Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
340 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 89 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×#91084 | C2 | semidirect |
| 3. #11750797 | C2 | semidirect |
| 4. C4×D120 | C2 | semidirect |
| 5. C3×C5×C4⋊C16 | C2 | semidirect |
| 6. #11746330 | C2 | semidirect |
| 7. #11746324 | C2 | semidirect |
| 27. C5×C4⋊C16 | D3 | semidirect |
| 54. C3×C4⋊C16 | D5 | semidirect |
| 125. C4⋊C16 | D15 | semidirect |
| 246. C3×C5 | #2210 | semidirect |
| 287. C5 | #69288 | semidirect |
| 301. C3 | #10600081 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#91084 | 2 |
| C2×D240 | 2 |
| #11750797 | 2 |
| C4×D120 | 2 |
| C3×C5×C4⋊C16 | 2 |
| #11746330 | 2 |
| #11746324 | 2 |
| #10600081 | 3 |
| #69288 | 5 |