Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
456 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 114 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×#5722 | C2 | semidirect |
| 4. C3×C5×#333 | C2 | semidirect |
| 5. C5×#4484 | C2 | semidirect |
| 18. #68504 | C5 | direct (N × H) |
| 22. C5×#333 | D3 | semidirect |
| 40. #5722 | C2×C5 | semidirect |
| 43. C3×#333 | C2×C5 | semidirect |
| 44. #4484 | C2×C5 | semidirect |
| 69. C5×Dic6 | SD16 | semidirect |
| 102. #333 | C5×D3 | semidirect |
| 170. Dic6 | C5×SD16 | semidirect |
| 198. C3×C5 | #1623 | semidirect |
| 229. C5 | #68504 | direct (N × H) |
| 239. C3 | C5×#1623 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5722 | 2 |
| C5×#5085 | 2 |
| C5×#4848 | 2 |
| C3×C5×#333 | 2 |
| C5×#4484 | 2 |
| C5×#1623 | 3 |
| #68504 | 5 |