Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
406 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 99 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. C2×C5×C4⋊Q8 | C2 | semidirect |
| 3. C2×#3967 | C2 | semidirect |
| 5. #64744 | C2 | semidirect |
| 43. C2×C4⋊Q8 | D5 | semidirect |
| 62. C2×C4×C5 | SD16 | semidirect |
| 147. C2×C4 | #688 | semidirect |
| 153. C5 | #2013 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×C4⋊Q8 | 2 |
| C22×#688 | 2 |
| C2×#3967 | 2 |
| #65228 | 2 |
| #64744 | 2 |
| #2013 | 5 |