Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
380 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 380 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 |
|---|---|---|
| 3. #65765 | C2 | semidirect |
| 4. #64917 | C2 | semidirect |
| 6. C23×Dic5 | C4 | semidirect |
| 10. C2×C5×C22⋊C4 | C4 | semidirect |
| 12. C2×#683 | C4 | semidirect |
| 13. C2×C4×Dic5 | C4 | semidirect |
| 53. C23×C5 | C4⋊C4 | semidirect |
| 79. C2×Dic5 | C4⋊C4 | semidirect |
| 91. C2×C22⋊C4 | AGL(1,𝔽5) | semidirect |
| 118. Dic5 | #99 | semidirect |
| 163. C23 | C4⋊AGL(1,𝔽5) | semidirect |
| 186. C5 | #1799 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4027 | 2 |
| C2×#4011 | 2 |
| #65765 | 2 |
| #64917 | 2 |
| #1799 | 5 |