Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
327 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 327 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. C2×C4⋊C4×C25 | C2 | semidirect |
| 3. #11716491 | C2 | semidirect |
| 4. C4×C22⋊D25 | C2 | semidirect |
| 5. #11716486 | C2 | semidirect |
| 6. #11716460 | C2 | semidirect |
| 7. #11716458 | C2 | semidirect |
| 8. #11716456 | C2 | semidirect |
| 9. #11716451 | C2 | semidirect |
| 122. C2×C4⋊C4 | D25 | semidirect |
| 123. C25 | #539 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊C4×C25 | 2 |
| #11716492 | 2 |
| #11716491 | 2 |
| C4×C22⋊D25 | 2 |
| #11716486 | 2 |
| #11716460 | 2 |
| #11716458 | 2 |
| #11716456 | 2 |
| #11716451 | 2 |
| #65849 | 5 |