Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
396 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 396 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 |
| 4. C5×#5080 | C2 | semidirect |
| 5. C5×#5078 | C2 | semidirect |
| 7. C5×#4454 | C2 | semidirect |
| 22. #71216 | C5 | direct (N × H) |
| 27. C5×#487 | D3 | semidirect |
| 48. C3×#487 | C2×C5 | semidirect |
| 51. #5080 | C2×C5 | semidirect |
| 52. #5078 | C2×C5 | semidirect |
| 54. #4454 | C2×C5 | semidirect |
| 84. C5×C3⋊C8 | SD16 | semidirect |
| 120. #487 | C5×D3 | semidirect |
| 199. C3⋊C8 | C5×SD16 | semidirect |
| 228. C3×C5 | #1714 | semidirect |
| 263. C5 | #71216 | direct (N × H) |
| 274. C3 | C5×#1714 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#487 | 2 |
| C5×#5088 | 2 |
| C5×#5085 | 2 |
| C5×#5080 | 2 |
| C5×#5078 | 2 |
| C5×#4693 | 2 |
| C5×#4454 | 2 |
| C5×#1714 | 3 |
| #71216 | 5 |