Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
532 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 96 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×D120 | C2 | semidirect |
| 2. C3×#65404 | C2 | semidirect |
| 3. C2×#90938 | C2 | semidirect |
| 4. C5×#4549 | C2 | semidirect |
| 5. #11745895 | C2 | semidirect |
| 13. C2×C3×D40 | C22 | semidirect |
| 14. C2×C5×C3⋊C16 | C22 | semidirect |
| 16. C3×#3950 | C22 | semidirect |
| 20. #65404 | D3 | semidirect |
| 37. D120 | D4 | semidirect |
| 45. #4549 | D5 | semidirect |
| 53. C2×D40 | C2×D3 | semidirect |
| 56. #3950 | C2×D3 | semidirect |
| 88. C2×C3⋊C16 | C2×D5 | semidirect |
| 114. C22×C3×C5 | D16 | semidirect |
| 202. C22×C5 | #826 | semidirect |
| 233. C3×C5 | #2184 | semidirect |
| 239. C22×C3 | D80 | semidirect |
| 280. C5 | #71075 | semidirect |
| 290. C22 | #90938 | semidirect |
| 296. C3 | #10599901 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D120 | 2 |
| C3×#65404 | 2 |
| C2×#90938 | 2 |
| C5×#4549 | 2 |
| #11745895 | 2 |
| #10599901 | 3 |
| #71075 | 5 |