Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
166 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 55 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×#500 | C2 | semidirect |
| 4. #64767 | C2 | semidirect |
| 5. #64677 | C2 | semidirect |
| 32. #500 | D5 | semidirect |
| 49. C5×C8 | SD16 | semidirect |
| 105. C8 | #688 | semidirect |
| 106. C5 | #1693 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#500 | 2 |
| #65372 | 2 |
| #64977 | 2 |
| #64767 | 2 |
| #64677 | 2 |
| #1693 | 5 |