Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
512 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 3. C5×#2141 | C2 | semidirect |
| 4. #10602854 | C2 | semidirect |
| 6. #10598310 | C2 | semidirect |
| 7. #10598217 | C2 | semidirect |
| 16. #65478 | C4 | semidirect |
| 34. C2×C5×Q16 | C2×C4 | semidirect |
| 65. #3949 | C2×C4 | semidirect |
| 74. #2141 | D5 | semidirect |
| 188. C2×Q16 | C4×D5 | semidirect |
| 332. C5 | #13000 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65478 | 2 |
| #10610908 | 2 |
| C5×#2141 | 2 |
| #10602854 | 2 |
| C2×#64734 | 2 |
| #10598310 | 2 |
| #10598217 | 2 |
| #13000 | 5 |