Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
266 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 2. C5×#4034 | C2 | semidirect |
| 5. C5×#3950 | C2 | semidirect |
| 6. C5×#3946 | C2 | semidirect |
| 7. C5×#3939 | C2 | semidirect |
| 20. #65048 | C5 | direct (N × H) |
| 23. C52×D4 | Q8 | semidirect |
| 37. #4034 | C2×C5 | semidirect |
| 46. #3950 | C2×C5 | semidirect |
| 47. #3946 | C2×C5 | semidirect |
| 48. #3939 | C2×C5 | semidirect |
| 98. C5×D4 | Dic10 | semidirect |
| 99. C5×D4 | C5×Q8 | semidirect |
| 129. C52 | #474 | semidirect |
| 185. D4 | C5×Dic10 | semidirect |
| 196. C5 | #65048 | direct (N × H) |
| 197. C5 | C5×#474 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×D4×Dic5 | 2 |
| C5×#4034 | 2 |
| C52×#102 | 2 |
| C5×#3964 | 2 |
| C5×#3950 | 2 |
| C5×#3946 | 2 |
| C5×#3939 | 2 |
| C5×#474 | 5 |
| #65048 | 5 |