Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
330 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 82 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 |
|---|---|---|
| 1. C5×#4086 | C2 | semidirect |
| 2. C2×C5×#686 | C2 | semidirect |
| 3. C2×C5×D40 | C2 | semidirect |
| 4. C5×#4039 | C2 | semidirect |
| 5. C52×#102 | C2 | semidirect |
| 6. C5×#3946 | C2 | semidirect |
| 7. C5×#3941 | C2 | semidirect |
| 22. #65075 | C5 | direct (N × H) |
| 37. C5×D20 | D4 | semidirect |
| 45. #4086 | C2×C5 | semidirect |
| 46. C2×#686 | C2×C5 | semidirect |
| 47. C2×D40 | C2×C5 | semidirect |
| 48. #4039 | C2×C5 | semidirect |
| 52. C5×#102 | D5 | semidirect |
| 53. C5×#102 | C2×C5 | semidirect |
| 54. #3946 | C2×C5 | semidirect |
| 55. #3941 | C2×C5 | semidirect |
| 70. C5×Dic5 | D8 | semidirect |
| 142. D20 | C5×D4 | semidirect |
| 155. #102 | C5×D5 | semidirect |
| 156. C52 | #459 | semidirect |
| 193. Dic5 | C5×D8 | semidirect |
| 242. C5 | #65075 | direct (N × H) |
| 243. C5 | C5×#459 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4086 | 2 |
| C2×C5×#686 | 2 |
| C2×C5×D40 | 2 |
| C5×#4039 | 2 |
| C52×#102 | 2 |
| C5×#3946 | 2 |
| C5×#3941 | 2 |
| C5×#459 | 5 |
| #65075 | 5 |