Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
224 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 53 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. #11751020 | C2 | semidirect |
| 2. D15×D16 | C2 | semidirect |
| 3. C3×C5×SD64 | C2 | semidirect |
| 4. #11746342 | C2 | semidirect |
| 5. #11746340 | C2 | semidirect |
| 6. D480 | C2 | semidirect |
| 7. #11746268 | C2 | semidirect |
| 11. C3×C5×Q32 | C22 | semidirect |
| 16. D240 | C22 | semidirect |
| 18. C3×C5×C32 | C22 | semidirect |
| 19. C3⋊#3926 | C22 | semidirect |
| 23. C5×SD64 | D3 | semidirect |
| 41. C3×SD64 | D5 | semidirect |
| 48. C5×Q32 | C2×D3 | semidirect |
| 55. C5×C32 | C2×D3 | semidirect |
| 71. C3×Q32 | C2×D5 | semidirect |
| 78. C3×C32 | C2×D5 | semidirect |
| 94. SD64 | D15 | semidirect |
| 130. Q32 | C2×D15 | semidirect |
| 138. C32 | C2×D15 | semidirect |
| 174. C3×C5 | #2263 | semidirect |
| 204. C5 | #69380 | semidirect |
| 213. C3 | #10600173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11751020 | 2 |
| D15×D16 | 2 |
| C3×C5×SD64 | 2 |
| #11746342 | 2 |
| #11746340 | 2 |
| D480 | 2 |
| #11746268 | 2 |
| #10600173 | 3 |
| #69380 | 5 |