Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
572 conjugacy classes of subgroups; only the 377 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 377 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. #65411 | C2 | semidirect |
| 5. M16×Dic5 | C2 | semidirect |
| 6. #65390 | C2 | semidirect |
| 7. C2×C8×Dic5 | C2 | semidirect |
| 9. C5×#131 | C4 | semidirect |
| 12. #4094 | C4 | semidirect |
| 31. C5×M16 | C2×C4 | semidirect |
| 32. C2×C5×C8 | C2×C4 | semidirect |
| 40. #681 | C2×C4 | semidirect |
| 41. C2×#168 | C2×C4 | semidirect |
| 67. #131 | Dic5 | direct (N × H) |
| 88. Dic5 | #131 | direct (N × H) |
| 96. M16 | C2×Dic5 | semidirect |
| 100. C2×C8 | C2×Dic5 | semidirect |
| 125. C5 | C4×#131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#131 | 2 |
| #41×Dic5 | 2 |
| C2×#4094 | 2 |
| #65411 | 2 |
| M16×Dic5 | 2 |
| #65390 | 2 |
| C2×C8×Dic5 | 2 |
| C4×#131 | 5 |