Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
420 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 83 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. #11756512 | C2 | semidirect |
| 2. #11751243 | C2 | semidirect |
| 3. #11751009 | C2 | semidirect |
| 4. C2×#91084 | C2 | semidirect |
| 5. C3×C5×#350 | C2 | semidirect |
| 6. #11746338 | C2 | semidirect |
| 7. #11746331 | C2 | semidirect |
| 31. C5×#350 | D3 | semidirect |
| 65. C3×#350 | D5 | semidirect |
| 159. #350 | D15 | semidirect |
| 302. C3×C5 | #2193 | semidirect |
| 346. C5 | #69127 | semidirect |
| 357. C3 | #10599920 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11756512 | 2 |
| #11751243 | 2 |
| #11751009 | 2 |
| C2×#91084 | 2 |
| C3×C5×#350 | 2 |
| #11746338 | 2 |
| #11746331 | 2 |
| #10599920 | 3 |
| #69127 | 5 |