Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
219 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 219 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 4. #11716410 | C2 | direct (N × H) |
| 7. C2×#6016 | C4 | semidirect |
| 10. D25⋊C8 | C4 | semidirect |
| 12. C2×C8×C25 | C4 | semidirect |
| 13. C2×#6014 | C4 | semidirect |
| 14. C8×D25 | C4 | semidirect |
| 26. #6016 | C2×C4 | semidirect |
| 27. C8×C25 | C2×C4 | semidirect |
| 28. #6014 | C2×C4 | semidirect |
| 54. C2×C25 | #97 | semidirect |
| 56. D25 | #97 | semidirect |
| 74. C25 | C2×#97 | semidirect |
| 92. C2×C8 | #1035 | semidirect |
| 110. C8 | C2×#1035 | semidirect |
| 123. C2 | #11716410 | 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×D25⋊C8 | 2 |
| C2×C8×D25 | 2 |
| #11716410 | 2 |
| C2×#3992 | 5 |