Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
220 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 64 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 |
|---|---|---|
| 4. #64908 | C2 | semidirect |
| 7. C2×C5×Q16 | C4 | semidirect |
| 11. D5×Q16 | C4 | semidirect |
| 13. C2×Dic20 | C4 | semidirect |
| 79. C2×Q16 | AGL(1,𝔽5) | semidirect |
| 149. C5 | #2141 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×Q16 | 2 |
| #65721 | 2 |
| D5⋊M32 | 2 |
| #64908 | 2 |
| #2141 | 5 |