Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
372 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 97 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×D240 | C2 | semidirect |
| 2. #11750796 | C2 | semidirect |
| 3. C4×D120 | C2 | semidirect |
| 4. C3×C5×C4⋊C16 | C2 | semidirect |
| 5. #11746330 | C2 | semidirect |
| 21. C5×C4⋊C16 | D3 | semidirect |
| 37. D120 | D4 | semidirect |
| 42. C3×C4⋊C16 | D5 | semidirect |
| 100. C4⋊C16 | D15 | semidirect |
| 110. C3×C4×C5 | D16 | semidirect |
| 185. C4×C5 | D48 | semidirect |
| 205. C3×C5 | #2206 | semidirect |
| 214. C3×C4 | D80 | semidirect |
| 244. C5 | #69286 | semidirect |
| 254. C4 | D240 | semidirect |
| 257. C3 | #10600079 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D240 | 2 |
| #11750796 | 2 |
| C4×D120 | 2 |
| C3×C5×C4⋊C16 | 2 |
| #11746330 | 2 |
| #10600079 | 3 |
| #69286 | 5 |