Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
424 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 132 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. #91781 | C2 | semidirect |
| 2. C5×#892 | C2 | semidirect |
| 3. C3×#4033 | C2 | semidirect |
| 4. #91468 | C2 | semidirect |
| 5. C4×#1204 | C2 | semidirect |
| 7. #91390 | C2 | semidirect |
| 8. #91380 | C2 | semidirect |
| 9. #91369 | C2 | semidirect |
| 10. #91367 | C2 | semidirect |
| 43. #4033 | D3 | semidirect |
| 70. #892 | D5 | semidirect |
| 225. C3×C5 | #556 | semidirect |
| 268. C5 | #5584 | semidirect |
| 285. C3 | #65867 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #91781 | 2 |
| C5×#892 | 2 |
| C3×#4033 | 2 |
| #91468 | 2 |
| C4×#1204 | 2 |
| C4×#1203 | 2 |
| #91390 | 2 |
| #91380 | 2 |
| #91369 | 2 |
| #91367 | 2 |
| #91350 | 2 |
| #65867 | 3 |
| #5584 | 5 |