Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
237 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 237 conjugacy classes of subgroups — too many to draw. Only its 85 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. C2×#87716 | C2 | semidirect |
| 4. #11716368 | C2 | semidirect |
| 76. C22×C8 | D25 | semidirect |
| 78. C25 | #408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87744 | 2 |
| C22×C8×C25 | 2 |
| C2×#87716 | 2 |
| #11716368 | 2 |
| #65399 | 5 |