Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
294 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 107 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. C22×C5×C32 | C2 | semidirect |
| 3. C2×#64726 | C2 | semidirect |
| 4. #10598089 | C2 | direct (N × H) |
| 17. C2×C5×C32 | C22 | semidirect |
| 19. #64726 | C22 | semidirect |
| 47. C22×C32 | D5 | semidirect |
| 90. C2×C32 | C2×D5 | semidirect |
| 181. C2×C5 | #1417 | semidirect |
| 206. C5 | C2×#1417 | semidirect |
| 221. C2 | #10598089 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65193 | 2 |
| C22×C5×C32 | 2 |
| C2×#64726 | 2 |
| #10598089 | 2 |
| C2×#1417 | 5 |