Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
396 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 110 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×#4843 | C2 | semidirect |
| 2. C5×#4695 | C2 | semidirect |
| 3. C5×#4688 | C2 | semidirect |
| 4. C3×C5×#334 | C2 | semidirect |
| 5. C5×#4485 | C2 | semidirect |
| 18. #68540 | C5 | direct (N × H) |
| 22. C5×#334 | D3 | semidirect |
| 40. #4843 | C2×C5 | semidirect |
| 41. #4695 | C2×C5 | semidirect |
| 42. #4688 | C2×C5 | semidirect |
| 43. C3×#334 | C2×C5 | semidirect |
| 44. #4485 | C2×C5 | semidirect |
| 73. C3×C5×C8 | D8 | semidirect |
| 105. #334 | C5×D3 | semidirect |
| 152. C5×C8 | D24 | semidirect |
| 185. C3×C8 | C5×D8 | semidirect |
| 215. C3×C5 | #1687 | semidirect |
| 250. C8 | C5×D24 | semidirect |
| 256. C5 | #68540 | direct (N × H) |
| 269. C3 | C5×#1687 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4843 | 2 |
| C5×#4695 | 2 |
| C5×#4688 | 2 |
| C3×C5×#334 | 2 |
| C5×#4485 | 2 |
| C5×#1687 | 3 |
| #68540 | 5 |