Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
480 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 92 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. C3×#65919 | C2 | semidirect |
| 2. C5×#5027 | C2 | semidirect |
| 3. #11747060 | C2 | semidirect |
| 5. #11746356 | C2 | semidirect |
| 6. #11745852 | C2 | semidirect |
| 7. #11745840 | C2 | semidirect |
| 27. #65919 | D3 | semidirect |
| 62. #5027 | D5 | semidirect |
| 318. C3×C5 | #1620 | semidirect |
| 372. C5 | #71943 | semidirect |
| 389. C3 | #10601824 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65919 | 2 |
| C5×#5027 | 2 |
| #11747060 | 2 |
| #11747039 | 2 |
| #11746356 | 2 |
| #11745852 | 2 |
| #11745840 | 2 |
| #10601824 | 3 |
| #71943 | 5 |