| 1 | C. acutispiculumBoomker, 1982 | Boomker (1982); Rees (2018) | | + | |
| X | C. africana Mönnig, 1932: Synonym of C. punctata [Gibbons (1981); Rees (2018)] | Skrjabin et al. (1954); Yamaguti (1961) | | + | |
| X | C. asamatiSpiridonov, 1985Nomen nudum [this paper] | Gibson (2017); Rees (2018) | + | | |
| X | C. bisonis Cram, 1925: Synonym of C. oncophora [Yamaguti (1961); Lichtenfels (1977)] | Skrjabin et al. (1954), Besch (1965); Gibson (2017); Rees (2018) | + | | USA |
| X | C. borgesi Gutteres, 1947: Species inquirendae [Gibbons (1981)] | Skrjabin et al. (1954); Yamaguti (1961); Rees (2018) | | + | |
| 2 | C. chabaudi Diaouré, 1964 | Gibbons (1981); Rees (2018) | | + | |
| 3 | C. connochaeti Boomker, Horak et Alves, 1979 | Gibbons (1981); Rees (2018) | | + | |
| 4 | C. curticei (Giles, 1892) (type species of the genus) | Skrjabin et al. (1954); Yamaguti (1961); Lichtenfels (1977); Gibbons (1981); Gibson (2017); Rees (2018) | + | + | nearly worldvide |
| X | C. fieldingi Baylis, 1929: Synonym of C. puncata [Yamaguti (1961)] | Skrjabin et al. (1954) ); Yamaguti (1961) | | | Australia |
| 5 | C. fuelleborni Hung, 1926 | Skrjabin et al. (1954); Yamaguti (1961); Gibbons (1981); Taylor et al. (2013); Rees (2018) | | + | |
| 6 | C. hamiltoni (Mönig, 1932) | Gibbons (1981); Rees (2018) | | + | |
| X | C. hippotragusi Gutteres, 1947: Species inquirendae [Gibbons (1981)] | Skrjabin et al. (1954); Yamaguti (1961); Rees (2018) | | + | |
| 7 | C. hranktahensisWu, 1965 | Wu (1965) | | | China |
| 8 | C. hungi (Mönnig, 1931) | Skrjabin et al. (1954); Yamaguti (1961); Gibbons (1981); Taylor et al. (2013); Rees (2018) | | + | |
| 9 | C. laterouniformis Chen, 1937 | Skrjabin et al. (1954); Yamaguti (1961); Singh & Pande (1963); Rees (2018) | | | China India |
| X | C. mcmasteri Gordon, 1932: Synonym of C. oncophora [Lichtenfels (1977); Ramünke et al. (2018)] | Skrjabin et al. (1954); Yamaguti (1961); Besch (1963); Gibson (2017); Rees (2018) | + | | USA |
| X | C. minor Gutteres, 1947: Species inquirendae [Gibbons (1981)] | Skrjabin et al. (1954); Yamaguti (1961); Rees (2018) | | + | |
| 10 | C. neitzi Mönnig, 1932 | Skrjabin et al. (1954); Yamaguti (1961); Gibbons (1981); Rees (2018) | | + | |
| 11 | C. okapi Leiper, 1935 | Skrjabin et al. (1954); Yamaguti (1961); Gibbons (1981); Rees (2018) | | + | |
| X | C. okapiae Bearghe et Vuylsteke, 1937 [Skrjabin et al. (1954)] | Yamaguti (1961) | | + | |
| 12 | C. oncophora (Railliet, 1898) | Skrjabin et al. (1954); Yamaguti (1961); Lichtenfels (1977); Gibbons (1981); Gibson (2017); Rees (2018); Avramenko et al. (2017) | + | + | nearly worldwide |
| 13 | C. pectinata Ransom, 1907 | Skrjabin et al. (1954); Yamaguti (1961); Lichtenfels (1977); Gibbons (1981); Gibson (2017); Rees (2018) | + | + | USA |
| 14 | C. pigacheiBoomker et Taylor, 2004 | Boomker & Taylor (2004); Rees (2018) | | + | |
| 15 | C. punctata (von Linstow, 1906) | Skrjabin et al. (1954); Yamaguti (1961); Walker & Becklund (1968); Lichtenfels (1977); Gibbons (1981); Gibson (2017); Avramenko et al. (2017); Rees (2018) | + | + | nearly worldwide |
| X | C. reduncai Gutteres, 1947: Species inquirendae [Gibbons (1981)] | Skrjabin et al. (1954); Yamaguti (1961); Rees (2018) | | | |
| 16 | C. rotundispiculum Gibbons et Khalil, 1980 | Gibbons (1981); Rees (2018) | | + | |
| X | C. spatulata Baylis, 1938: Synonym of C. punctata [Ramünke et al. (2018); Sun et al. (2020)] | Skrjabin et al. (1954); Yamaguti (1961); Walker & Becklund (1968); Lichtenfels (1977); Gibbons (1981); Rees (2018) | | + | Australia Malaysia USA |
| X | C. surnabada Antipin, 1931: Synonym of C. oncophora [e.g. Isenstein (1971a); Gibbons (1981); Newton et al. (1998); Raműnke et al. (2018)] | Skrjabin et al. (1954); Yamaguti (1961); Besch (1963); Lichtenfels (1977); Gibson (2017); Rees (2018) | + | + | USA |
| 17 | C. svanetica Burdjanadze et Tschotschischvili, 1942 | Skrjabin et al. (1954); Yamaguti (1961) | | | Gruzia |
| 18 | C. verrucosa Mönnig, 1932 | Skrjabin et al. (1954); Yamaguti (1961); Gibbons (1981); Rees (2018) | | + | |
| 19 | C. yoshidai Mönnig, 1939 | Skrjabin et al. (1954); Yamaguti (1961); Gibbons (1981); Rees (2018) | | + | |
