Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
772 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 772 conjugacy classes of subgroups — too many to draw. Only its 202 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×#4130 | C2 | semidirect |
| 3. C2×D5⋊M16 | C2 | semidirect |
| 4. #65784 | C2 | direct (N × H) |
| 5. C2×#4010 | C2 | semidirect |
| 6. C22×C5×Q8 | C4 | semidirect |
| 11. C2×#713 | C4 | semidirect |
| 12. C2×#713 | C4 | semidirect |
| 16. C22×D20 | C4 | semidirect |
| 22. #4130 | C22 | semidirect |
| 24. C2×C4×AGL(1,𝔽5) | C22 | semidirect |
| 26. D5⋊M16 | C22 | semidirect |
| 27. C2×#700 | C22 | semidirect |
| 29. #4010 | C22 | semidirect |
| 37. C2×C5×Q8 | C2×C4 | semidirect |
| 49. #713 | C2×C4 | semidirect |
| 58. C2×D20 | C2×C4 | semidirect |
| 76. C4×AGL(1,𝔽5) | C23 | semidirect |
| 78. #700 | C23 | semidirect |
| 137. C22×Q8 | AGL(1,𝔽5) | semidirect |
| 189. C2×Q8 | C2×AGL(1,𝔽5) | semidirect |
| 224. C2×C5 | #421 | semidirect |
| 274. C5 | C2×#421 | semidirect |
| 301. C2 | #65784 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#713 | 2 |
| C2×#4130 | 2 |
| C2×D5⋊M16 | 2 |
| #65784 | 2 |
| C2×#4010 | 2 |
| C2×#421 | 5 |