Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
700 conjugacy classes of subgroups; only the 207 normal subgroups are shown.
This group has 700 conjugacy classes of subgroups — too many to draw. Only its 207 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. C3×C5×#578 | C2 | semidirect |
| 2. #11756512 | C2 | semidirect |
| 3. #11751296 | C2 | semidirect |
| 4. #11751295 | C2 | semidirect |
| 5. C2×#91113 | C2 | semidirect |
| 6. #11751280 | C2 | semidirect |
| 7. #11751241 | C2 | semidirect |
| 26. C5×#578 | D3 | semidirect |
| 54. C3×#578 | D5 | semidirect |
| 133. #578 | D15 | semidirect |
| 249. C3×C5 | #3417 | semidirect |
| 282. C5 | #84017 | semidirect |
| 290. C3 | #10615748 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#578 | 2 |
| #11756512 | 2 |
| #11751296 | 2 |
| #11751295 | 2 |
| C2×#91113 | 2 |
| #11751280 | 2 |
| #11751241 | 2 |
| #10615748 | 3 |
| #84017 | 5 |