Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
424 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 424 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. C5×#4694 | C2 | semidirect |
| 2. C3×#64983 | C2 | semidirect |
| 3. #11747103 | C2 | semidirect |
| 5. #11746901 | C2 | semidirect |
| 6. #11746895 | C2 | semidirect |
| 7. C8×C3⋊#168 | C2 | semidirect |
| 28. #64983 | D3 | semidirect |
| 53. #4694 | D5 | semidirect |
| 239. C3×C5 | #1709 | semidirect |
| 280. C5 | #71182 | semidirect |
| 293. C3 | #10601975 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4694 | 2 |
| C3×#64983 | 2 |
| #11747103 | 2 |
| #11747039 | 2 |
| #11746901 | 2 |
| #11746895 | 2 |
| C8×C3⋊#168 | 2 |
| #10601975 | 3 |
| #71182 | 5 |