Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1218 conjugacy classes of subgroups; only the 264 normal subgroups are shown.
This group has 1218 conjugacy classes of subgroups — too many to draw. Only its 264 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. #10604295 | C2 | direct (N × H) |
| 241. C2×C5 | #1467 | semidirect |
| 278. C5 | C2×#1467 | semidirect |
| 299. C2 | #10604295 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#4033 | 2 |
| C2×#65757 | 2 |
| C2×#64914 | 2 |
| #10604295 | 2 |
| C2×#1467 | 5 |