Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
429 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 429 conjugacy classes of subgroups — too many to draw. Only its 101 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. C22×C4×D25 | C2 | semidirect |
| 3. C2×C22⋊C4×C25 | C2 | semidirect |
| 4. C2×C22⋊Dic25 | C2 | semidirect |
| 5. C2×#87720 | C2 | semidirect |
| 6. #11716379 | C2 | semidirect |
| 7. #11716379 | C2 | semidirect |
| 14. C2×C22⋊D25 | C4 | semidirect |
| 31. C23×C25 | C2×C4 | semidirect |
| 45. C2×C4×C25 | D4 | semidirect |
| 54. C2×Dic25 | C2×C4 | semidirect |
| 55. C2×Dic25 | D4 | semidirect |
| 84. C2×D25 | C22⋊C4 | semidirect |
| 152. C2×C22⋊C4 | D25 | semidirect |
| 155. C25 | #386 | semidirect |
| 220. C23 | C4×D25 | semidirect |
| 238. C2×C4 | C22⋊D25 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊D25 | 2 |
| C22×C4×D25 | 2 |
| C2×C22⋊C4×C25 | 2 |
| C2×C22⋊Dic25 | 2 |
| C2×#87720 | 2 |
| #11716379 | 2 |
| #65245 | 5 |