Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
300 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 81 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. C5×#1334 | C2 | semidirect |
| 5. #10598255 | C2 | semidirect |
| 6. #10598008 | C2 | semidirect |
| 7. #10597957 | C2 | semidirect |
| 67. #1334 | D5 | semidirect |
| 271. C5 | #11653 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10611456 | 2 |
| #10599866 | 2 |
| #10599320 | 2 |
| C5×#1334 | 2 |
| #10598255 | 2 |
| #10598008 | 2 |
| #10597957 | 2 |
| #11653 | 5 |