Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
387 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 387 conjugacy classes of subgroups — too many to draw. Only its 121 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×C42×C25 | C2 | semidirect |
| 3. C2×#87720 | C2 | semidirect |
| 4. C2×C4⋊Dic25 | C2 | semidirect |
| 11. C2×D100 | C4 | semidirect |
| 27. C2×C4×C25 | D4 | semidirect |
| 46. C4×C25 | C22⋊C4 | semidirect |
| 83. C2×C42 | D25 | semidirect |
| 84. C25 | #390 | semidirect |
| 127. C2×C4 | D100 | semidirect |
| 142. C4 | #87720 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D100 | 2 |
| C2×C42×C25 | 2 |
| C2×#87720 | 2 |
| C2×C4⋊Dic25 | 2 |
| #65228 | 5 |