Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
627 conjugacy classes of subgroups; only the 223 normal subgroups are shown.
This group has 627 conjugacy classes of subgroups — too many to draw. Only its 223 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 |
|---|---|---|
| 3. C2×C4⋊#1035 | C2 | direct (N × H) |
| 7. C22×C4×C25 | C4 | semidirect |
| 8. C22×Dic25 | C4 | semidirect |
| 9. C2×C4×D25 | C4 | semidirect |
| 11. C4⋊#1035 | C22 | direct (N × H) |
| 20. C2×C4×C25 | C2×C4 | semidirect |
| 21. C2×Dic25 | C2×C4 | semidirect |
| 22. C4×D25 | C2×C4 | semidirect |
| 27. C22×C25 | C4⋊C4 | semidirect |
| 29. C2×D25 | C4⋊C4 | semidirect |
| 35. C4×C25 | C22×C4 | semidirect |
| 36. Dic25 | C22×C4 | semidirect |
| 46. C2×C25 | C2×C4⋊C4 | semidirect |
| 48. D25 | C2×C4⋊C4 | semidirect |
| 65. C25 | C22×C4⋊C4 | semidirect |
| 82. C22×C4 | #1035 | semidirect |
| 99. C2×C4 | C2×#1035 | semidirect |
| 106. C22 | C4⋊#1035 | direct (N × H) |
| 110. C4 | C22×#1035 | semidirect |
| 114. C2 | C2×C4⋊#1035 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#1035 | 2 |
| C22×C4×D25 | 2 |
| C2×C4⋊#1035 | 2 |
| C22×C4⋊AGL(1,𝔽5) | 5 |