Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
703 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 703 conjugacy classes of subgroups — too many to draw. Only its 174 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. #11717425 | C2 | semidirect |
| 3. C5×#4130 | C2 | semidirect |
| 4. D5×C22⋊AGL(1,𝔽5) | C2 | semidirect |
| 5. #11717337 | C2 | semidirect |
| 6. AGL(1,𝔽5)×D20 | C2 | semidirect |
| 8. C2×D5×AGL(1,𝔽5) | C22 | semidirect |
| 9. C2×C4⋊(C5⋊D5) | C4 | semidirect |
| 10. C2×C5×D20 | C4 | semidirect |
| 12. C2×#6038 | C4 | semidirect |
| 13. D5×D20 | C4 | semidirect |
| 14. D5×D20 | C4 | semidirect |
| 18. C4⋊#1042 | C22 | semidirect |
| 19. C4×#1042 | C22 | semidirect |
| 21. C5×C4⋊AGL(1,𝔽5) | C22 | semidirect |
| 22. C4×C5×AGL(1,𝔽5) | C22 | semidirect |
| 23. (C2×AGL(1,𝔽5))⋊D5 | C22 | semidirect |
| 26. C22×C5⋊D5 | C2×C4 | semidirect |
| 27. C22×C5×D5 | C2×C4 | semidirect |
| 30. C2×D52 | C2×C4 | semidirect |
| 35. C2×C4×C52 | C2×C4 | semidirect |
| 36. C4⋊(C5⋊D5) | C2×C4 | semidirect |
| 37. C4⋊(C5⋊D5) | C2×C4 | semidirect |
| 38. C2×C5×Dic5 | C2×C4 | semidirect |
| 39. C5×D20 | C2×C4 | semidirect |
| 40. C5×D20 | C2×C4 | semidirect |
| 41. C4×C5×D5 | C2×C4 | semidirect |
| 42. C4×C5×D5 | C2×C4 | semidirect |
| 45. #6038 | C2×C4 | semidirect |
| 46. #6038 | C2×C4 | semidirect |
| 53. #4130 | D5 | semidirect |
| 93. C2×D20 | AGL(1,𝔽5) | semidirect |
| 100. C4⋊AGL(1,𝔽5) | C2×D5 | semidirect |
| 102. C4×AGL(1,𝔽5) | C2×D5 | semidirect |
| 128. C22×D5 | C2×AGL(1,𝔽5) | semidirect |
| 142. C2×C4×C5 | C4×D5 | semidirect |
| 143. C2×C4×C5 | C2×AGL(1,𝔽5) | semidirect |
| 147. C2×Dic5 | C4×D5 | semidirect |
| 156. D20 | C2×AGL(1,𝔽5) | semidirect |
| 157. D20 | C2×AGL(1,𝔽5) | semidirect |
| 159. C4×D5 | C4×D5 | semidirect |
| 160. C4×D5 | C4×D5 | semidirect |
| 169. C52 | #518 | semidirect |
| 259. C2×C4 | D5×AGL(1,𝔽5) | semidirect |
| 261. C5 | #65855 | semidirect |
| 262. C5 | #66258 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×D20 | 2 |
| #11717425 | 2 |
| C5×#4130 | 2 |
| D5×C22⋊AGL(1,𝔽5) | 2 |
| #11717337 | 2 |
| AGL(1,𝔽5)×D20 | 2 |
| #66258 | 5 |
| #65855 | 5 |