Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
272 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 12. C5×#97 | C4 | semidirect |
| 14. #3950 | C4 | semidirect |
| 15. #3949 | C4 | semidirect |
| 56. C5×C8 | C42 | semidirect |
| 65. #97 | Dic5 | semidirect |
| 118. C8 | C4×Dic5 | semidirect |
| 119. C5 | #1776 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#97 | 2 |
| C2×#3950 | 2 |
| C2×#3949 | 2 |
| C4×C4⋊Dic5 | 2 |
| #64771 | 2 |
| #1776 | 5 |