Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
323 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 323 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 12. C4×#1039 | C4 | semidirect |
| 13. C4×C5×Dic5 | C4 | semidirect |
| 14. Dic52 | C4 | semidirect |
| 15. Dic52 | C4 | semidirect |
| 78. C4×Dic5 | AGL(1,𝔽5) | semidirect |
| 127. C52 | #382 | semidirect |
| 199. C5 | #64939 | semidirect |
| 200. C5 | #65689 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87825 | 2 |
| C4×D5×Dic5 | 2 |
| #11716849 | 2 |
| C5×(C2×AGL(1,𝔽5))⋊C4 | 2 |
| (C2×AGL(1,𝔽5))⋊Dic5 | 2 |
| #65689 | 5 |
| #64939 | 5 |