Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
426 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 23. C5×#358 | C4 | semidirect |
| 24. #64784 | C4 | semidirect |
| 25. #64723 | C4 | semidirect |
| 26. #64712 | C4 | semidirect |
| 99. C5×Q16 | C4⋊C4 | semidirect |
| 108. Dic20 | C4⋊C4 | semidirect |
| 133. #358 | AGL(1,𝔽5) | semidirect |
| 248. Q16 | C4⋊AGL(1,𝔽5) | semidirect |
| 318. C5 | #12936 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×AGL(1,𝔽5) | 2 |
| C2×#64908 | 2 |
| C2×#64849 | 2 |
| #10604075 | 2 |
| D5×#358 | 2 |
| (C2×AGL(1,𝔽5))⋊C16 | 2 |
| #10598619 | 2 |
| #12936 | 5 |