Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
285 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 285 conjugacy classes of subgroups — too many to draw. Only its 89 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. C2×M16×C25 | C2 | semidirect |
| 3. C2×#87716 | C2 | semidirect |
| 4. #11716368 | C2 | semidirect |
| 13. C2×C8×C25 | C22 | semidirect |
| 15. C2×#6014 | C22 | semidirect |
| 42. C2×D25 | M16 | semidirect |
| 80. C2×M16 | D25 | semidirect |
| 82. C25 | #407 | semidirect |
| 104. C2×C8 | C2×D25 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D25 | 2 |
| C2×M16×C25 | 2 |
| C2×#87716 | 2 |
| #11716368 | 2 |
| #65415 | 5 |