Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
402 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 156 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. #65708 | C2 | semidirect |
| 5. #65701 | C2 | semidirect |
| 6. #65697 | C2 | semidirect |
| 7. #65683 | C2 | semidirect |
| 8. #65678 | C2 | semidirect |
| 24. #4004 | C22 | semidirect |
| 28. #4002 | C22 | semidirect |
| 29. C4⋊#170 | C22 | semidirect |
| 30. C4×#170 | C22 | semidirect |
| 195. C5 | #2924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×#117 | 2 |
| #65756 | 2 |
| D5⋊(C22⋊C8) | 2 |
| #65708 | 2 |
| #65701 | 2 |
| #65697 | 2 |
| #65683 | 2 |
| #65678 | 2 |
| #2924 | 5 |