Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
403 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 403 conjugacy classes of subgroups — too many to draw. Only its 118 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 |
|---|---|---|
| 11. #87825 | C4 | semidirect |
| 13. C4×#1039 | C4 | semidirect |
| 14. C4×C5×Dic5 | C4 | semidirect |
| 15. Dic52 | C4 | semidirect |
| 16. Dic52 | C4 | semidirect |
| 54. #1039 | C42 | semidirect |
| 55. #1039 | C4⋊C4 | semidirect |
| 57. C5×Dic5 | C42 | semidirect |
| 58. C5×Dic5 | C4⋊C4 | semidirect |
| 81. C4×Dic5 | AGL(1,𝔽5) | semidirect |
| 130. C52 | C4×C4⋊C4 | semidirect |
| 159. Dic5 | C4×AGL(1,𝔽5) | semidirect |
| 160. Dic5 | C4⋊AGL(1,𝔽5) | semidirect |
| 203. C5 | #64938 | semidirect |
| 204. C5 | C4×C4⋊AGL(1,𝔽5) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87825 | 2 |
| C2×Dic5×AGL(1,𝔽5) | 2 |
| C4×D5×Dic5 | 2 |
| #11716849 | 2 |
| C5×(C2×AGL(1,𝔽5))⋊C4 | 2 |
| C4×C4⋊AGL(1,𝔽5) | 5 |
| #64938 | 5 |