Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
554 conjugacy classes of subgroups; only the 199 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 199 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 |
|---|---|---|
| 3. C5×#1381 | C2 | semidirect |
| 4. #10598299 | C2 | semidirect |
| 5. #10598219 | C2 | semidirect |
| 45. #1381 | D5 | semidirect |
| 186. C5 | #12559 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3930 | 2 |
| C2×D5×#108 | 2 |
| C5×#1381 | 2 |
| #10598299 | 2 |
| #10598219 | 2 |
| #12559 | 5 |