Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
420 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 72 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. #11754008 | C2 | semidirect |
| 2. C2×C5×#800 | C2 | semidirect |
| 3. #11748090 | C2 | semidirect |
| 4. #11747540 | C2 | semidirect |
| 5. #11746329 | C2 | semidirect |
| 6. C3×#64730 | C2 | semidirect |
| 7. #11745923 | C2 | semidirect |
| 32. #64730 | D3 | semidirect |
| 63. C2×#800 | D5 | semidirect |
| 302. C3×C5 | #2193 | semidirect |
| 346. C5 | #69243 | semidirect |
| 357. C3 | #10602282 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11754008 | 2 |
| C2×C5×#800 | 2 |
| #11748090 | 2 |
| #11747540 | 2 |
| #11746329 | 2 |
| C3×#64730 | 2 |
| #11745923 | 2 |
| #10602282 | 3 |
| #69243 | 5 |