Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
308 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 98 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×#443 | C2 | semidirect |
| 2. C5×#5195 | C2 | semidirect |
| 4. C5×#4696 | C2 | semidirect |
| 5. C5×#4496 | C2 | semidirect |
| 6. C5×#4495 | C2 | semidirect |
| 7. C5×#4463 | C2 | semidirect |
| 24. #70925 | C5 | direct (N × H) |
| 28. C5×#443 | D3 | semidirect |
| 53. C3×#443 | C2×C5 | semidirect |
| 54. #5195 | C2×C5 | semidirect |
| 56. #4696 | C2×C5 | semidirect |
| 57. #4496 | C2×C5 | semidirect |
| 58. #4495 | C2×C5 | semidirect |
| 59. #4463 | C2×C5 | semidirect |
| 132. #443 | C5×D3 | semidirect |
| 249. C3×C5 | #2212 | semidirect |
| 284. C5 | #70925 | direct (N × H) |
| 294. C3 | C5×#2212 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#443 | 2 |
| C5×#5195 | 2 |
| C5×#5193 | 2 |
| C5×#4696 | 2 |
| C5×#4496 | 2 |
| C5×#4495 | 2 |
| C5×#4463 | 2 |
| C5×#2212 | 3 |
| #70925 | 5 |