Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
308 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 94 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 |
|---|---|---|
| 11. C4×C5×Q8 | C4 | semidirect |
| 12. Q8×Dic5 | C4 | semidirect |
| 16. #4033 | C4 | semidirect |
| 20. C4×Dic10 | C4 | semidirect |
| 70. C5×Q8 | C4⋊C4 | semidirect |
| 96. Dic10 | C4⋊C4 | semidirect |
| 105. C4×Q8 | AGL(1,𝔽5) | semidirect |
| 127. C4×C5 | #103 | semidirect |
| 133. Dic5 | #103 | semidirect |
| 184. Q8 | C4⋊AGL(1,𝔽5) | semidirect |
| 211. C5 | #1803 | semidirect |
| 229. C4 | #4009 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Q8×D5 | 2 |
| C2×#4009 | 2 |
| #65688 | 2 |
| D5⋊(C4⋊C8) | 2 |
| #64874 | 2 |
| #1803 | 5 |