Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
222 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 1. C5×#430 | C2 | semidirect |
| 4. #65413 | C2 | semidirect |
| 5. #64780 | C2 | semidirect |
| 34. #430 | D5 | semidirect |
| 114. C5 | #2091 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#430 | 2 |
| #65415 | 2 |
| #65413 | 2 |
| #64780 | 2 |
| #2091 | 5 |