Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
346 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 346 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 |
|---|---|---|
| 4. #10598582 | C2 | direct (N × H) |
| 186. C2×C5 | #1338 | semidirect |
| 213. C5 | C2×#1338 | semidirect |
| 227. C2 | #10598582 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65120 | 2 |
| C2×C4⋊#674 | 2 |
| C2×#64859 | 2 |
| #10598582 | 2 |
| C2×#1338 | 5 |