Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
344 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 344 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. #11750800 | C2 | semidirect |
| 4. C5×#4458 | C2 | semidirect |
| 5. #11745860 | C2 | semidirect |
| 43. #4458 | D5 | semidirect |
| 65. C3×D20 | Q16 | semidirect |
| 136. D20 | Dic12 | semidirect |
| 202. C3×C5 | #1669 | semidirect |
| 238. C5 | #70850 | semidirect |
| 250. C3 | #10599370 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11750800 | 2 |
| C3×C8×D20 | 2 |
| #11746889 | 2 |
| C5×#4458 | 2 |
| #11745860 | 2 |
| #10599370 | 3 |
| #70850 | 5 |