Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
512 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 90 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. #11750943 | C2 | semidirect |
| 3. #11747066 | C2 | semidirect |
| 4. #11746916 | C2 | semidirect |
| 5. C5×#4485 | C2 | semidirect |
| 6. C3×#64704 | C2 | semidirect |
| 7. #11745839 | C2 | semidirect |
| 32. #64704 | D3 | semidirect |
| 64. #4485 | D5 | semidirect |
| 104. C3×Dic10 | SD16 | semidirect |
| 224. Dic10 | #204 | semidirect |
| 318. C3×C5 | #1631 | semidirect |
| 372. C5 | #68261 | semidirect |
| 389. C3 | #10599198 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11752536 | 2 |
| #11750943 | 2 |
| #11747066 | 2 |
| #11746916 | 2 |
| C5×#4485 | 2 |
| C3×#64704 | 2 |
| #11745839 | 2 |
| #10599198 | 3 |
| #68261 | 5 |