Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
297 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 297 conjugacy classes of subgroups — too many to draw. Only its 71 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. C22×D4×C25 | C2 | semidirect |
| 2. C2×#87722 | C2 | semidirect |
| 3. #11716492 | C2 | semidirect |
| 4. #11716381 | C2 | semidirect |
| 5. C22⋊#6014 | C2 | semidirect |
| 12. C2×D100 | C22 | semidirect |
| 15. C4⋊Dic25 | C22 | semidirect |
| 16. C2×#6014 | C22 | semidirect |
| 26. D4×C25 | D4 | semidirect |
| 45. C22×C25 | D8 | semidirect |
| 87. C22×D4 | D25 | semidirect |
| 92. C25 | #447 | semidirect |
| 134. D4 | C22⋊D25 | semidirect |
| 150. C22 | #87722 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D4×C25 | 2 |
| C2×#87722 | 2 |
| #11716492 | 2 |
| #11716381 | 2 |
| C22⋊#6014 | 2 |
| #65506 | 5 |