Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
262 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 4. #64751 | C2 | semidirect |
| 5. #64743 | C2 | semidirect |
| 10. C5×#117 | C4 | semidirect |
| 12. C2×C42×C5 | C4 | semidirect |
| 74. #117 | Dic5 | semidirect |
| 76. C2×C42 | Dic5 | semidirect |
| 141. C5 | #1827 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C5×#41 | 2 |
| #65529 | 2 |
| #65526 | 2 |
| #64751 | 2 |
| #64743 | 2 |
| #1827 | 5 |