Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
358 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 93 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. #10601587 | C2 | semidirect |
| 4. C4×#3954 | C2 | semidirect |
| 6. C5×#1291 | C2 | semidirect |
| 7. #10598244 | C2 | semidirect |
| 80. #1291 | D5 | semidirect |
| 310. C5 | #8690 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10611056 | 2 |
| #10601598 | 2 |
| #10601587 | 2 |
| C4×#3954 | 2 |
| #10600654 | 2 |
| C5×#1291 | 2 |
| #10598244 | 2 |
| #8690 | 5 |