Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
372 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 84 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×#4872 | C2 | semidirect |
| 2. #11748005 | C2 | semidirect |
| 3. C2×#90939 | C2 | semidirect |
| 4. C2×#90937 | C2 | semidirect |
| 5. #11746312 | C2 | semidirect |
| 6. C3×#64711 | C2 | semidirect |
| 7. Dic3⋊#672 | C2 | semidirect |
| 28. #64711 | D3 | semidirect |
| 44. C5×D24 | D4 | semidirect |
| 53. #4872 | D5 | semidirect |
| 144. C5×Dic3 | D16 | semidirect |
| 162. D24 | D20 | semidirect |
| 257. C3×C5 | #2206 | semidirect |
| 272. Dic3 | #3958 | semidirect |
| 304. C5 | #69202 | semidirect |
| 320. C3 | #10601682 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4872 | 2 |
| #11748005 | 2 |
| C2×#90939 | 2 |
| C2×#90937 | 2 |
| #11746312 | 2 |
| C3×#64711 | 2 |
| Dic3⋊#672 | 2 |
| #10601682 | 3 |
| #69202 | 5 |