Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
441 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 441 conjugacy classes of subgroups — too many to draw. Only its 181 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×C4⋊C4×C25 | C2 | semidirect |
| 3. C4×C22⋊D25 | C2 | semidirect |
| 4. #11716488 | C2 | semidirect |
| 5. #11716455 | C2 | semidirect |
| 6. #11716454 | C2 | semidirect |
| 7. C4⋊C4×D25 | C2 | semidirect |
| 8. #11716449 | C2 | semidirect |
| 12. #87744 | C4 | semidirect |
| 30. C2×C4×C25 | C2×C4 | semidirect |
| 34. C22⋊D25 | C2×C4 | semidirect |
| 38. D100 | C2×C4 | semidirect |
| 40. C4×D25 | C2×C4 | semidirect |
| 41. Dic50 | C2×C4 | semidirect |
| 108. C2×C4⋊C4 | D25 | semidirect |
| 109. C25 | #520 | semidirect |
| 156. C2×C4 | C4×D25 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87744 | 2 |
| C2×C4⋊C4×C25 | 2 |
| C4×C22⋊D25 | 2 |
| #11716488 | 2 |
| #11716455 | 2 |
| #11716454 | 2 |
| C4⋊C4×D25 | 2 |
| #11716449 | 2 |
| #65838 | 5 |