Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
490 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 490 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. #10602233 | C2 | semidirect |
| 4. #10601457 | C2 | semidirect |
| 5. #10601445 | C2 | semidirect |
| 6. C5×#1384 | C2 | semidirect |
| 7. #10598216 | C2 | semidirect |
| 22. #65154 | C4 | semidirect |
| 52. C2×C5×C16 | D4 | semidirect |
| 61. C2×#672 | D4 | semidirect |
| 72. #1384 | D5 | semidirect |
| 201. C2×C16 | D20 | semidirect |
| 314. C5 | #13074 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10613738 | 2 |
| #10610914 | 2 |
| #10602233 | 2 |
| #10601457 | 2 |
| #10601445 | 2 |
| C5×#1384 | 2 |
| #10598216 | 2 |
| #13074 | 5 |