Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
272 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 94 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×#4878 | C2 | semidirect |
| 3. C3×C5×#366 | C2 | semidirect |
| 5. C5×Dic3⋊C16 | C2 | semidirect |
| 7. C5×#4490 | C2 | semidirect |
| 20. #69334 | C5 | direct (N × H) |
| 24. C5×#366 | D3 | semidirect |
| 43. #4878 | C2×C5 | semidirect |
| 45. C3×#366 | C2×C5 | semidirect |
| 47. Dic3⋊C16 | C2×C5 | semidirect |
| 49. #4490 | C2×C5 | semidirect |
| 104. #366 | C5×D3 | semidirect |
| 201. C3×C5 | #2228 | semidirect |
| 234. C5 | #69334 | direct (N × H) |
| 246. C3 | C5×#2228 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4878 | 2 |
| C5×#4872 | 2 |
| C3×C5×#366 | 2 |
| C5×#4509 | 2 |
| C5×Dic3⋊C16 | 2 |
| C5×#4491 | 2 |
| C5×#4490 | 2 |
| C5×#2228 | 3 |
| #69334 | 5 |