Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
652 conjugacy classes of subgroups; only the 182 normal subgroups are shown.
This group has 652 conjugacy classes of subgroups — too many to draw. Only its 182 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 |
|---|---|---|
| 1. C2×Q8×AGL(1,𝔽5) | C2 | semidirect |
| 4. (C2×AGL(1,𝔽5))⋊Q8 | C2 | semidirect |
| 6. #65700 | C2 | semidirect |
| 7. C22⋊C4×AGL(1,𝔽5) | C2 | semidirect |
| 8. #65689 | C2 | semidirect |
| 9. C42×AGL(1,𝔽5) | C2 | semidirect |
| 25. C5×#124 | C4 | semidirect |
| 26. #4093 | C4 | semidirect |
| 27. #4082 | C4 | semidirect |
| 28. #4031 | C4 | semidirect |
| 30. #4021 | C4 | semidirect |
| 43. C2×C5×Q8 | C2×C4 | semidirect |
| 54. C2×Dic10 | C2×C4 | semidirect |
| 55. C2×Dic10 | C2×C4 | semidirect |
| 66. C5×C22⋊C4 | C2×C4 | semidirect |
| 67. C42×C5 | C2×C4 | semidirect |
| 68. C22⋊Dic5 | C2×C4 | semidirect |
| 69. #685 | C2×C4 | semidirect |
| 70. #685 | C2×C4 | semidirect |
| 71. C4×Dic5 | C2×C4 | semidirect |
| 72. C4×Dic5 | C2×C4 | semidirect |
| 126. #124 | AGL(1,𝔽5) | direct (N × H) |
| 159. AGL(1,𝔽5) | #124 | direct (N × H) |
| 171. C2×Q8 | C2×AGL(1,𝔽5) | semidirect |
| 195. C22⋊C4 | C2×AGL(1,𝔽5) | semidirect |
| 203. C42 | C2×AGL(1,𝔽5) | semidirect |
| 248. C5 | C4×#124 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×AGL(1,𝔽5) | 2 |
| C2×D4×AGL(1,𝔽5) | 2 |
| D5×#124 | 2 |
| (C2×AGL(1,𝔽5))⋊Q8 | 2 |
| #65780 | 2 |
| #65700 | 2 |
| C22⋊C4×AGL(1,𝔽5) | 2 |
| #65689 | 2 |
| C42×AGL(1,𝔽5) | 2 |
| C4×#124 | 5 |