Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
340 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 340 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×#5070 | C2 | semidirect |
| 3. #11747010 | C2 | semidirect |
| 4. #11746880 | C2 | semidirect |
| 5. #11746365 | C2 | semidirect |
| 6. #11745869 | C2 | semidirect |
| 7. #11745862 | C2 | semidirect |
| 51. #5070 | D5 | semidirect |
| 263. C3×C5 | #1697 | semidirect |
| 310. C5 | #71010 | semidirect |
| 325. C3 | #10601995 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5070 | 2 |
| C3×#65361 | 2 |
| #11747010 | 2 |
| #11746880 | 2 |
| #11746365 | 2 |
| #11745869 | 2 |
| #11745862 | 2 |
| #10601995 | 3 |
| #71010 | 5 |