Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
353 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 353 conjugacy classes of subgroups — too many to draw. Only its 106 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 |
|---|---|---|
| 14. C4⋊#1039 | C4 | semidirect |
| 15. C5×C4⋊Dic5 | C4 | semidirect |
| 16. #87780 | C4 | semidirect |
| 57. C4×C52 | C4⋊C4 | semidirect |
| 60. C5×Dic5 | C4⋊C4 | semidirect |
| 81. C4⋊Dic5 | AGL(1,𝔽5) | semidirect |
| 135. C52 | #389 | semidirect |
| 159. C4×C5 | #683 | semidirect |
| 160. C4×C5 | C4⋊AGL(1,𝔽5) | semidirect |
| 166. Dic5 | #683 | semidirect |
| 214. C5 | #65217 | semidirect |
| 215. C5 | #65712 | semidirect |
| 229. C4 | #87825 | 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×C4×C5×AGL(1,𝔽5) | 2 |
| C2×#87825 | 2 |
| D5×C4⋊Dic5 | 2 |
| (C2×AGL(1,𝔽5))⋊Dic5 | 2 |
| #65712 | 5 |
| #65217 | 5 |