Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1502 conjugacy classes of subgroups; only the 240 normal subgroups are shown.
This group has 1502 conjugacy classes of subgroups — too many to draw. Only its 240 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 |
|---|---|---|
| 3. C2×#64928 | C2 | direct (N × H) |
| 4. C23×C5×Q8 | C4 | semidirect |
| 8. C2×#4093 | C4 | semidirect |
| 11. C22×C4×Dic5 | C4 | semidirect |
| 14. #64928 | C22 | direct (N × H) |
| 21. C22×C5×Q8 | C2×C4 | semidirect |
| 34. #4093 | C2×C4 | semidirect |
| 39. C2×C4×Dic5 | C2×C4 | semidirect |
| 58. C2×C5×Q8 | C22×C4 | semidirect |
| 83. C4×Dic5 | C22×C4 | semidirect |
| 84. C23×Q8 | AGL(1,𝔽5) | semidirect |
| 132. C22×Q8 | C2×AGL(1,𝔽5) | semidirect |
| 156. C22×C5 | #354 | semidirect |
| 184. C2×Q8 | C22×AGL(1,𝔽5) | semidirect |
| 214. C2×C5 | C2×#354 | semidirect |
| 251. C5 | C22×#354 | semidirect |
| 262. C22 | #64928 | direct (N × H) |
| 275. C2 | C2×#64928 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#4093 | 2 |
| C22×#3999 | 2 |
| C2×#64928 | 2 |
| C22×#354 | 5 |