Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
357 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 357 conjugacy classes of subgroups — too many to draw. Only its 87 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. C2×C22⋊C4×C25 | C2 | semidirect |
| 3. C2×C22⋊Dic25 | C2 | semidirect |
| 4. C2×#87720 | C2 | semidirect |
| 5. C2×#87720 | C2 | semidirect |
| 6. C2×C4⋊Dic25 | C2 | semidirect |
| 7. #11716379 | C2 | semidirect |
| 44. C2×C4×C25 | D4 | semidirect |
| 149. C2×C22⋊C4 | D25 | semidirect |
| 151. C25 | #394 | semidirect |
| 232. 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 |
| C2×C22⋊C4×C25 | 2 |
| C2×C22⋊Dic25 | 2 |
| C2×#87720 | 2 |
| C2×C4⋊Dic25 | 2 |
| #11716379 | 2 |
| #65250 | 5 |