Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1310 conjugacy classes of subgroups; only the 232 normal subgroups are shown.
This group has 1310 conjugacy classes of subgroups — too many to draw. Only its 232 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×#65683 | C2 | semidirect |
| 3. C2×#64927 | C2 | semidirect |
| 4. C2×#64921 | C2 | semidirect |
| 5. #10604543 | C2 | direct (N × H) |
| 19. C2×#4002 | C22 | semidirect |
| 22. #65683 | C22 | semidirect |
| 23. #64927 | C22 | semidirect |
| 24. #64921 | C22 | semidirect |
| 69. #4002 | C23 | semidirect |
| 315. C2×C5 | #1533 | semidirect |
| 363. C5 | C2×#1533 | semidirect |
| 388. C2 | #10604543 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×#124 | 2 |
| C2×#65683 | 2 |
| C2×#64927 | 2 |
| C2×#64921 | 2 |
| #10604543 | 2 |
| C2×#1533 | 5 |