Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1022 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 1022 conjugacy classes of subgroups — too many to draw. Only its 219 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×D16 | C2 | semidirect |
| 2. C2×#65440 | C2 | semidirect |
| 3. C22×#3958 | C2 | semidirect |
| 4. C22×D80 | C2 | semidirect |
| 5. #10602257 | C2 | direct (N × H) |
| 6. C2×C16×Dic5 | C2 | semidirect |
| 12. C2×C5×D16 | C22 | semidirect |
| 15. #65440 | C22 | semidirect |
| 17. C2×#3958 | C22 | semidirect |
| 21. C2×D80 | C22 | semidirect |
| 22. C16×Dic5 | C22 | semidirect |
| 43. C2×C5×C16 | D4 | semidirect |
| 48. C2×#672 | D4 | semidirect |
| 53. C22×D16 | D5 | semidirect |
| 86. C5×C16 | C2×D4 | semidirect |
| 87. #672 | C2×D4 | semidirect |
| 97. C2×D16 | C2×D5 | semidirect |
| 119. C2×Dic5 | D16 | semidirect |
| 151. C2×C16 | C22⋊D5 | semidirect |
| 167. Dic5 | C2×D16 | semidirect |
| 198. C16 | C2×C22⋊D5 | semidirect |
| 200. C2×C5 | #2246 | semidirect |
| 228. C5 | C2×#2246 | semidirect |
| 244. C2 | #10602257 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×D16 | 2 |
| C2×#65440 | 2 |
| C22×#3958 | 2 |
| C22×D80 | 2 |
| #10602257 | 2 |
| C2×C16×Dic5 | 2 |
| C2×#2246 | 5 |