Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
285 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 285 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 2. C25×#117 | C2 | semidirect |
| 3. C2×#87716 | C2 | semidirect |
| 4. #11716358 | C2 | semidirect |
| 9. C2×D100 | C4 | semidirect |
| 11. C4⋊C4×C25 | C22 | semidirect |
| 15. C2×#6014 | C22 | semidirect |
| 75. #117 | D25 | semidirect |
| 77. C25 | #418 | semidirect |
| 96. C4⋊C4 | C2×D25 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D100 | 2 |
| C25×#117 | 2 |
| C2×#87716 | 2 |
| #11716358 | 2 |
| #65290 | 5 |