Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
280 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 17. C5×#364 | C4 | semidirect |
| 18. #64731 | C4 | semidirect |
| 19. #64683 | C4 | semidirect |
| 91. #364 | AGL(1,𝔽5) | semidirect |
| 203. C5 | #13182 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10604119 | 2 |
| #10603860 | 2 |
| #10603851 | 2 |
| D5×#364 | 2 |
| #10598677 | 2 |
| #13182 | 5 |