Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
234 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 74 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 |
|---|---|---|
| 3. C52×#103 | C2 | semidirect |
| 4. C5×#3967 | C2 | semidirect |
| 6. C5×#3949 | C2 | semidirect |
| 7. C5×#3939 | C2 | semidirect |
| 20. #65104 | C5 | direct (N × H) |
| 42. C5×#103 | D5 | semidirect |
| 43. C5×#103 | C2×C5 | semidirect |
| 45. #3967 | C2×C5 | semidirect |
| 47. #3949 | C2×C5 | semidirect |
| 48. #3939 | C2×C5 | semidirect |
| 127. #103 | C5×D5 | semidirect |
| 129. C52 | #485 | semidirect |
| 193. C5 | #65104 | direct (N × H) |
| 194. C5 | C5×#485 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4092 | 2 |
| C5×#4038 | 2 |
| C52×#103 | 2 |
| C5×#3967 | 2 |
| C5×#3952 | 2 |
| C5×#3949 | 2 |
| C5×#3939 | 2 |
| C5×#485 | 5 |
| #65104 | 5 |