Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
586 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 586 conjugacy classes of subgroups — too many to draw. Only its 103 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×#65436 | C2 | semidirect |
| 2. C22×#3958 | C2 | semidirect |
| 3. #10610296 | C2 | semidirect |
| 4. C5×#1978 | C2 | semidirect |
| 5. C2×#64717 | C2 | semidirect |
| 6. C2×#64715 | C2 | semidirect |
| 7. #10598162 | C2 | semidirect |
| 40. C2×C5×D8 | D4 | semidirect |
| 76. #3944 | D4 | semidirect |
| 80. C2×#672 | D4 | semidirect |
| 86. #1978 | D5 | semidirect |
| 235. C2×D8 | D20 | semidirect |
| 385. C5 | #13336 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65436 | 2 |
| C22×#3958 | 2 |
| #10610296 | 2 |
| C5×#1978 | 2 |
| C2×#64717 | 2 |
| C2×#64715 | 2 |
| #10598162 | 2 |
| #13336 | 5 |