Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
384 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 109 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. C2×C5×#107 | C2 | semidirect |
| 3. C2×C8×Dic5 | C2 | semidirect |
| 4. #65277 | C2 | semidirect |
| 5. C2×#3941 | C2 | semidirect |
| 14. C2×D40 | C4 | semidirect |
| 42. C2×#107 | D5 | semidirect |
| 62. C2×Dic5 | D8 | semidirect |
| 67. C5×C8 | C22⋊C4 | semidirect |
| 147. C8 | #685 | semidirect |
| 148. C5 | #1970 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D40 | 2 |
| C2×C5×#107 | 2 |
| C2×C8×Dic5 | 2 |
| #65277 | 2 |
| C2×#3941 | 2 |
| #1970 | 5 |