Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
336 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 76 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 |
|---|---|---|
| 7. C2×C5×#108 | C4 | semidirect |
| 9. C2×#3951 | C4 | semidirect |
| 13. #64887 | C4 | semidirect |
| 85. C2×#108 | AGL(1,𝔽5) | semidirect |
| 249. C5 | #7260 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10604721 | 2 |
| C2×#64887 | 2 |
| #10601504 | 2 |
| #7260 | 5 |