Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
380 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 122 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×#487 | C2 | semidirect |
| 2. C3×#65382 | C2 | semidirect |
| 5. C3×#65368 | C2 | semidirect |
| 7. C3×C8×#168 | C2 | semidirect |
| 8. #10602006 | C3 | direct (N × H) |
| 23. C5×#487 | C2×C3 | semidirect |
| 24. #65382 | C2×C3 | semidirect |
| 27. #65368 | C2×C3 | semidirect |
| 29. C8×#168 | C2×C3 | semidirect |
| 50. C3×#487 | D5 | semidirect |
| 117. #487 | C3×D5 | semidirect |
| 224. C3×C5 | #1708 | semidirect |
| 259. C5 | C3×#1708 | semidirect |
| 270. C3 | #10602006 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#487 | 2 |
| C3×#65382 | 2 |
| C3×#65377 | 2 |
| C3×#65374 | 2 |
| C3×#65368 | 2 |
| C3×#64983 | 2 |
| C3×C8×#168 | 2 |
| #10602006 | 3 |
| C3×#1708 | 5 |