Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
488 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 141 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. #65377 | C2 | semidirect |
| 4. #65374 | C2 | semidirect |
| 5. #65335 | C2 | semidirect |
| 6. #65316 | C2 | semidirect |
| 7. #65214 | C2 | semidirect |
| 11. C5×C4⋊Q8 | C22 | semidirect |
| 12. C5×C4⋊Q8 | C22 | semidirect |
| 17. C4×C5×Q8 | C22 | semidirect |
| 20. C2×#688 | C22 | semidirect |
| 26. #3941 | C22 | semidirect |
| 27. C4⋊#168 | C22 | semidirect |
| 28. C4×#168 | C22 | semidirect |
| 59. #533 | D5 | semidirect |
| 77. C2×C4×C5 | SD16 | semidirect |
| 95. C4⋊Q8 | C2×D5 | semidirect |
| 96. C4⋊Q8 | C2×D5 | semidirect |
| 105. C4×Q8 | C2×D5 | semidirect |
| 179. C2×C4 | #688 | semidirect |
| 187. C5 | #3208 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#533 | 2 |
| C2×#4020 | 2 |
| #65377 | 2 |
| #65374 | 2 |
| #65335 | 2 |
| #65316 | 2 |
| #65214 | 2 |
| #3208 | 5 |