Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
400 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 160 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 |
|---|---|---|
| 3. C5×#4461 | C2 | semidirect |
| 4. C3×#64681 | C2 | semidirect |
| 5. #11745875 | C2 | semidirect |
| 16. #90933 | C4 | semidirect |
| 22. #64681 | D3 | semidirect |
| 34. C3×#672 | C2×C4 | semidirect |
| 35. C5×C3⋊C16 | C2×C4 | semidirect |
| 40. #4461 | D5 | semidirect |
| 86. #672 | C4×D3 | semidirect |
| 112. C3⋊C16 | C4×D5 | semidirect |
| 137. D15 | #346 | semidirect |
| 171. C3×C5 | C2×#346 | semidirect |
| 198. C5 | D3×#346 | semidirect |
| 207. C3 | D5×#346 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C8×D15 | 2 |
| C2×#90933 | 2 |
| C5×#4461 | 2 |
| C3×#64681 | 2 |
| #11745875 | 2 |
| D5×#346 | 3 |
| D3×#346 | 5 |