Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
400 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 121 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. C5×#533 | C2 | semidirect |
| 3. #65378 | C2 | semidirect |
| 4. #65375 | C2 | semidirect |
| 5. #65339 | C2 | semidirect |
| 7. #65317 | C2 | semidirect |
| 8. #65215 | C2 | semidirect |
| 11. C5×C4⋊Q8 | C22 | semidirect |
| 12. C5×C4⋊Q8 | C22 | semidirect |
| 17. C4×C5×Q8 | C22 | semidirect |
| 20. C2×#689 | C22 | semidirect |
| 29. #3942 | C22 | semidirect |
| 31. C4⋊#168 | C22 | semidirect |
| 32. #3935 | C22 | semidirect |
| 66. #533 | D5 | semidirect |
| 103. C4⋊Q8 | C2×D5 | semidirect |
| 104. C4⋊Q8 | C2×D5 | semidirect |
| 113. C4×Q8 | C2×D5 | semidirect |
| 202. C5 | #3215 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#533 | 2 |
| C2×#4021 | 2 |
| #65378 | 2 |
| #65375 | 2 |
| #65339 | 2 |
| #65335 | 2 |
| #65317 | 2 |
| #65215 | 2 |
| #3215 | 5 |