Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
552 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 93 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. #10615659 | C2 | semidirect |
| 2. C2×#65482 | C2 | semidirect |
| 3. #10610914 | C2 | semidirect |
| 4. C5×#2145 | C2 | semidirect |
| 5. C2×#64736 | C2 | semidirect |
| 6. #10602230 | C2 | semidirect |
| 7. #10598218 | C2 | semidirect |
| 39. C2×C5×Q16 | D4 | semidirect |
| 41. C2×C5×D8 | D4 | semidirect |
| 77. #3951 | D4 | semidirect |
| 79. #3944 | D4 | semidirect |
| 86. #2145 | D5 | semidirect |
| 228. C2×Q16 | D20 | semidirect |
| 236. C2×D8 | D20 | semidirect |
| 396. C5 | #13310 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10615659 | 2 |
| C2×#65482 | 2 |
| #10610914 | 2 |
| C5×#2145 | 2 |
| C2×#64736 | 2 |
| #10602230 | 2 |
| #10598218 | 2 |
| #13310 | 5 |