Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
328 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 55 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 |
|---|---|---|
| 8. #87863 | C4 | semidirect |
| 10. C4×#1043 | C4 | semidirect |
| 11. C5×C4⋊Dic5 | C4 | semidirect |
| 53. C4⋊Dic5 | AGL(1,𝔽5) | semidirect |
| 85. C52 | #339 | semidirect |
| 138. C5 | #64875 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87863 | 2 |
| C2×C4×#1043 | 2 |
| #11716967 | 2 |
| #64875 | 5 |