Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1434 conjugacy classes of subgroups; only the 275 normal subgroups are shown.
This group has 1434 conjugacy classes of subgroups — too many to draw. Only its 275 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×C5×#543 | C2 | semidirect |
| 3. #10602689 | C2 | direct (N × H) |
| 4. C2×#64747 | C2 | semidirect |
| 7. C5×#543 | C22 | semidirect |
| 14. #64747 | C22 | semidirect |
| 17. C24×D5 | Q8 | semidirect |
| 24. C22×C22⋊D5 | Q8 | semidirect |
| 27. C23×Dic5 | Q8 | semidirect |
| 44. C2×#543 | D5 | semidirect |
| 59. C23×D5 | C2×Q8 | semidirect |
| 82. C22×Dic5 | C2×Q8 | semidirect |
| 94. #543 | C2×D5 | semidirect |
| 249. C2×C5 | #2032 | semidirect |
| 294. C5 | C2×#2032 | semidirect |
| 329. C2 | #10602689 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#543 | 2 |
| C22×#3938 | 2 |
| #10602689 | 2 |
| C2×#64747 | 2 |
| C2×#2032 | 5 |