Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
512 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 113 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. #10610910 | C2 | semidirect |
| 3. C2×#64729 | C2 | semidirect |
| 4. C2×#64728 | C2 | semidirect |
| 5. #10601445 | C2 | semidirect |
| 6. C5×#1382 | C2 | semidirect |
| 7. #10598223 | C2 | semidirect |
| 20. #65186 | C4 | semidirect |
| 44. C2×D40 | C2×C4 | semidirect |
| 61. C5×#108 | C2×C4 | semidirect |
| 79. #1382 | D5 | semidirect |
| 223. #108 | C4×D5 | semidirect |
| 348. C5 | #12996 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65186 | 2 |
| #10610910 | 2 |
| C2×#64729 | 2 |
| C2×#64728 | 2 |
| #10601445 | 2 |
| C5×#1382 | 2 |
| #10598223 | 2 |
| #12996 | 5 |