Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
556 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 556 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 |
|---|---|---|
| 1. #11752536 | C2 | semidirect |
| 2. C5×#4695 | C2 | semidirect |
| 3. #11747060 | C2 | semidirect |
| 4. #11747045 | C2 | semidirect |
| 5. #11746280 | C2 | semidirect |
| 6. C3×#64676 | C2 | semidirect |
| 7. #11745853 | C2 | semidirect |
| 33. #64676 | D3 | semidirect |
| 64. #4695 | D5 | semidirect |
| 110. C3×Dic10 | D8 | semidirect |
| 240. Dic10 | D24 | semidirect |
| 343. C3×C5 | #1621 | semidirect |
| 405. C5 | #68259 | semidirect |
| 424. C3 | #10602078 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11752536 | 2 |
| C5×#4695 | 2 |
| #11747060 | 2 |
| #11747045 | 2 |
| #11746280 | 2 |
| C3×#64676 | 2 |
| #11745853 | 2 |
| #10602078 | 3 |
| #68259 | 5 |