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×#87722 | C2 | semidirect |
| 3. C2×D200 | C2 | semidirect |
| 4. #11716457 | C2 | semidirect |
| 5. C25×#102 | C2 | semidirect |
| 6. #11716368 | C2 | semidirect |
| 7. #11716358 | C2 | semidirect |
| 15. C2×D100 | C22 | semidirect |
| 17. C2×C8×C25 | C22 | semidirect |
| 18. C4⋊C4×C25 | C22 | semidirect |
| 21. C2×#6014 | C22 | semidirect |
| 32. D4×C25 | D4 | semidirect |
| 41. D100 | D4 | semidirect |
| 66. C2×D25 | D8 | semidirect |
| 121. #102 | D25 | semidirect |
| 123. C25 | #447 | semidirect |
| 154. C2×C8 | C2×D25 | semidirect |
| 155. C4⋊C4 | C2×D25 | semidirect |
| 178. D4 | D100 | 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×#87722 | 2 |
| C2×D200 | 2 |
| #11716457 | 2 |
| C25×#102 | 2 |
| #11716368 | 2 |
| #11716358 | 2 |
| #65062 | 5 |