Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
354 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 123 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. C4×Q8×C25 | C2 | semidirect |
| 2. #11716509 | C2 | semidirect |
| 3. #11716456 | C2 | semidirect |
| 4. #11716455 | C2 | semidirect |
| 5. #11716437 | C2 | semidirect |
| 7. C4×D100 | C2 | semidirect |
| 8. C4×Dic50 | C2 | semidirect |
| 99. C4×Q8 | D25 | semidirect |
| 102. C25 | #559 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Q8×C25 | 2 |
| #11716509 | 2 |
| #11716456 | 2 |
| #11716455 | 2 |
| #11716437 | 2 |
| #11716436 | 2 |
| C4×D100 | 2 |
| C4×Dic50 | 2 |
| #65919 | 5 |