Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
195 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 195 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×M16×C25 | C2 | semidirect |
| 2. #11716492 | C2 | semidirect |
| 3. C2×D200 | C2 | semidirect |
| 4. #11716369 | C2 | semidirect |
| 5. #11716366 | C2 | semidirect |
| 27. C8×C25 | D4 | semidirect |
| 70. C2×M16 | D25 | semidirect |
| 74. C25 | #469 | semidirect |
| 109. C8 | C22⋊D25 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×C25 | 2 |
| #11716492 | 2 |
| C2×D200 | 2 |
| #11716369 | 2 |
| #11716366 | 2 |
| #65424 | 5 |