Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
303 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 303 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 2. C22×C8×C25 | C2 | semidirect |
| 3. C22×#6014 | C2 | semidirect |
| 4. #11716368 | C2 | direct (N × H) |
| 13. C2×C8×C25 | C22 | semidirect |
| 15. C2×#6014 | C22 | semidirect |
| 20. C22×D25 | C8 | semidirect |
| 44. C2×D25 | C2×C8 | semidirect |
| 61. C2×C25 | C22⋊C8 | semidirect |
| 84. C22×C8 | D25 | semidirect |
| 86. C25 | C2×C22⋊C8 | semidirect |
| 109. C2×C8 | C2×D25 | semidirect |
| 145. C2 | #11716368 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D25 | 2 |
| C22×C8×C25 | 2 |
| C22×#6014 | 2 |
| #11716368 | 2 |
| C2×#3952 | 5 |