Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
494 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 147 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. C2×C5×#347 | C2 | semidirect |
| 4. C2×#64686 | C2 | semidirect |
| 5. #10598301 | C2 | semidirect |
| 18. #64734 | C4 | semidirect |
| 40. C5×M32 | C2×C4 | semidirect |
| 48. #3944 | C2×C4 | semidirect |
| 54. C2×#347 | D5 | semidirect |
| 155. M32 | C4×D5 | semidirect |
| 248. C5 | #12607 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64996 | 2 |
| C2×C5×#347 | 2 |
| C2×#64734 | 2 |
| C2×#64686 | 2 |
| #10598301 | 2 |
| #12607 | 5 |