Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
432 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 94 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C5×#5195 | C2 | semidirect |
| 3. C2×C5×#800 | C2 | semidirect |
| 4. C5×#4896 | C2 | semidirect |
| 5. C3×C5×#359 | C2 | semidirect |
| 6. C5×#4508 | C2 | semidirect |
| 7. C5×#4495 | C2 | semidirect |
| 16. C2×C5×Dic12 | C22 | semidirect |
| 19. C2×C3×C5×C16 | C22 | semidirect |
| 20. C3×C5×#108 | C22 | semidirect |
| 24. C5×#812 | C22 | semidirect |
| 26. #69244 | C5 | direct (N × H) |
| 32. C5×#359 | D3 | semidirect |
| 62. #5195 | C2×C5 | semidirect |
| 63. C2×#800 | C2×C5 | semidirect |
| 64. #4896 | C2×C5 | semidirect |
| 65. C3×#359 | C2×C5 | semidirect |
| 66. #4508 | C2×C5 | semidirect |
| 67. #4495 | C2×C5 | semidirect |
| 82. C2×C5×C16 | C2×D3 | semidirect |
| 83. C5×#108 | C2×D3 | semidirect |
| 116. C2×Dic12 | C22×C5 | semidirect |
| 119. C2×C3×C16 | C22×C5 | semidirect |
| 120. C3×#108 | C22×C5 | semidirect |
| 124. #812 | C22×C5 | semidirect |
| 158. #359 | C5×D3 | semidirect |
| 235. C2×C16 | C2×C5×D3 | semidirect |
| 236. #108 | C2×C5×D3 | semidirect |
| 304. C3×C5 | #2194 | semidirect |
| 349. C5 | #69244 | direct (N × H) |
| 361. C3 | C5×#2194 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5769 | 2 |
| C5×#5195 | 2 |
| C2×C5×#800 | 2 |
| C5×#4896 | 2 |
| C3×C5×#359 | 2 |
| C5×#4508 | 2 |
| C5×#4495 | 2 |
| C5×#2194 | 3 |
| #69244 | 5 |