Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
165 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 165 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 14. #87723 | C4 | direct (N × H) |
| 45. C4×C25 | Q16 | semidirect |
| 86. C25 | C4×Q16 | semidirect |
| 131. C4 | #87723 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Q8×C25 | 2 |
| C2×#87723 | 2 |
| C4×Dic50 | 2 |
| #11716384 | 2 |
| #11716357 | 2 |
| #11716355 | 2 |
| C4×#6014 | 2 |
| C4×#689 | 5 |