Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
466 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 109 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. #10613738 | C2 | semidirect |
| 3. #10602241 | C2 | semidirect |
| 4. #10601511 | C2 | semidirect |
| 5. #10601483 | C2 | semidirect |
| 6. C5×#1383 | C2 | semidirect |
| 7. #10598211 | C2 | semidirect |
| 55. C2×C5×C16 | D4 | semidirect |
| 66. C2×#672 | D4 | semidirect |
| 77. #1383 | D5 | semidirect |
| 217. C2×C16 | D20 | semidirect |
| 338. C5 | #13076 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10613738 | 2 |
| #10610851 | 2 |
| #10602241 | 2 |
| #10601511 | 2 |
| #10601483 | 2 |
| C5×#1383 | 2 |
| #10598211 | 2 |
| #13076 | 5 |