Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
450 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 79 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×#1800 | C2 | semidirect |
| 3. #10602395 | C2 | semidirect |
| 4. #10597987 | C2 | semidirect |
| 5. #10597984 | C2 | semidirect |
| 59. #1800 | D5 | semidirect |
| 354. C5 | #11832 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10614153 | 2 |
| C5×#1800 | 2 |
| #10602395 | 2 |
| #10597987 | 2 |
| #10597984 | 2 |
| #11832 | 5 |