Finite Group DatabasebetaFinite Group DatabasebetaOrder 4000.
290 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 82 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. C22×AGL(1,ℤ/25) | C2 | semidirect |
| 3. C22⋊AGL(1,ℤ/25) | C2 | semidirect |
| 4. C4⋊AGL(1,ℤ/25) | C2 | semidirect |
| 5. C4×AGL(1,ℤ/25) | C2 | semidirect |
| 11. D4×5−1+2 | C4 | semidirect |
| 12. C22⋊(D25⋊C5) | C4 | semidirect |
| 13. C4⋊(D25⋊C5) | C4 | semidirect |
| 16. D4×#1035 | C5 | semidirect |
| 17. C22×5−1+2 | C2×C4 | semidirect |
| 20. C2×D25⋊C5 | C2×C4 | semidirect |
| 24. AGL(1,ℤ/25) | D4 | direct (N × H) |
| 25. C4×5−1+2 | C2×C4 | semidirect |
| 26. Dic25⋊C5 | C2×C4 | semidirect |
| 32. C22×#1035 | C2×C5 | semidirect |
| 34. C22⋊#1035 | C2×C5 | semidirect |
| 35. C4⋊#1035 | C2×C5 | semidirect |
| 36. C4×#1035 | C2×C5 | semidirect |
| 57. D4×C25 | C4×C5 | semidirect |
| 58. C22⋊D25 | C4×C5 | semidirect |
| 59. D100 | C4×C5 | semidirect |
| 63. 5−1+2 | C4×D4 | semidirect |
| 75. C22×C25 | C2×C4×C5 | semidirect |
| 78. C2×D25 | C2×C4×C5 | semidirect |
| 82. #1035 | C5×D4 | semidirect |
| 84. C4×C25 | C2×C4×C5 | semidirect |
| 85. Dic25 | C2×C4×C5 | semidirect |
| 129. C25 | C4×C5×D4 | semidirect |
| 168. D4 | AGL(1,ℤ/25) | direct (N × H) |
| 180. C22 | C2×AGL(1,ℤ/25) | semidirect |
| 185. C4 | C2×AGL(1,ℤ/25) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×AGL(1,ℤ/25) | 2 |
| D4×D25⋊C5 | 2 |
| C22⋊AGL(1,ℤ/25) | 2 |
| C4⋊AGL(1,ℤ/25) | 2 |
| C4×AGL(1,ℤ/25) | 2 |
| C5×D4×AGL(1,𝔽5) | 5 |
| D4×#1035 | 5 |