Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
460 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 107 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. #10601456 | C2 | semidirect |
| 5. C2×#64707 | C2 | semidirect |
| 6. C5×#1386 | C2 | semidirect |
| 7. #10598302 | C2 | semidirect |
| 22. #64711 | C4 | semidirect |
| 45. C5×#107 | C2×C4 | semidirect |
| 55. C2×#672 | C2×C4 | semidirect |
| 63. #1386 | D5 | semidirect |
| 172. #107 | C4×D5 | semidirect |
| 267. C5 | #12956 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65158 | 2 |
| C2×#64736 | 2 |
| #10601456 | 2 |
| #10601445 | 2 |
| C2×#64707 | 2 |
| C5×#1386 | 2 |
| #10598302 | 2 |
| #12956 | 5 |