Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
578 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 3. #10605442 | C2 | semidirect |
| 4. #10601559 | C2 | semidirect |
| 5. #10601299 | C2 | semidirect |
| 7. C5×#1303 | C2 | semidirect |
| 86. #1303 | D5 | semidirect |
| 395. C5 | #10243 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10610999 | 2 |
| #10610798 | 2 |
| #10605442 | 2 |
| #10601559 | 2 |
| #10601299 | 2 |
| #10600262 | 2 |
| C5×#1303 | 2 |
| #10243 | 5 |