Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
296 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 68 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 |
|---|---|---|
| 2. D5⋊#101 | C2 | semidirect |
| 3. #65782 | C2 | semidirect |
| 6. D5⋊#108 | C2 | semidirect |
| 7. #65718 | C2 | semidirect |
| 14. C2×C5×SD16 | C4 | semidirect |
| 15. C2×#688 | C4 | semidirect |
| 16. C2×#687 | C4 | semidirect |
| 21. C2×#677 | C4 | semidirect |
| 127. C2×SD16 | AGL(1,𝔽5) | semidirect |
| 243. C5 | #1977 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×SD16 | 2 |
| D5⋊#101 | 2 |
| #65782 | 2 |
| D5⋊#100 | 2 |
| #65767 | 2 |
| D5⋊#108 | 2 |
| #65718 | 2 |
| #1977 | 5 |