Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
320 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 102 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 |
|---|---|---|
| 2. C5×#4874 | C2 | semidirect |
| 3. C3×C5×#357 | C2 | semidirect |
| 4. C5×#4562 | C2 | semidirect |
| 5. C5×#4509 | C2 | semidirect |
| 6. C5×Dic3×C16 | C2 | semidirect |
| 7. C5×#4491 | C2 | semidirect |
| 20. #69183 | C5 | direct (N × H) |
| 26. C5×#357 | D3 | semidirect |
| 47. #4874 | C2×C5 | semidirect |
| 48. C3×#357 | C2×C5 | semidirect |
| 49. #4562 | C2×C5 | semidirect |
| 50. #4509 | C2×C5 | semidirect |
| 51. Dic3×C16 | C2×C5 | semidirect |
| 52. #4491 | C2×C5 | semidirect |
| 116. #357 | C5×D3 | semidirect |
| 230. C3×C5 | #2240 | semidirect |
| 271. C5 | #69183 | direct (N × H) |
| 285. C3 | C5×#2240 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5151 | 2 |
| C5×#4874 | 2 |
| C3×C5×#357 | 2 |
| C5×#4562 | 2 |
| C5×#4509 | 2 |
| C5×Dic3×C16 | 2 |
| C5×#4491 | 2 |
| C5×#2240 | 3 |
| #69183 | 5 |