Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
280 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 110 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. #3993 | C4 | direct (N × H) |
| 12. C4×C5×C8 | C4 | semidirect |
| 13. C8×Dic5 | C4 | semidirect |
| 14. C8×Dic5 | C4 | semidirect |
| 15. C4×#168 | C4 | semidirect |
| 53. C5×C8 | C42 | semidirect |
| 55. #168 | C42 | semidirect |
| 65. C4×C8 | AGL(1,𝔽5) | semidirect |
| 73. C4×C5 | #106 | semidirect |
| 77. Dic5 | #106 | semidirect |
| 117. C8 | C4×AGL(1,𝔽5) | semidirect |
| 118. C5 | C4×#106 | semidirect |
| 128. C4 | #3993 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3993 | 2 |
| C4×C4⋊AGL(1,𝔽5) | 2 |
| C4×C8×D5 | 2 |
| #64893 | 2 |
| C4×#106 | 5 |