Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
616 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 123 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. #10602393 | C2 | semidirect |
| 3. #10598131 | C2 | semidirect |
| 4. #10598126 | C2 | semidirect |
| 24. C5×#127 | C8 | semidirect |
| 60. C2×C5×D4 | C2×C8 | semidirect |
| 88. C42×C5 | C2×C8 | semidirect |
| 150. #127 | #168 | semidirect |
| 205. C2×D4 | C2×#168 | semidirect |
| 235. C42 | C2×#168 | semidirect |
| 283. C5 | #11475 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C5×#127 | 2 |
| #10602393 | 2 |
| #10598131 | 2 |
| #10598126 | 2 |
| #11475 | 5 |