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. C5×#5007 | C2 | semidirect |
| 3. #11747105 | C2 | semidirect |
| 4. #11746912 | C2 | semidirect |
| 5. C3×D4⋊#168 | C2 | semidirect |
| 6. #11745854 | C2 | semidirect |
| 7. #11745845 | C2 | semidirect |
| 31. D4⋊#168 | D3 | semidirect |
| 60. #5007 | D5 | semidirect |
| 321. C3×C5 | #1641 | semidirect |
| 376. C5 | #68190 | semidirect |
| 393. C3 | #10601905 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11756312 | 2 |
| C5×#5007 | 2 |
| #11747105 | 2 |
| #11746912 | 2 |
| C3×D4⋊#168 | 2 |
| #11745854 | 2 |
| #11745845 | 2 |
| #10601905 | 3 |
| #68190 | 5 |