Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
233 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 233 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 |
|---|---|---|
| 8. C4×#1042 | C4 | semidirect |
| 10. #87849 | C4 | semidirect |
| 11. C52×C4⋊C4 | C4 | semidirect |
| 13. C5×C4⋊Dic5 | C4 | semidirect |
| 59. C5×C4⋊C4 | Dic5 | semidirect |
| 60. C5×C4⋊C4 | AGL(1,𝔽5) | semidirect |
| 64. C4⋊Dic5 | Dic5 | semidirect |
| 108. C52 | #339 | semidirect |
| 143. C4⋊C4 | #1042 | semidirect |
| 175. C5 | #64752 | semidirect |
| 176. C5 | #64875 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#1042 | 2 |
| C2×#87849 | 2 |
| C5×#4038 | 2 |
| #64875 | 5 |
| #64752 | 5 |