Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
402 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 91 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×#2117 | C2 | semidirect |
| 3. #10602807 | C2 | semidirect |
| 4. C2×#64736 | C2 | semidirect |
| 5. C2×#64736 | C2 | semidirect |
| 6. #10602222 | C2 | semidirect |
| 7. #10598312 | C2 | semidirect |
| 68. #2117 | D5 | semidirect |
| 305. C5 | #13389 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65431 | 2 |
| C5×#2117 | 2 |
| #10602807 | 2 |
| C2×#64736 | 2 |
| #10602222 | 2 |
| #10598312 | 2 |
| #13389 | 5 |