Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
447 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 447 conjugacy classes of subgroups — too many to draw. Only its 213 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 |
|---|---|---|
| 6. #11716449 | C2 | direct (N × H) |
| 12. C2×Dic50 | C4 | semidirect |
| 26. C2×Dic25 | Q8 | semidirect |
| 30. Dic50 | C2×C4 | semidirect |
| 45. Dic25 | C2×Q8 | semidirect |
| 58. C2×C25 | C4×Q8 | semidirect |
| 80. C25 | C2×C4×Q8 | semidirect |
| 127. C2 | #11716449 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic50 | 2 |
| C2×C4⋊C4×C25 | 2 |
| C2×#87718 | 2 |
| C2×C4×Dic25 | 2 |
| #11716449 | 2 |
| C2×#4033 | 5 |