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×Dic3×D20 | C2 | semidirect |
| 3. #11751036 | C2 | semidirect |
| 4. C42×C5×Dic3 | C2 | semidirect |
| 5. #11748785 | C2 | semidirect |
| 13. C3×#4020 | C4 | semidirect |
| 29. C2×C3×D20 | C2×C4 | semidirect |
| 31. C3×C42×C5 | C2×C4 | semidirect |
| 34. C4×C5×Dic3 | D4 | semidirect |
| 40. C42×Dic3 | D5 | semidirect |
| 48. #4020 | Dic3 | direct (N × H) |
| 80. C2×D20 | C2×Dic3 | semidirect |
| 84. C42×C5 | C2×Dic3 | semidirect |
| 98. C3×C4×C5 | C4×D4 | semidirect |
| 101. C5×Dic3 | #127 | semidirect |
| 111. C3×C42 | C4×D5 | semidirect |
| 115. C4×Dic3 | D20 | semidirect |
| 163. C4×C5 | D4×Dic3 | semidirect |
| 178. C42 | D5×Dic3 | semidirect |
| 179. C3×C5 | C4×#127 | semidirect |
| 186. C3×C4 | C4×D20 | semidirect |
| 189. Dic3 | #4020 | direct (N × H) |
| 211. C5 | Dic3×#127 | semidirect |
| 221. C4 | Dic3×D20 | semidirect |
| 222. C3 | C4×#4020 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#4020 | 2 |
| C2×Dic3×D20 | 2 |
| #11751036 | 2 |
| C42×C5×Dic3 | 2 |
| #11748785 | 2 |
| C4×#4020 | 3 |
| Dic3×#127 | 5 |