Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
285 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 285 conjugacy classes of subgroups — too many to draw. Only its 63 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×C4×#1035 | C2 | semidirect |
| 6. (C2×#1035)⋊C4 | C2 | semidirect |
| 7. (C2×#1035)⋊C4 | C2 | semidirect |
| 19. C22⋊C4×C25 | C4 | semidirect |
| 20. C22⋊Dic25 | C4 | semidirect |
| 21. #87720 | C4 | semidirect |
| 22. #87720 | C4 | semidirect |
| 146. C25 | #388 | semidirect |
| 185. C22⋊C4 | #1035 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊#1035 | 2 |
| C2×C4⋊#1035 | 2 |
| C2×C4×#1035 | 2 |
| C22⋊C4×D25 | 2 |
| (C2×#1035)⋊C4 | 2 |
| #65700 | 5 |