Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
324 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 117 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. #11716508 | C2 | semidirect |
| 4. #11716458 | C2 | semidirect |
| 6. #11716456 | C2 | semidirect |
| 7. #11716450 | C2 | semidirect |
| 8. #11716438 | C2 | semidirect |
| 9. #11716437 | C2 | semidirect |
| 10. C4×D100 | C2 | semidirect |
| 11. #11716434 | C2 | semidirect |
| 134. C4×Q8 | D25 | semidirect |
| 137. C25 | #542 | 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 |
| #11716508 | 2 |
| #11716458 | 2 |
| #11716457 | 2 |
| #11716456 | 2 |
| #11716450 | 2 |
| #11716438 | 2 |
| #11716437 | 2 |
| C4×D100 | 2 |
| #11716434 | 2 |
| #65916 | 5 |