Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
658 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 658 conjugacy classes of subgroups — too many to draw. Only its 101 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. #10615048 | C2 | semidirect |
| 3. #10605531 | C2 | semidirect |
| 4. C5×#1502 | C2 | semidirect |
| 5. #10601572 | C2 | semidirect |
| 6. #10601550 | C2 | semidirect |
| 7. #10598111 | C2 | semidirect |
| 83. #1502 | D5 | semidirect |
| 108. C2×D20 | SD16 | semidirect |
| 400. C5 | #10240 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10615048 | 2 |
| #10615028 | 2 |
| #10605531 | 2 |
| C5×#1502 | 2 |
| #10601572 | 2 |
| #10601550 | 2 |
| #10598111 | 2 |
| #10240 | 5 |