Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
241 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 241 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 9. C4⋊#1042 | C4 | semidirect |
| 11. D5⋊#168 | C4 | semidirect |
| 12. C52×C4⋊C4 | C4 | semidirect |
| 13. C5×C4⋊Dic5 | C4 | semidirect |
| 66. C5×C4⋊C4 | Dic5 | semidirect |
| 67. C5×C4⋊C4 | AGL(1,𝔽5) | semidirect |
| 70. C4⋊Dic5 | Dic5 | semidirect |
| 118. C52 | #340 | semidirect |
| 161. C4⋊C4 | #1042 | semidirect |
| 195. C5 | #64749 | semidirect |
| 196. C5 | #64874 | 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×D5⋊#168 | 2 |
| C5×D5×C4⋊C4 | 2 |
| #64874 | 5 |
| #64749 | 5 |