Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
398 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 95 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×#2151 | C2 | semidirect |
| 3. C2×#64737 | C2 | semidirect |
| 5. #10600697 | C2 | semidirect |
| 7. #10598299 | C2 | semidirect |
| 63. #2151 | D5 | semidirect |
| 287. C5 | #13440 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3932 | 2 |
| C5×#2151 | 2 |
| C2×#64737 | 2 |
| C2×#64736 | 2 |
| #10600697 | 2 |
| #10600696 | 2 |
| #10598299 | 2 |
| #13440 | 5 |