Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
344 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 96 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. C4×C5×#168 | C2 | semidirect |
| 3. #11716613 | C2 | semidirect |
| 23. C4×C5⋊D5 | C8 | semidirect |
| 30. C4×#168 | D5 | semidirect |
| 88. C52 | #431 | semidirect |
| 137. C5 | #64974 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C42×C5⋊D5 | 2 |
| C4×C5×#168 | 2 |
| #11716613 | 2 |
| #11716598 | 2 |
| #64974 | 5 |