Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
268 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 82 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. C5×#4893 | C2 | semidirect |
| 3. C3×C5×#365 | C2 | semidirect |
| 4. C5×#4516 | C2 | semidirect |
| 5. C5×#4514 | C2 | semidirect |
| 6. C5×#4495 | C2 | semidirect |
| 7. C5×#4487 | C2 | semidirect |
| 20. #69313 | C5 | direct (N × H) |
| 24. C5×#365 | D3 | semidirect |
| 45. #4893 | C2×C5 | semidirect |
| 47. C3×#365 | C2×C5 | semidirect |
| 48. #4516 | C2×C5 | semidirect |
| 49. #4514 | C2×C5 | semidirect |
| 50. #4495 | C2×C5 | semidirect |
| 51. #4487 | C2×C5 | semidirect |
| 110. #365 | C5×D3 | semidirect |
| 213. C3×C5 | #2238 | semidirect |
| 247. C5 | #69313 | direct (N × H) |
| 258. C3 | C5×#2238 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4893 | 2 |
| C5×#4865 | 2 |
| C3×C5×#365 | 2 |
| C5×#4516 | 2 |
| C5×#4514 | 2 |
| C5×#4495 | 2 |
| C5×#4487 | 2 |
| C5×#2238 | 3 |
| #69313 | 5 |