Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
336 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 88 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. #11751125 | C2 | semidirect |
| 2. C5×#5020 | C2 | semidirect |
| 5. #11745868 | C2 | semidirect |
| 6. #11745857 | C2 | semidirect |
| 54. #5020 | D5 | semidirect |
| 92. C3⋊#168 | SD16 | semidirect |
| 259. C3×C5 | #1686 | semidirect |
| 301. C5 | #71024 | semidirect |
| 314. C3 | #10601913 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11751125 | 2 |
| C5×#5020 | 2 |
| C3×#65316 | 2 |
| #11747079 | 2 |
| #11745868 | 2 |
| #11745857 | 2 |
| #11745852 | 2 |
| #10601913 | 3 |
| #71024 | 5 |