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. #11752538 | C2 | semidirect |
| 2. #11751174 | C2 | semidirect |
| 3. C5×#5072 | C2 | semidirect |
| 4. C3×#65364 | C2 | semidirect |
| 5. #11745854 | C2 | semidirect |
| 6. #11745840 | C2 | semidirect |
| 7. #11745836 | C2 | semidirect |
| 29. #65364 | D3 | semidirect |
| 64. #5072 | D5 | semidirect |
| 110. C3×Dic10 | D8 | semidirect |
| 240. Dic10 | #213 | semidirect |
| 343. C3×C5 | #1621 | semidirect |
| 405. C5 | #71032 | semidirect |
| 424. C3 | #10601806 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11752538 | 2 |
| #11751174 | 2 |
| C5×#5072 | 2 |
| C3×#65364 | 2 |
| #11745854 | 2 |
| #11745840 | 2 |
| #11745836 | 2 |
| #10601806 | 3 |
| #71032 | 5 |