Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
371 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 371 conjugacy classes of subgroups — too many to draw. Only its 125 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×#1042 | C4 | semidirect |
| 8. C42×C52 | C4 | semidirect |
| 9. C4×C5×Dic5 | C4 | semidirect |
| 10. C4×C5×Dic5 | C4 | semidirect |
| 46. C42×C5 | Dic5 | semidirect |
| 47. C42×C5 | AGL(1,𝔽5) | semidirect |
| 49. C4×Dic5 | Dic5 | semidirect |
| 50. C4×Dic5 | Dic5 | semidirect |
| 78. C52 | #376 | semidirect |
| 104. C42 | #1042 | semidirect |
| 123. C5 | #65221 | semidirect |
| 124. C5 | #65686 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#1042 | 2 |
| C42×C5×D5 | 2 |
| #11716849 | 2 |
| #65686 | 5 |
| #65221 | 5 |