Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
446 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 106 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. #10603847 | C2 | semidirect |
| 4. #10603827 | C2 | semidirect |
| 5. #10598621 | C2 | semidirect |
| 12. C4×C5×Q16 | C4 | semidirect |
| 13. Q16×Dic5 | C4 | semidirect |
| 16. #65161 | C4 | semidirect |
| 19. C4×D40 | C4 | semidirect |
| 89. C5×Q16 | C4⋊C4 | semidirect |
| 111. D40 | C4⋊C4 | semidirect |
| 123. C4×Q16 | AGL(1,𝔽5) | semidirect |
| 225. C4×C5 | #360 | semidirect |
| 230. Dic5 | #360 | semidirect |
| 248. Q16 | C4⋊AGL(1,𝔽5) | semidirect |
| 324. C5 | #12816 | semidirect |
| 342. C4 | #64907 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#4065 | 2 |
| C2×#64907 | 2 |
| #10603847 | 2 |
| #10603827 | 2 |
| #10598621 | 2 |
| #12816 | 5 |