Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
452 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 100 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. C22×C3×Dic20 | C2 | semidirect |
| 3. C2×#90943 | C2 | semidirect |
| 4. C5×#4549 | C2 | semidirect |
| 5. #11745898 | C2 | semidirect |
| 19. C22×Dic20 | D3 | semidirect |
| 40. C3×Dic20 | D4 | semidirect |
| 46. #4549 | D5 | semidirect |
| 102. Dic20 | #67 | semidirect |
| 112. C22×C3×C5 | SD32 | semidirect |
| 192. C22×C5 | #828 | semidirect |
| 220. C3×C5 | #2185 | semidirect |
| 223. C22×C3 | #3932 | semidirect |
| 260. C5 | #72063 | semidirect |
| 266. C22 | #90943 | semidirect |
| 273. C3 | #10599905 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×Dic20 | 2 |
| #11751216 | 2 |
| C2×#90943 | 2 |
| C5×#4549 | 2 |
| #11745898 | 2 |
| #10599905 | 3 |
| #72063 | 5 |