Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
320 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 320 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×#4481 | C2 | semidirect |
| 18. #68579 | C5 | direct (N × H) |
| 22. C5×#335 | D3 | semidirect |
| 39. #4682 | C2×C5 | semidirect |
| 40. C3×#335 | C2×C5 | semidirect |
| 41. #4481 | C2×C5 | semidirect |
| 96. #335 | C5×D3 | semidirect |
| 191. C3×C5 | #1675 | semidirect |
| 226. C5 | #68579 | direct (N × H) |
| 238. C3 | C5×#1675 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4842 | 2 |
| C5×C8×D12 | 2 |
| C5×#4682 | 2 |
| C3×C5×#335 | 2 |
| C5×#4481 | 2 |
| C5×#1675 | 3 |
| #68579 | 5 |