Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
447 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 447 conjugacy classes of subgroups — too many to draw. Only its 175 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 |
|---|---|---|
| 2. Q8×#1035 | C2 | direct (N × H) |
| 7. C2×Q8×C25 | C4 | semidirect |
| 8. Q8×D25 | C4 | semidirect |
| 11. C2×Dic50 | C4 | semidirect |
| 17. C2×#1035 | Q8 | direct (N × H) |
| 20. Q8×C25 | C2×C4 | semidirect |
| 25. Dic50 | C2×C4 | semidirect |
| 36. #1035 | C2×Q8 | direct (N × H) |
| 49. C2×C25 | C4×Q8 | semidirect |
| 51. D25 | C4×Q8 | semidirect |
| 69. C25 | C2×C4×Q8 | semidirect |
| 82. C2×Q8 | #1035 | direct (N × H) |
| 95. Q8 | C2×#1035 | direct (N × H) |
| 117. C2 | Q8×#1035 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×D25 | 2 |
| Q8×#1035 | 2 |
| C2×C4⋊#1035 | 2 |
| C2×C4×#1035 | 2 |
| C2×Q8×AGL(1,𝔽5) | 5 |