Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
650 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 99 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. C2×#65440 | C2 | semidirect |
| 2. C2×#65436 | C2 | semidirect |
| 3. C2×#65197 | C2 | semidirect |
| 4. C2×C5×#361 | C2 | semidirect |
| 5. #10601489 | C2 | semidirect |
| 6. C2×#64715 | C2 | semidirect |
| 7. #10598301 | C2 | semidirect |
| 51. C2×Dic20 | D4 | semidirect |
| 62. C2×D40 | D4 | semidirect |
| 65. C5×M32 | D4 | semidirect |
| 76. #3944 | D4 | semidirect |
| 84. C2×#361 | D5 | semidirect |
| 248. M32 | C22⋊D5 | semidirect |
| 383. C5 | #13331 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65440 | 2 |
| C2×#65436 | 2 |
| C2×#65197 | 2 |
| C2×C5×#361 | 2 |
| #10601489 | 2 |
| C2×#64715 | 2 |
| #10598301 | 2 |
| #13331 | 5 |