Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
552 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 171 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 |
|---|---|---|
| 4. #10601517 | C2 | direct (N × H) |
| 5. C2×#64716 | C2 | semidirect |
| 6. C2×#64714 | C2 | semidirect |
| 21. #64716 | C22 | semidirect |
| 22. #64714 | C22 | semidirect |
| 233. C2×C5 | #2239 | semidirect |
| 266. C5 | C2×#2239 | semidirect |
| 285. C2 | #10601517 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#430 | 2 |
| C2×#65426 | 2 |
| C2×#64773 | 2 |
| #10601517 | 2 |
| C2×#64716 | 2 |
| C2×#64714 | 2 |
| C2×#2239 | 5 |