Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
726 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 128 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. #10598819 | C2 | direct (N × H) |
| 22. C23×C4×C5 | C8 | semidirect |
| 66. C22×C4×C5 | C2×C8 | semidirect |
| 143. C23×C4 | #170 | semidirect |
| 218. C22×C4 | C2×#170 | semidirect |
| 232. C2×C5 | #1317 | semidirect |
| 277. C5 | C2×#1317 | semidirect |
| 312. C2 | #10598819 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65500 | 2 |
| C2×#64933 | 2 |
| #10598819 | 2 |
| C2×#1317 | 5 |