Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
602 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 602 conjugacy classes of subgroups — too many to draw. Only its 105 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. #10611019 | C2 | semidirect |
| 3. #10601555 | C2 | semidirect |
| 4. #10601320 | C2 | semidirect |
| 5. #10601289 | C2 | semidirect |
| 6. C5×#1286 | C2 | semidirect |
| 7. #10598122 | C2 | semidirect |
| 58. C4×C5×C8 | D4 | semidirect |
| 68. C4×#168 | D4 | semidirect |
| 75. #1286 | D5 | semidirect |
| 238. C4×C8 | D20 | semidirect |
| 383. C5 | #9489 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10611019 | 2 |
| #10605970 | 2 |
| #10601555 | 2 |
| #10601320 | 2 |
| #10601289 | 2 |
| C5×#1286 | 2 |
| #10598122 | 2 |
| #9489 | 5 |