Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
284 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 66 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 |
|---|---|---|
| 2. #65785 | C2 | semidirect |
| 3. #65784 | C2 | semidirect |
| 4. #65721 | C2 | semidirect |
| 5. #65718 | C2 | semidirect |
| 10. C2×C5×Q16 | C4 | semidirect |
| 11. C2×#688 | C4 | semidirect |
| 16. C2×D40 | C4 | semidirect |
| 89. C2×Q16 | AGL(1,𝔽5) | semidirect |
| 174. C5 | #1976 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4065 | 2 |
| #65785 | 2 |
| #65784 | 2 |
| #65721 | 2 |
| #65718 | 2 |
| #1976 | 5 |