Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
201 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 201 conjugacy classes of subgroups — too many to draw. Only its 51 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 |
|---|---|---|
| 1. D4×#1035 | C2 | semidirect |
| 3. #11716424 | C2 | semidirect |
| 4. #11716412 | C2 | semidirect |
| 5. C8×#1035 | C2 | semidirect |
| 12. D8×C25 | C4 | semidirect |
| 13. #87722 | C4 | semidirect |
| 14. D200 | C4 | semidirect |
| 22. D4×C25 | C2×C4 | semidirect |
| 24. D100 | C2×C4 | semidirect |
| 27. C8×C25 | C2×C4 | semidirect |
| 28. #6014 | C2×C4 | semidirect |
| 41. #1035 | D8 | direct (N × H) |
| 77. C25 | C4×D8 | semidirect |
| 92. D8 | #1035 | direct (N × H) |
| 106. D4 | C2×#1035 | semidirect |
| 114. C8 | C2×#1035 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×#1035 | 2 |
| D8×D25 | 2 |
| #11716424 | 2 |
| #11716412 | 2 |
| C8×#1035 | 2 |
| D8×AGL(1,𝔽5) | 5 |