Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
460 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 109 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×#1946 | C2 | semidirect |
| 4. C2×#64714 | C2 | semidirect |
| 6. #10598217 | C2 | semidirect |
| 7. #10598154 | C2 | semidirect |
| 23. #64711 | C4 | semidirect |
| 44. C5×#107 | C2×C4 | semidirect |
| 57. C2×#672 | C2×C4 | semidirect |
| 62. #1946 | 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×#65000 | 2 |
| C5×#1946 | 2 |
| C2×#64715 | 2 |
| C2×#64714 | 2 |
| #10601445 | 2 |
| #10598217 | 2 |
| #10598154 | 2 |
| #12956 | 5 |