Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
532 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 86 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. C2×D5×D24 | C2 | semidirect |
| 2. C2×D240 | C2 | semidirect |
| 3. #11747899 | C2 | semidirect |
| 4. C2×#90939 | C2 | semidirect |
| 5. C5×#4509 | C2 | semidirect |
| 6. C3×#64727 | C2 | semidirect |
| 7. #11745896 | C2 | semidirect |
| 11. C2×D120 | C22 | semidirect |
| 18. C2×C3×C5×C16 | C22 | semidirect |
| 20. C5×#818 | C22 | semidirect |
| 21. C2×C3×#672 | C22 | semidirect |
| 30. #64727 | D3 | semidirect |
| 45. D120 | D4 | semidirect |
| 48. C5×D24 | D4 | semidirect |
| 62. #4509 | D5 | semidirect |
| 72. C2×C5×C16 | C2×D3 | semidirect |
| 75. C2×#672 | C2×D3 | semidirect |
| 112. C2×C3×C16 | C2×D5 | semidirect |
| 114. #818 | C2×D5 | semidirect |
| 160. C2×C3×D5 | D16 | semidirect |
| 187. D24 | D20 | semidirect |
| 225. C2×C16 | D3×D5 | semidirect |
| 271. C2×D5 | D48 | semidirect |
| 300. C3×C5 | #2184 | semidirect |
| 356. C5 | #69108 | semidirect |
| 375. C3 | #10599984 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×D24 | 2 |
| C2×D240 | 2 |
| #11747899 | 2 |
| C2×#90939 | 2 |
| C5×#4509 | 2 |
| C3×#64727 | 2 |
| #11745896 | 2 |
| #10599984 | 3 |
| #69108 | 5 |