Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
416 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 114 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×#486 | C2 | semidirect |
| 2. C5×#5088 | C2 | semidirect |
| 3. C5×#5079 | C2 | semidirect |
| 4. C5×#5076 | C2 | semidirect |
| 6. C5×#4694 | C2 | semidirect |
| 7. C5×#4455 | C2 | semidirect |
| 22. #71187 | C5 | direct (N × H) |
| 28. C5×#486 | D3 | semidirect |
| 48. C3×#486 | C2×C5 | semidirect |
| 49. #5088 | C2×C5 | semidirect |
| 50. #5079 | C2×C5 | semidirect |
| 51. #5076 | C2×C5 | semidirect |
| 53. #4694 | C2×C5 | semidirect |
| 54. #4455 | C2×C5 | semidirect |
| 123. #486 | C5×D3 | semidirect |
| 239. C3×C5 | #1717 | semidirect |
| 280. C5 | #71187 | direct (N × H) |
| 293. C3 | C5×#1717 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#486 | 2 |
| C5×#5088 | 2 |
| C5×#5079 | 2 |
| C5×#5076 | 2 |
| C5×#5073 | 2 |
| C5×#4694 | 2 |
| C5×#4455 | 2 |
| C5×#1717 | 3 |
| #71187 | 5 |