Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
184 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 59 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. C5×#2258 | C2 | semidirect |
| 2. #10602249 | C2 | semidirect |
| 4. C2×#64669 | C2 | semidirect |
| 5. #10598096 | C2 | semidirect |
| 6. #10598095 | C2 | semidirect |
| 7. #10598084 | C2 | semidirect |
| 45. #2258 | D5 | semidirect |
| 170. C5 | #13702 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2258 | 2 |
| #10602249 | 2 |
| #10602247 | 2 |
| C2×#64669 | 2 |
| #10598096 | 2 |
| #10598095 | 2 |
| #10598084 | 2 |
| #13702 | 5 |