Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
364 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 2. #11750942 | C2 | semidirect |
| 3. #11750795 | C2 | semidirect |
| 4. C8×D60 | C2 | semidirect |
| 5. C3×C5×#335 | C2 | semidirect |
| 6. #11746306 | C2 | semidirect |
| 7. #11746303 | C2 | semidirect |
| 29. C5×#335 | D3 | semidirect |
| 55. C3×#335 | D5 | semidirect |
| 135. #335 | D15 | semidirect |
| 270. C3×C5 | #1681 | semidirect |
| 318. C5 | #68580 | semidirect |
| 333. C3 | #10599373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11750944 | 2 |
| #11750942 | 2 |
| #11750795 | 2 |
| C8×D60 | 2 |
| C3×C5×#335 | 2 |
| #11746306 | 2 |
| #11746303 | 2 |
| #10599373 | 3 |
| #68580 | 5 |