Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
682 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 682 conjugacy classes of subgroups — too many to draw. Only its 144 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 |
|---|---|---|
| 2. C2×C22⋊#674 | C2 | semidirect |
| 3. #10598760 | C2 | direct (N × H) |
| 13. C22⋊#674 | C22 | semidirect |
| 48. C23×D5 | C16 | semidirect |
| 115. C22×D5 | C2×C16 | semidirect |
| 238. C2×C5 | #1314 | semidirect |
| 288. C5 | C2×#1314 | semidirect |
| 319. C2 | #10598760 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3952 | 2 |
| C2×C22⋊#674 | 2 |
| #10598760 | 2 |
| C2×#1314 | 5 |