Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
279 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 279 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. C2×M16×C25 | C2 | semidirect |
| 3. C2×#87716 | C2 | semidirect |
| 4. #11716372 | C2 | direct (N × H) |
| 14. M16×C25 | C22 | semidirect |
| 17. #87716 | C22 | semidirect |
| 70. C2×C25 | #100 | semidirect |
| 92. C2×M16 | D25 | semidirect |
| 94. C25 | C2×#100 | semidirect |
| 118. M16 | C2×D25 | semidirect |
| 159. C2 | #11716372 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D100 | 2 |
| C2×M16×C25 | 2 |
| C2×#87716 | 2 |
| #11716372 | 2 |
| C2×#3955 | 5 |