Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
814 conjugacy classes of subgroups; only the 199 normal subgroups are shown.
This group has 814 conjugacy classes of subgroups — too many to draw. Only its 199 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×#2247 | C2 | semidirect |
| 4. #10602292 | C2 | semidirect |
| 5. #10602105 | C2 | semidirect |
| 6. #10599859 | C2 | semidirect |
| 58. #2247 | D5 | direct (N × H) |
| 115. C4×D5 | Q32 | semidirect |
| 156. C4×C5 | C2×Q32 | semidirect |
| 161. Dic5 | C2×Q32 | semidirect |
| 192. D5 | #2247 | direct (N × H) |
| 213. C5 | C2×#2247 | semidirect |
| 221. C4 | D5×Q32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×Q32 | 2 |
| D5×#494 | 2 |
| C5×#2247 | 2 |
| #10602292 | 2 |
| #10602105 | 2 |
| #10599859 | 2 |
| C4×D5×C16 | 2 |
| C2×#2247 | 5 |