Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
291 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 291 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 9. C4⋊#1035 | C4 | direct (N × H) |
| 11. C42×C25 | C4 | semidirect |
| 12. C4×Dic25 | C4 | semidirect |
| 13. C4×Dic25 | C4 | semidirect |
| 14. C4×Dic25 | C4 | semidirect |
| 41. C4×C25 | C42 | semidirect |
| 42. C4×C25 | C4⋊C4 | semidirect |
| 44. Dic25 | C42 | semidirect |
| 45. Dic25 | C4⋊C4 | semidirect |
| 80. C25 | C4×C4⋊C4 | semidirect |
| 102. C42 | #1035 | semidirect |
| 133. C4 | C4×#1035 | semidirect |
| 134. C4 | C4⋊#1035 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊#1035 | 2 |
| C2×C4×#1035 | 2 |
| C42×D25 | 2 |
| (C2×#1035)⋊C4 | 2 |
| C4×C4⋊AGL(1,𝔽5) | 5 |