Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
250 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 78 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×#3950 | C2 | semidirect |
| 7. C5×#3939 | C2 | semidirect |
| 20. #65098 | C5 | direct (N × H) |
| 43. C5×#103 | D5 | semidirect |
| 44. C5×#103 | C2×C5 | semidirect |
| 46. #3967 | C2×C5 | semidirect |
| 48. #3950 | C2×C5 | semidirect |
| 49. #3939 | C2×C5 | semidirect |
| 130. #103 | C5×D5 | semidirect |
| 132. C52 | #484 | semidirect |
| 197. C5 | #65098 | direct (N × H) |
| 198. C5 | C5×#484 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4092 | 2 |
| C5×D5×C4⋊C4 | 2 |
| C52×#103 | 2 |
| C5×#3967 | 2 |
| C5×#3952 | 2 |
| C5×#3950 | 2 |
| C5×#3939 | 2 |
| C5×#484 | 5 |
| #65098 | 5 |