Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
239 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 239 conjugacy classes of subgroups — too many to draw. Only its 84 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. C5×C4⋊AGL(1,𝔽5) | C4 | semidirect |
| 11. C2×#6029 | C4 | semidirect |
| 12. C2×C5×#168 | C4 | semidirect |
| 60. C4⋊AGL(1,𝔽5) | Dic5 | semidirect |
| 71. C2×#168 | AGL(1,𝔽5) | semidirect |
| 117. C52 | #340 | semidirect |
| 191. C5 | #64749 | semidirect |
| 192. C5 | #64893 | 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×C5×C4⋊AGL(1,𝔽5) | 2 |
| C2×D5×#168 | 2 |
| #64893 | 5 |
| #64749 | 5 |