Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
540 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 2. C2×C5×#355 | C2 | semidirect |
| 3. C2×#64762 | C2 | semidirect |
| 4. C2×#64697 | C2 | semidirect |
| 5. C2×#64697 | C2 | semidirect |
| 6. #10600890 | C2 | semidirect |
| 7. Dic5×#101 | C2 | semidirect |
| 73. C5×#101 | D4 | semidirect |
| 77. #3968 | D4 | semidirect |
| 87. C2×#355 | D5 | semidirect |
| 287. #101 | C22⋊D5 | semidirect |
| 322. Dic5 | #355 | semidirect |
| 457. C5 | #13226 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10614705 | 2 |
| C2×C5×#355 | 2 |
| C2×#64762 | 2 |
| C2×#64697 | 2 |
| #10600890 | 2 |
| Dic5×#101 | 2 |
| #13226 | 5 |