Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
276 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 68 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 |
|---|---|---|
| 10. C2×C5×Q16 | C4 | semidirect |
| 11. C2×#689 | C4 | semidirect |
| 16. C2×Dic20 | C4 | semidirect |
| 91. C2×Q16 | AGL(1,𝔽5) | semidirect |
| 171. C5 | #1979 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×Q16 | 2 |
| D5⋊#101 | 2 |
| #65782 | 2 |
| D5⋊#108 | 2 |
| #65718 | 2 |
| #1979 | 5 |