Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
147 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 147 conjugacy classes of subgroups — too many to draw. Only its 53 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×D8×C25 | C2 | semidirect |
| 2. C2×D200 | C2 | semidirect |
| 3. #11716374 | C2 | direct (N × H) |
| 4. C2×#87707 | C2 | semidirect |
| 8. D8×C25 | C22 | semidirect |
| 11. D200 | C22 | semidirect |
| 12. #87707 | C22 | semidirect |
| 44. C2×C25 | D16 | semidirect |
| 57. C2×D8 | D25 | semidirect |
| 60. C25 | C2×D16 | semidirect |
| 73. D8 | C2×D25 | semidirect |
| 99. C2 | #11716374 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×C25 | 2 |
| C2×D200 | 2 |
| #11716374 | 2 |
| C2×#87707 | 2 |
| C2×#3958 | 5 |