Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
408 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 74 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 |
|---|---|---|
| 2. C2×#4011 | C2 | semidirect |
| 3. #65765 | C2 | semidirect |
| 4. C4×C22⋊AGL(1,𝔽5) | C2 | semidirect |
| 5. C22×C5×D4 | C4 | semidirect |
| 12. C2×C22⋊Dic5 | C4 | semidirect |
| 17. C2×C4⋊Dic5 | C4 | semidirect |
| 43. C22⋊AGL(1,𝔽5) | D4 | semidirect |
| 89. C22×D4 | AGL(1,𝔽5) | semidirect |
| 124. C4×C5 | #99 | semidirect |
| 198. C5 | #1964 | semidirect |
| 222. C4 | #4011 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4084 | 2 |
| C2×#4011 | 2 |
| #65765 | 2 |
| C4×C22⋊AGL(1,𝔽5) | 2 |
| #1964 | 5 |