Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
344 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 344 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 |
|---|---|---|
| 3. C5×#4682 | C2 | semidirect |
| 4. C3×C5×#335 | C2 | semidirect |
| 5. C5×#4482 | C2 | semidirect |
| 18. #68578 | C5 | direct (N × H) |
| 22. C5×#335 | D3 | semidirect |
| 40. #4682 | C2×C5 | semidirect |
| 41. C3×#335 | C2×C5 | semidirect |
| 42. #4482 | C2×C5 | semidirect |
| 69. C3×C5×C8 | SD16 | semidirect |
| 99. #335 | C5×D3 | semidirect |
| 141. C5×C8 | #204 | semidirect |
| 171. C3×C8 | C5×SD16 | semidirect |
| 198. C3×C5 | #1673 | semidirect |
| 229. C8 | C5×#204 | semidirect |
| 234. C5 | #68578 | direct (N × H) |
| 246. C3 | C5×#1673 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4841 | 2 |
| C5×C8×D12 | 2 |
| C5×#4682 | 2 |
| C3×C5×#335 | 2 |
| C5×#4482 | 2 |
| C5×#1673 | 3 |
| #68578 | 5 |