Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
914 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 914 conjugacy classes of subgroups — too many to draw. Only its 251 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×#494 | C2 | semidirect |
| 2. C2×#65367 | C2 | semidirect |
| 5. #10602094 | C2 | direct (N × H) |
| 6. C2×#64675 | C2 | semidirect |
| 13. C5×#494 | C22 | semidirect |
| 18. #65367 | C22 | semidirect |
| 24. #64675 | C22 | semidirect |
| 57. C2×#494 | D5 | semidirect |
| 102. #494 | C2×D5 | semidirect |
| 210. C2×C5 | #1722 | semidirect |
| 238. C5 | C2×#1722 | semidirect |
| 252. C2 | #10602094 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#494 | 2 |
| C2×#65367 | 2 |
| C2×#65377 | 2 |
| C2×#64982 | 2 |
| #10602094 | 2 |
| C2×#64675 | 2 |
| C2×#1722 | 5 |