Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
380 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 130 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×#498 | C2 | semidirect |
| 3. C3×#65370 | C2 | semidirect |
| 5. C3×C8×#168 | C2 | semidirect |
| 6. #10602127 | C3 | direct (N × H) |
| 17. C5×#498 | C2×C3 | semidirect |
| 19. #65370 | C2×C3 | semidirect |
| 21. C8×#168 | C2×C3 | semidirect |
| 33. C3×#498 | D5 | semidirect |
| 79. #498 | C3×D5 | semidirect |
| 154. C3×C5 | #1708 | semidirect |
| 179. C5 | C3×#1708 | semidirect |
| 187. C3 | #10602127 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#498 | 2 |
| C3×#65377 | 2 |
| C3×#65370 | 2 |
| C3×#64982 | 2 |
| C3×C8×#168 | 2 |
| #10602127 | 3 |
| C3×#1708 | 5 |