Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
784 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 156 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. D15×#125 | C2 | semidirect |
| 3. C5×#5069 | C2 | semidirect |
| 4. C3×#65356 | C2 | semidirect |
| 5. #11747507 | C2 | semidirect |
| 6. #11747382 | C2 | semidirect |
| 7. #11746931 | C2 | semidirect |
| 8. #11746892 | C2 | semidirect |
| 9. #11746844 | C2 | semidirect |
| 37. #65356 | D3 | semidirect |
| 70. #5069 | D5 | semidirect |
| 305. C3×C5 | #3142 | semidirect |
| 345. C5 | #81716 | semidirect |
| 358. C3 | #10613471 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D15×#125 | 2 |
| #11752556 | 2 |
| C5×#5069 | 2 |
| C3×#65356 | 2 |
| #11747507 | 2 |
| #11747382 | 2 |
| #11746931 | 2 |
| #11746892 | 2 |
| #11746844 | 2 |
| #10613471 | 3 |
| #81716 | 5 |