Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
400 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 2. C5×#2159 | C2 | semidirect |
| 5. C2×#64709 | C2 | semidirect |
| 6. #10598308 | C2 | semidirect |
| 7. #10598215 | C2 | semidirect |
| 24. #64735 | C4 | semidirect |
| 46. C5×M32 | C2×C4 | semidirect |
| 59. C2×#672 | C2×C4 | semidirect |
| 65. #2159 | D5 | semidirect |
| 179. M32 | C4×D5 | semidirect |
| 291. C5 | #12925 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10610910 | 2 |
| C5×#2159 | 2 |
| C2×#64735 | 2 |
| #10601439 | 2 |
| C2×#64709 | 2 |
| #10598308 | 2 |
| #10598215 | 2 |
| #12925 | 5 |