Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
348 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 104 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 |
|---|---|---|
| 4. C2×#3992 | C2 | semidirect |
| 5. C2×C8×AGL(1,𝔽5) | C2 | semidirect |
| 6. (C2×AGL(1,𝔽5))⋊C8 | C2 | semidirect |
| 7. (C2×AGL(1,𝔽5))⋊C8 | C2 | semidirect |
| 14. C2×C5×M16 | C4 | semidirect |
| 15. C2×#681 | C4 | semidirect |
| 18. C2×#676 | C4 | semidirect |
| 19. C2×#676 | C4 | semidirect |
| 22. C22⋊#170 | C4 | semidirect |
| 24. #4003 | C4 | semidirect |
| 83. C2×AGL(1,𝔽5) | M16 | semidirect |
| 105. C5×C8 | C22⋊C4 | semidirect |
| 107. #168 | C22⋊C4 | semidirect |
| 114. C2×M16 | AGL(1,𝔽5) | semidirect |
| 227. C8 | C22⋊AGL(1,𝔽5) | semidirect |
| 228. C5 | #1753 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×M16 | 2 |
| C4×C22⋊AGL(1,𝔽5) | 2 |
| D5⋊(C22⋊C8) | 2 |
| C2×#3992 | 2 |
| C2×C8×AGL(1,𝔽5) | 2 |
| (C2×AGL(1,𝔽5))⋊C8 | 2 |
| #1753 | 5 |