Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
495 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 495 conjugacy classes of subgroups — too many to draw. Only its 143 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×#1035)⋊C4 | C2 | direct (N × H) |
| 7. C22×#1035 | C4 | semidirect |
| 9. C22×C4×C25 | C4 | semidirect |
| 10. C22×Dic25 | C4 | semidirect |
| 12. C2×C4×D25 | C4 | semidirect |
| 25. C2×#1035 | C2×C4 | semidirect |
| 27. C2×C4×C25 | C2×C4 | semidirect |
| 29. C2×Dic25 | C2×C4 | semidirect |
| 62. C2×C25 | #95 | semidirect |
| 66. D25 | #95 | semidirect |
| 89. C25 | C2×#95 | semidirect |
| 115. C22×C4 | #1035 | semidirect |
| 139. C2×C4 | C2×#1035 | semidirect |
| 160. C2 | (C2×#1035)⋊C4 | 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×#1035)⋊C4 | 2 |
| C2×(C2×AGL(1,𝔽5))⋊C4 | 5 |