Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
316 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 51 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. #65968 | C2 | semidirect |
| 2. C5×#450 | C2 | semidirect |
| 4. #65507 | C2 | semidirect |
| 5. #64758 | C2 | semidirect |
| 6. #64688 | C2 | semidirect |
| 7. #64687 | C2 | semidirect |
| 30. C2×C5×Q8 | D4 | semidirect |
| 43. C2×Dic10 | D4 | semidirect |
| 47. C5×C4⋊C4 | D4 | semidirect |
| 57. C4⋊Dic5 | D4 | semidirect |
| 64. #450 | D5 | semidirect |
| 81. C22×D5 | SD16 | semidirect |
| 154. C2×Q8 | C22⋊D5 | semidirect |
| 176. C4⋊C4 | C22⋊D5 | semidirect |
| 228. C5 | #1596 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #65968 | 2 |
| C5×#450 | 2 |
| #65512 | 2 |
| #65507 | 2 |
| #64758 | 2 |
| #64688 | 2 |
| #64687 | 2 |
| #1596 | 5 |