Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
532 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 99 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×C5×#466 | C2 | semidirect |
| 3. C2×#91110 | C2 | semidirect |
| 4. #11746370 | C2 | semidirect |
| 5. #11746312 | C2 | semidirect |
| 8. C2×C3×C5×D8 | C22 | semidirect |
| 14. C3×C5×#107 | C22 | semidirect |
| 17. C2×C3⋊#672 | C22 | semidirect |
| 20. C5×#466 | D3 | semidirect |
| 40. D120 | D4 | semidirect |
| 43. C3×#466 | D5 | semidirect |
| 48. C2×C5×D8 | C2×D3 | semidirect |
| 54. C5×#107 | C2×D3 | semidirect |
| 79. C2×C3×D8 | C2×D5 | semidirect |
| 85. C3×#107 | C2×D5 | semidirect |
| 109. #466 | D15 | semidirect |
| 117. C22×C3×C5 | D16 | semidirect |
| 168. C2×D8 | C2×D15 | semidirect |
| 173. #107 | C2×D15 | semidirect |
| 205. C22×C5 | #826 | semidirect |
| 233. C3×C5 | #2184 | semidirect |
| 239. C22×C3 | #3958 | semidirect |
| 280. C5 | #71075 | semidirect |
| 290. C22 | #91110 | 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×D120 | 2 |
| C3×C5×#466 | 2 |
| C2×#91110 | 2 |
| #11746370 | 2 |
| #11746312 | 2 |
| #10601868 | 3 |
| #71075 | 5 |