Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
240 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 15. C5×#107 | C4 | semidirect |
| 16. #3950 | C4 | semidirect |
| 17. #3939 | C4 | semidirect |
| 61. C5×C8 | C4⋊C4 | semidirect |
| 62. #168 | C4⋊C4 | semidirect |
| 71. #107 | AGL(1,𝔽5) | semidirect |
| 131. C8 | C4⋊AGL(1,𝔽5) | semidirect |
| 132. C5 | #1943 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3993 | 2 |
| C2×#3992 | 2 |
| #65712 | 2 |
| D5×#107 | 2 |
| #64874 | 2 |
| #1943 | 5 |