Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
158 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 53 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. C4×C5×Q16 | C2 | semidirect |
| 2. C2×#3961 | C2 | semidirect |
| 5. #64712 | C2 | semidirect |
| 7. C4⋊#672 | C2 | semidirect |
| 45. C4×Q16 | D5 | semidirect |
| 129. C5 | #2211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C5×Q16 | 2 |
| C2×#3961 | 2 |
| C2×#3960 | 2 |
| #64985 | 2 |
| #64712 | 2 |
| #64711 | 2 |
| C4⋊#672 | 2 |
| #2211 | 5 |