Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
224 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 68 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. C2×D240 | C2 | semidirect |
| 2. C5×#4904 | C2 | semidirect |
| 3. C3×#64719 | C2 | semidirect |
| 4. #11745826 | C2 | semidirect |
| 5. #11745820 | C2 | semidirect |
| 12. C5×Dic24 | C22 | semidirect |
| 14. C5×D48 | C22 | semidirect |
| 15. C3×#3926 | C22 | semidirect |
| 21. #64719 | D3 | semidirect |
| 32. #4904 | D5 | semidirect |
| 45. #3926 | C2×D3 | semidirect |
| 60. Dic24 | C2×D5 | semidirect |
| 64. D48 | C2×D5 | semidirect |
| 148. C3×C5 | #2263 | semidirect |
| 174. C5 | #69373 | semidirect |
| 182. C3 | #10602302 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D240 | 2 |
| C5×#4904 | 2 |
| C3×#64719 | 2 |
| #11745826 | 2 |
| #11745820 | 2 |
| #10602302 | 3 |
| #69373 | 5 |