Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
294 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 1. C22×C5×Q32 | C2 | semidirect |
| 2. C2×#64741 | C2 | semidirect |
| 4. #10598317 | C2 | semidirect |
| 5. C22⋊#3926 | C2 | semidirect |
| 28. C5×Q32 | D4 | semidirect |
| 36. C22×Q32 | D5 | semidirect |
| 101. Q32 | C22⋊D5 | semidirect |
| 111. C22×C5 | SD64 | semidirect |
| 165. C5 | #13662 | semidirect |
| 171. C22 | #64741 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×Q32 | 2 |
| C2×#64741 | 2 |
| #10602206 | 2 |
| #10598317 | 2 |
| C22⋊#3926 | 2 |
| #13662 | 5 |