Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
387 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 387 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 |
|---|---|---|
| 3. C2×C4×#1035 | C2 | semidirect |
| 4. (C2×#1035)⋊C4 | C2 | semidirect |
| 7. C22×C4×C25 | C4 | semidirect |
| 8. C22×Dic25 | C4 | semidirect |
| 10. C2×C4×D25 | C4 | semidirect |
| 11. C2×C4×D25 | C4 | semidirect |
| 14. C22⋊#1035 | C4 | direct (N × H) |
| 25. C2×#1035 | C2×C4 | semidirect |
| 42. C22×C25 | C42 | semidirect |
| 47. C2×D25 | C42 | semidirect |
| 53. C4×C25 | C22⋊C4 | semidirect |
| 55. Dic25 | C22⋊C4 | semidirect |
| 97. C25 | C4×C22⋊C4 | semidirect |
| 122. C22×C4 | #1035 | semidirect |
| 160. C22 | C4×#1035 | semidirect |
| 166. C4 | C22⋊#1035 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D25 | 2 |
| C2×C22⋊#1035 | 2 |
| C2×C4×#1035 | 2 |
| (C2×#1035)⋊C4 | 2 |
| C4×C22⋊AGL(1,𝔽5) | 5 |