Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
298 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 63 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. #10601664 | C2 | semidirect |
| 3. #10600080 | C2 | semidirect |
| 4. #10599876 | C2 | semidirect |
| 5. C5×#1330 | C2 | semidirect |
| 6. #10598054 | C2 | semidirect |
| 7. #10598007 | C2 | semidirect |
| 68. #1330 | D5 | semidirect |
| 269. C5 | #12350 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10611264 | 2 |
| #10601664 | 2 |
| #10600080 | 2 |
| #10599876 | 2 |
| C5×#1330 | 2 |
| #10598054 | 2 |
| #10598007 | 2 |
| #12350 | 5 |