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×#494 | C2 | semidirect |
| 4. #64784 | C2 | semidirect |
| 5. C4⋊#672 | C2 | semidirect |
| 34. #494 | D5 | semidirect |
| 68. C4×C5 | SD32 | semidirect |
| 106. C5 | #2208 | semidirect |
| 114. C4 | #3960 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#494 | 2 |
| C2×#3960 | 2 |
| C4×D40 | 2 |
| #64784 | 2 |
| C4⋊#672 | 2 |
| #2208 | 5 |