Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
496 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 107 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×H(3,ℤ/4) | C2 | semidirect |
| 3. C2×#64773 | C2 | semidirect |
| 4. #10597972 | C2 | direct (N × H) |
| 8. C22×D40 | C4 | semidirect |
| 11. #65424 | C4 | semidirect |
| 14. C2×#3949 | C4 | semidirect |
| 17. C5×H(3,ℤ/4) | C22 | semidirect |
| 19. #64773 | C22 | semidirect |
| 48. C2×D40 | C2×C4 | semidirect |
| 52. #3949 | C2×C4 | semidirect |
| 58. C2×H(3,ℤ/4) | D5 | semidirect |
| 122. H(3,ℤ/4) | C2×D5 | semidirect |
| 276. C2×C5 | #1339 | semidirect |
| 322. C5 | C2×#1339 | semidirect |
| 351. C2 | #10597972 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65424 | 2 |
| C2×C5×H(3,ℤ/4) | 2 |
| C2×#64773 | 2 |
| #10597972 | 2 |
| C2×#1339 | 5 |