Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
872 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 872 conjugacy classes of subgroups — too many to draw. Only its 126 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 |
|---|---|---|
| 3. #11716874 | C2 | semidirect |
| 6. C22×C4×C52 | C4 | semidirect |
| 7. C22×#1039 | C4 | semidirect |
| 9. C2×C4×C5⋊D5 | C4 | semidirect |
| 42. C22×C4×C5 | AGL(1,𝔽5) | semidirect |
| 70. C52 | #381 | semidirect |
| 88. C22×C4 | #1043 | semidirect |
| 108. C5 | #65764 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×C5⋊D5 | 2 |
| C2×C22⋊#1043 | 2 |
| #11716874 | 2 |
| #65764 | 5 |