Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
532 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 100 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. C22×C3×D40 | C2 | semidirect |
| 2. C5×#5115 | C2 | semidirect |
| 3. C2×#90937 | C2 | semidirect |
| 4. #11746370 | C2 | semidirect |
| 5. #11745891 | C2 | semidirect |
| 10. C2×C5×D24 | C22 | semidirect |
| 14. C2×C3⋊#672 | C22 | semidirect |
| 16. C5×#818 | C22 | semidirect |
| 19. C22×D40 | D3 | semidirect |
| 40. C3×D40 | D4 | semidirect |
| 44. #5115 | D5 | semidirect |
| 84. C2×D24 | C2×D5 | semidirect |
| 87. #818 | C2×D5 | semidirect |
| 105. D40 | #67 | semidirect |
| 114. C22×C3×C5 | D16 | semidirect |
| 205. C22×C5 | #826 | semidirect |
| 233. C3×C5 | #2184 | semidirect |
| 240. C22×C3 | #3958 | semidirect |
| 280. C5 | #72035 | semidirect |
| 290. C22 | #90937 | semidirect |
| 296. C3 | #10601868 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×D40 | 2 |
| C5×#5115 | 2 |
| C2×#90937 | 2 |
| #11746370 | 2 |
| #11745891 | 2 |
| #10601868 | 3 |
| #72035 | 5 |