Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
3950 conjugacy classes of subgroups; only the 987 normal subgroups are shown.
This group has 3950 conjugacy classes of subgroups — too many to draw. Only its 987 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. C22×C5×C4⋊Q8 | C2 | semidirect |
| 2. C23×#688 | C2 | semidirect |
| 4. C2×#65374 | C2 | direct (N × H) |
| 5. C22×C4×#168 | C2 | semidirect |
| 10. C2×C5×C4⋊Q8 | C22 | semidirect |
| 14. C22×#688 | C22 | semidirect |
| 18. #65374 | C22 | direct (N × H) |
| 19. C2×C4×#168 | C22 | semidirect |
| 34. C5×C4⋊Q8 | C23 | semidirect |
| 39. C2×#688 | C23 | semidirect |
| 40. C22×#168 | D4 | semidirect |
| 44. C4×#168 | C23 | semidirect |
| 46. C22×C4⋊Q8 | D5 | semidirect |
| 60. C22×C4×C5 | SD16 | semidirect |
| 75. C2×#168 | C2×D4 | semidirect |
| 84. C2×C4⋊Q8 | C2×D5 | semidirect |
| 103. C2×C4×C5 | C2×SD16 | semidirect |
| 111. #168 | C22×D4 | semidirect |
| 129. C4⋊Q8 | C22×D5 | semidirect |
| 136. C22×C5 | #492 | semidirect |
| 145. C4×C5 | C22×SD16 | semidirect |
| 163. C22×C4 | #688 | semidirect |
| 174. C2×C5 | C2×#492 | semidirect |
| 193. C2×C4 | C2×#688 | semidirect |
| 199. C5 | C22×#492 | semidirect |
| 203. C22 | #65374 | direct (N × H) |
| 209. C4 | C22×#688 | semidirect |
| 212. C2 | C2×#65374 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×C4⋊Q8 | 2 |
| C23×#688 | 2 |
| C22×#4020 | 2 |
| C2×#65374 | 2 |
| C22×C4×#168 | 2 |
| C22×#492 | 5 |