Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
371 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 371 conjugacy classes of subgroups — too many to draw. Only its 152 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 |
|---|---|---|
| 7. C4×C5×AGL(1,𝔽5) | C4 | semidirect |
| 8. C42×C52 | C4 | semidirect |
| 9. C4×C5×Dic5 | C4 | semidirect |
| 10. C4×C5×Dic5 | C4 | semidirect |
| 11. #65686 | C5 | direct (N × H) |
| 42. C4×AGL(1,𝔽5) | C4×C5 | semidirect |
| 47. C42×C5 | C4×C5 | semidirect |
| 48. C42×C5 | AGL(1,𝔽5) | semidirect |
| 49. C4×Dic5 | C4×C5 | semidirect |
| 50. C4×Dic5 | C4×C5 | semidirect |
| 78. C52 | #376 | semidirect |
| 104. C42 | C5×AGL(1,𝔽5) | semidirect |
| 123. C5 | C5×#376 | semidirect |
| 124. C5 | #65686 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C5×AGL(1,𝔽5) | 2 |
| C42×C5×D5 | 2 |
| C5×(C2×AGL(1,𝔽5))⋊C4 | 2 |
| #65686 | 5 |
| C5×#376 | 5 |