsp. hadropyrum (Flaksb.) Tzvelev | |
| subsp. macha (Dekapr. & Menabde) MacKey | |
| subsp. spelta (L.) Thell. | |
| subsp. sphaerococcum (Percival) MacKey | |
| subsp. vavilovii (Jakubz.) MacKey |