Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
568 conjugacy classes of subgroups; only the 228 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 228 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 |
|---|---|---|
| 13. C4×C5×Q8 | C4 | semidirect |
| 14. Q8×Dic5 | C4 | semidirect |
| 16. #4033 | C4 | semidirect |
| 18. C4×Dic10 | C4 | semidirect |
| 33. C4⋊AGL(1,𝔽5) | Q8 | direct (N × H) |
| 54. C5×Q8 | C4⋊C4 | semidirect |
| 67. Dic10 | C4⋊C4 | semidirect |
| 73. C4×Q8 | AGL(1,𝔽5) | semidirect |
| 93. C4×C5 | C4×Q8 | semidirect |
| 96. Dic5 | C4×Q8 | semidirect |
| 127. Q8 | C4⋊AGL(1,𝔽5) | direct (N × H) |
| 146. C5 | Q8×C4⋊C4 | semidirect |
| 161. C4 | Q8×AGL(1,𝔽5) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×AGL(1,𝔽5) | 2 |
| C4×Q8×D5 | 2 |
| #65712 | 2 |
| #65688 | 2 |
| C4×C4⋊AGL(1,𝔽5) | 2 |
| Q8×C4⋊C4 | 5 |