Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
368 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 368 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×#4848 | C2 | semidirect |
| 3. C5×#4679 | C2 | semidirect |
| 4. C3×C5×#334 | C2 | semidirect |
| 5. C5×#4485 | C2 | semidirect |
| 18. #68550 | C5 | direct (N × H) |
| 22. C5×#334 | D3 | semidirect |
| 39. #4848 | C2×C5 | semidirect |
| 41. #4679 | C2×C5 | semidirect |
| 42. C3×#334 | C2×C5 | semidirect |
| 43. #4485 | C2×C5 | semidirect |
| 70. C3×C5×C8 | SD16 | semidirect |
| 101. #334 | C5×D3 | semidirect |
| 143. C5×C8 | #204 | semidirect |
| 173. C3×C8 | C5×SD16 | semidirect |
| 200. C3×C5 | #1688 | semidirect |
| 230. C8 | C5×#204 | semidirect |
| 235. C5 | #68550 | direct (N × H) |
| 246. C3 | C5×#1688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4848 | 2 |
| C5×#4695 | 2 |
| C5×#4679 | 2 |
| C3×C5×#334 | 2 |
| C5×#4485 | 2 |
| C5×#1688 | 3 |
| #68550 | 5 |