Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
429 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 429 conjugacy classes of subgroups — too many to draw. Only its 121 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. C23×C4×C25 | C2 | semidirect |
| 3. C2×C22⋊Dic25 | C2 | semidirect |
| 4. C2×#87720 | C2 | semidirect |
| 5. #11716379 | C2 | semidirect |
| 13. C2×C22⋊D25 | C4 | semidirect |
| 29. C22×D25 | C2×C4 | semidirect |
| 33. C2×C4×C25 | D4 | semidirect |
| 40. C2×Dic25 | C2×C4 | semidirect |
| 50. C22×C25 | C22⋊C4 | semidirect |
| 107. C23×C4 | D25 | semidirect |
| 111. C25 | #386 | semidirect |
| 170. C2×C4 | C22⋊D25 | semidirect |
| 181. C22 | #87720 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×C25 | 2 |
| C22×C22⋊D25 | 2 |
| C2×C22⋊Dic25 | 2 |
| C2×#87720 | 2 |
| #11716379 | 2 |
| #65502 | 5 |