Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
284 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 82 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. #11748019 | C2 | semidirect |
| 4. C5×#4505 | C2 | semidirect |
| 5. C3×#64721 | C2 | semidirect |
| 6. #11745942 | C2 | semidirect |
| 25. #64721 | D3 | semidirect |
| 34. D120 | Q8 | semidirect |
| 49. #4505 | D5 | semidirect |
| 204. C3×C5 | #2226 | semidirect |
| 238. C5 | #69290 | semidirect |
| 250. C3 | #10600146 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11748019 | 2 |
| #11747766 | 2 |
| #11746330 | 2 |
| C5×#4505 | 2 |
| C3×#64721 | 2 |
| #11745942 | 2 |
| #11745896 | 2 |
| #10600146 | 3 |
| #69290 | 5 |