Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
201 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 201 conjugacy classes of subgroups — too many to draw. Only its 73 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. C4×D4×C25 | C2 | semidirect |
| 3. C4×D100 | C2 | semidirect |
| 4. #11716381 | C2 | semidirect |
| 5. #11716358 | C2 | semidirect |
| 6. #11716355 | C2 | semidirect |
| 7. C4×#6014 | C2 | semidirect |
| 15. #87722 | C4 | direct (N × H) |
| 24. D4×C25 | C2×C4 | semidirect |
| 32. D100 | C2×C4 | semidirect |
| 35. #6014 | C2×C4 | semidirect |
| 52. C4×C25 | D8 | semidirect |
| 91. C4×D4 | D25 | semidirect |
| 96. C25 | C4×D8 | semidirect |
| 132. D4 | C4×D25 | semidirect |
| 153. C4 | #87722 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D4×C25 | 2 |
| C2×#87722 | 2 |
| C4×D100 | 2 |
| #11716381 | 2 |
| #11716358 | 2 |
| #11716355 | 2 |
| C4×#6014 | 2 |
| C4×#686 | 5 |