Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
354 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 21. C5×#358 | C4 | semidirect |
| 22. #64784 | C4 | semidirect |
| 23. #64723 | C4 | semidirect |
| 24. #64712 | C4 | semidirect |
| 125. #358 | AGL(1,𝔽5) | semidirect |
| 306. C5 | #13132 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10604848 | 2 |
| C2×#64908 | 2 |
| C2×#64850 | 2 |
| AGL(1,𝔽5)×#107 | 2 |
| D5×#358 | 2 |
| (C2×AGL(1,𝔽5))⋊C16 | 2 |
| #10598619 | 2 |
| #13132 | 5 |