Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
432 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 77 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. #11751296 | C2 | semidirect |
| 3. C2×#91084 | C2 | semidirect |
| 4. #11750997 | C2 | semidirect |
| 5. C3×C5×#359 | C2 | semidirect |
| 6. #11746329 | C2 | semidirect |
| 7. #11746316 | C2 | semidirect |
| 16. C2×Dic60 | C22 | semidirect |
| 19. C2×C3×C5×C16 | C22 | semidirect |
| 20. C3×C5×#108 | C22 | semidirect |
| 24. #91096 | C22 | semidirect |
| 31. C5×#359 | D3 | semidirect |
| 65. C3×#359 | D5 | semidirect |
| 78. C2×C5×C16 | C2×D3 | semidirect |
| 79. C5×#108 | C2×D3 | semidirect |
| 119. C2×C3×C16 | C2×D5 | semidirect |
| 120. C3×#108 | C2×D5 | semidirect |
| 158. #359 | D15 | semidirect |
| 235. C2×C16 | C2×D15 | semidirect |
| 236. #108 | C2×D15 | semidirect |
| 304. C3×C5 | #2194 | semidirect |
| 349. C5 | #69244 | semidirect |
| 361. C3 | #10600037 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11756528 | 2 |
| #11751296 | 2 |
| C2×#91084 | 2 |
| #11750997 | 2 |
| C3×C5×#359 | 2 |
| #11746329 | 2 |
| #11746316 | 2 |
| #10600037 | 3 |
| #69244 | 5 |