Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
220 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 88 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. #3996 | C4 | semidirect |
| 12. #3995 | C4 | semidirect |
| 17. C5×#108 | C4 | semidirect |
| 18. #3954 | C4 | semidirect |
| 19. #3951 | C4 | semidirect |
| 72. #108 | AGL(1,𝔽5) | semidirect |
| 127. C5 | #1778 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| M16×AGL(1,𝔽5) | 2 |
| D5⋊#108 | 2 |
| C2×#3992 | 2 |
| D5×#108 | 2 |
| #64901 | 2 |
| #1778 | 5 |