Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
454 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 109 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. C2×#64737 | C2 | semidirect |
| 5. C2×#64716 | C2 | semidirect |
| 6. C5×#1389 | C2 | semidirect |
| 7. #10598218 | C2 | semidirect |
| 73. #1389 | D5 | semidirect |
| 306. C5 | #13078 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10613738 | 2 |
| #10610915 | 2 |
| C2×#64737 | 2 |
| #10601511 | 2 |
| C2×#64716 | 2 |
| C5×#1389 | 2 |
| #10598218 | 2 |
| #13078 | 5 |