Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
254 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 116 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 |
|---|---|---|
| 23. #3998 | C8 | semidirect |
| 27. C2×C5×C16 | C8 | semidirect |
| 34. C2×#672 | C8 | semidirect |
| 96. C2×C16 | #170 | semidirect |
| 154. C5 | #7141 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10604702 | 2 |
| #10604687 | 2 |
| C2×C16×Dic5 | 2 |
| #7141 | 5 |