Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
568 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 4. #11716776 | C2 | semidirect |
| 8. C22×C5×Dic5 | C4 | semidirect |
| 11. C2×#6036 | C4 | semidirect |
| 55. C22×Dic5 | AGL(1,𝔽5) | semidirect |
| 99. C52 | #381 | semidirect |
| 163. C5 | #65764 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6036 | 2 |
| C2×C22⋊#1044 | 2 |
| C2×C22⋊#1043 | 2 |
| #11716776 | 2 |
| #65764 | 5 |