Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
132 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 50 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 |
|---|---|---|
| 7. #3996 | C4 | semidirect |
| 11. C2×C5×C16 | C4 | semidirect |
| 12. C2×#672 | C4 | semidirect |
| 53. C2×C16 | AGL(1,𝔽5) | semidirect |
| 99. C5 | #1382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5⋊#108 | 2 |
| #65721 | 2 |
| C2×D5×C16 | 2 |
| #1382 | 5 |