Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
500 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 500 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. #11750947 | C2 | semidirect |
| 3. #11747095 | C2 | semidirect |
| 4. #11746906 | C2 | semidirect |
| 5. C5×#4485 | C2 | semidirect |
| 6. C3×#64704 | C2 | semidirect |
| 7. #11745839 | C2 | semidirect |
| 32. #64704 | D3 | semidirect |
| 64. #4485 | D5 | semidirect |
| 321. C3×C5 | #1641 | semidirect |
| 376. C5 | #68263 | semidirect |
| 393. C3 | #10599200 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11752536 | 2 |
| #11750947 | 2 |
| #11747095 | 2 |
| #11746906 | 2 |
| C5×#4485 | 2 |
| C3×#64704 | 2 |
| #11745839 | 2 |
| #10599200 | 3 |
| #68263 | 5 |