Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
312 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 80 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 |
|---|---|---|
| 3. C4×C4⋊AGL(1,𝔽5) | C2 | semidirect |
| 4. #65681 | C2 | semidirect |
| 5. #64875 | C2 | semidirect |
| 10. C4×C5×Q8 | C4 | semidirect |
| 11. Q8×Dic5 | C4 | semidirect |
| 13. #4039 | C4 | semidirect |
| 17. C4×D20 | C4 | semidirect |
| 70. C5×Q8 | C4⋊C4 | semidirect |
| 83. D20 | C4⋊C4 | semidirect |
| 98. C4×Q8 | AGL(1,𝔽5) | semidirect |
| 125. C4×C5 | #104 | semidirect |
| 176. Q8 | C4⋊AGL(1,𝔽5) | semidirect |
| 204. C5 | #1806 | semidirect |
| 222. C4 | #4010 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#713 | 2 |
| C2×#4010 | 2 |
| C4×C4⋊AGL(1,𝔽5) | 2 |
| #65681 | 2 |
| #64875 | 2 |
| #1806 | 5 |