Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
716 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 198 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. #66262 | C2 | semidirect |
| 3. #65771 | C2 | semidirect |
| 4. #65745 | C2 | semidirect |
| 5. C2×C5×#41 | C4 | semidirect |
| 7. C2×Q8×D5 | C4 | semidirect |
| 9. C2×#711 | C4 | semidirect |
| 12. C22×Dic10 | C4 | semidirect |
| 68. C2×#41 | AGL(1,𝔽5) | semidirect |
| 135. C5 | #2884 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4150 | 2 |
| #66262 | 2 |
| #65771 | 2 |
| #65745 | 2 |
| #2884 | 5 |