Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
340 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 86 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. C4×D120 | C2 | semidirect |
| 2. C3×#64985 | C2 | semidirect |
| 3. C2×#90943 | C2 | semidirect |
| 5. C5×C4⋊(C3⋊C16) | C2 | semidirect |
| 6. #11745898 | C2 | semidirect |
| 7. #11745892 | C2 | semidirect |
| 25. #64985 | D3 | semidirect |
| 56. C4⋊(C3⋊C16) | D5 | semidirect |
| 246. C3×C5 | #2210 | semidirect |
| 287. C5 | #71323 | semidirect |
| 301. C3 | #10600081 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D120 | 2 |
| C3×#64985 | 2 |
| C2×#90943 | 2 |
| C2×#90938 | 2 |
| C5×C4⋊(C3⋊C16) | 2 |
| #11745898 | 2 |
| #11745892 | 2 |
| #10600081 | 3 |
| #71323 | 5 |