Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
311 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 311 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 5. C22×C4×C52 | C4 | semidirect |
| 6. C22×C5×Dic5 | C4 | semidirect |
| 8. C22⋊#1042 | C4 | semidirect |
| 50. C22×C4×C5 | Dic5 | semidirect |
| 51. C22×C4×C5 | AGL(1,𝔽5) | semidirect |
| 53. C22×Dic5 | Dic5 | semidirect |
| 101. C52 | #342 | semidirect |
| 141. C22×C4 | #1042 | semidirect |
| 179. C5 | #64746 | semidirect |
| 180. C5 | #64917 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊#1042 | 2 |
| C2×C5×#685 | 2 |
| #64917 | 5 |
| #64746 | 5 |