Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
372 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 372 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. C5×#5151 | C2 | semidirect |
| 2. C2×C5×#826 | C2 | semidirect |
| 3. C2×C5×D48 | C2 | semidirect |
| 4. C5×#4872 | C2 | semidirect |
| 5. C3×C5×#357 | C2 | semidirect |
| 6. C5×Dic3⋊C16 | C2 | semidirect |
| 7. C5×#4491 | C2 | semidirect |
| 22. #69202 | C5 | direct (N × H) |
| 29. C5×#357 | D3 | semidirect |
| 47. C5×D24 | D4 | semidirect |
| 50. #5151 | C2×C5 | semidirect |
| 51. C2×#826 | C2×C5 | semidirect |
| 52. C2×D48 | C2×C5 | semidirect |
| 53. #4872 | C2×C5 | semidirect |
| 54. C3×#357 | C2×C5 | semidirect |
| 55. Dic3⋊C16 | C2×C5 | semidirect |
| 56. #4491 | C2×C5 | semidirect |
| 129. #357 | C5×D3 | semidirect |
| 144. C5×Dic3 | D16 | semidirect |
| 162. D24 | C5×D4 | semidirect |
| 257. C3×C5 | #2206 | semidirect |
| 272. Dic3 | C5×D16 | semidirect |
| 304. C5 | #69202 | direct (N × H) |
| 320. C3 | C5×#2206 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5151 | 2 |
| C2×C5×#826 | 2 |
| C2×C5×D48 | 2 |
| C5×#4872 | 2 |
| C3×C5×#357 | 2 |
| C5×Dic3⋊C16 | 2 |
| C5×#4491 | 2 |
| C5×#2206 | 3 |
| #69202 | 5 |