Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
224 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 56 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 |
|---|---|---|
| 1. #11746834 | C2 | semidirect |
| 2. D5×D48 | C2 | semidirect |
| 3. D480 | C2 | semidirect |
| 4. C5×#4449 | C2 | semidirect |
| 5. C3×#64667 | C2 | semidirect |
| 6. #11745826 | C2 | semidirect |
| 7. #11745820 | C2 | semidirect |
| 12. D240 | C22 | semidirect |
| 13. C5×Dic24 | C22 | semidirect |
| 18. C3×C5×C32 | C22 | semidirect |
| 19. C3×#3926 | C22 | semidirect |
| 27. #64667 | D3 | semidirect |
| 43. #4449 | D5 | semidirect |
| 55. C5×C32 | C2×D3 | semidirect |
| 56. #3926 | C2×D3 | semidirect |
| 72. Dic24 | C2×D5 | semidirect |
| 79. C3×C32 | C2×D5 | semidirect |
| 138. C32 | D3×D5 | semidirect |
| 174. C3×C5 | #2263 | semidirect |
| 204. C5 | #69373 | semidirect |
| 213. C3 | #10600173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11746834 | 2 |
| D5×D48 | 2 |
| D480 | 2 |
| C5×#4449 | 2 |
| C3×#64667 | 2 |
| #11745826 | 2 |
| #11745820 | 2 |
| #10600173 | 3 |
| #69373 | 5 |