Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
297 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 297 conjugacy classes of subgroups — too many to draw. Only its 59 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. C2×D4×D25 | C2 | semidirect |
| 2. C2×D8×C25 | C2 | semidirect |
| 3. #11716500 | C2 | semidirect |
| 4. C2×#87722 | C2 | semidirect |
| 5. #11716381 | C2 | semidirect |
| 6. #11716369 | C2 | semidirect |
| 7. #11716368 | C2 | semidirect |
| 10. C2×D4×C25 | C22 | semidirect |
| 18. C2×C8×C25 | C22 | semidirect |
| 21. C4⋊Dic25 | C22 | semidirect |
| 22. C2×#6014 | C22 | semidirect |
| 34. D4×C25 | D4 | semidirect |
| 41. D100 | D4 | semidirect |
| 66. C2×D25 | D8 | semidirect |
| 118. C2×D8 | D25 | semidirect |
| 123. C25 | #447 | semidirect |
| 149. C2×D4 | C2×D25 | semidirect |
| 154. C2×C8 | C2×D25 | semidirect |
| 178. D4 | C22⋊D25 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×D25 | 2 |
| C2×D8×C25 | 2 |
| #11716500 | 2 |
| C2×#87722 | 2 |
| #11716381 | 2 |
| #11716369 | 2 |
| #11716368 | 2 |
| #65445 | 5 |