Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
456 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 152 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×Dic30 | C2 | semidirect |
| 2. C5×#869 | C2 | semidirect |
| 5. #91421 | C2 | semidirect |
| 6. D5×C4⋊Dic3 | C2 | semidirect |
| 7. #91384 | C2 | semidirect |
| 8. #91360 | C2 | semidirect |
| 45. C3×D20 | Q8 | semidirect |
| 54. #869 | D5 | semidirect |
| 109. D20 | Dic6 | semidirect |
| 165. C3×C5 | #554 | semidirect |
| 198. C5 | #5543 | semidirect |
| 210. C3 | #66064 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Dic30 | 2 |
| C5×#869 | 2 |
| C3×C4×D20 | 2 |
| #91434 | 2 |
| #91421 | 2 |
| D5×C4⋊Dic3 | 2 |
| #91384 | 2 |
| #91360 | 2 |
| #66064 | 3 |
| #5543 | 5 |