Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
1848 conjugacy classes of subgroups; only the 436 normal subgroups are shown.
This group has 1848 conjugacy classes of subgroups — too many to draw. Only its 436 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 |
|---|---|---|
| 2. C2×Dic5×D12 | C2 | semidirect |
| 3. #11751036 | C2 | semidirect |
| 4. C3×C42×Dic5 | C2 | semidirect |
| 5. #11748764 | C2 | semidirect |
| 11. C5×#874 | C4 | semidirect |
| 21. C42×Dic5 | D3 | semidirect |
| 27. C2×C5×D12 | C2×C4 | semidirect |
| 31. C3×C42×C5 | C2×C4 | semidirect |
| 34. C3×C4×Dic5 | D4 | semidirect |
| 71. #874 | Dic5 | direct (N × H) |
| 82. C42×C5 | C4×D3 | semidirect |
| 86. C4×Dic5 | D12 | semidirect |
| 98. C3×C4×C5 | C4×D4 | semidirect |
| 101. C3×Dic5 | #127 | semidirect |
| 109. C2×D12 | C2×Dic5 | semidirect |
| 113. C3×C42 | C2×Dic5 | semidirect |
| 161. C4×C5 | C4×D12 | semidirect |
| 164. Dic5 | #874 | direct (N × H) |
| 178. C42 | D3×Dic5 | semidirect |
| 179. C3×C5 | C4×#127 | semidirect |
| 188. C3×C4 | D4×Dic5 | semidirect |
| 211. C5 | C4×#874 | semidirect |
| 221. C4 | Dic5×D12 | semidirect |
| 222. C3 | Dic5×#127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#874 | 2 |
| C2×Dic5×D12 | 2 |
| #11751036 | 2 |
| C3×C42×Dic5 | 2 |
| #11748764 | 2 |
| Dic5×#127 | 3 |
| C4×#874 | 5 |