Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
602 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 602 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 2. C5×#1566 | C2 | semidirect |
| 3. #10601314 | C2 | semidirect |
| 4. #10601295 | C2 | semidirect |
| 5. #10600518 | C2 | semidirect |
| 48. #1566 | D5 | semidirect |
| 116. C5×C8 | #100 | semidirect |
| 216. C8 | #3955 | semidirect |
| 217. C5 | #9811 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64984 | 2 |
| C5×#1566 | 2 |
| #10601314 | 2 |
| #10601295 | 2 |
| #10600518 | 2 |
| #9811 | 5 |