Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
680 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 148 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. C5×#5819 | C2 | semidirect |
| 3. C3×#65526 | C2 | semidirect |
| 4. C2×#90960 | C2 | semidirect |
| 5. #11745991 | C2 | semidirect |
| 24. #65526 | D3 | semidirect |
| 46. C5×#208 | D4 | semidirect |
| 53. #5819 | D5 | semidirect |
| 173. #208 | C22⋊D5 | semidirect |
| 277. C3×C5 | #1914 | semidirect |
| 323. C5 | #70137 | semidirect |
| 337. C3 | #10602823 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11756589 | 2 |
| C5×#5819 | 2 |
| C3×#65526 | 2 |
| C2×#90960 | 2 |
| #11745991 | 2 |
| #10602823 | 3 |
| #70137 | 5 |