Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
336 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 82 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. #64926 | C2 | direct (N × H) |
| 6. C22×C5×Q8 | C4 | semidirect |
| 11. #4092 | C4 | semidirect |
| 14. C2×C4⋊Dic5 | C4 | semidirect |
| 28. C2×C5×Q8 | C2×C4 | semidirect |
| 43. C4⋊Dic5 | C2×C4 | semidirect |
| 78. C22×Q8 | AGL(1,𝔽5) | semidirect |
| 116. C2×Q8 | C2×AGL(1,𝔽5) | semidirect |
| 138. C2×C5 | #328 | semidirect |
| 173. C5 | C2×#328 | semidirect |
| 197. C2 | #64926 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4092 | 2 |
| C2×(C2×AGL(1,𝔽5))⋊C4 | 2 |
| C2×#4003 | 2 |
| #64926 | 2 |
| C2×#328 | 5 |