Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
820 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 237 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 |
|---|---|---|
| 1. C22×C5×C4⋊C4 | C2 | semidirect |
| 4. C2×#3963 | C2 | semidirect |
| 5. C2×#3963 | C2 | semidirect |
| 6. #65282 | C2 | direct (N × H) |
| 13. C2×C5×C4⋊C4 | C22 | semidirect |
| 18. #3963 | C22 | semidirect |
| 19. #3963 | C22 | semidirect |
| 45. C22×C4⋊C4 | D5 | semidirect |
| 87. C2×C4⋊C4 | C2×D5 | semidirect |
| 138. C2×C5 | #397 | semidirect |
| 175. C5 | C2×#397 | semidirect |
| 197. C2 | #65282 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×C4⋊C4 | 2 |
| C22×#685 | 2 |
| C2×#3963 | 2 |
| #65282 | 2 |
| C2×#397 | 5 |