Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
282 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 282 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 |
|---|---|---|
| 1. C5×#4092 | C2 | semidirect |
| 2. C2×C5×#688 | C2 | semidirect |
| 3. C2×C5×#676 | C2 | semidirect |
| 5. C52×#103 | C2 | semidirect |
| 6. C5×#3953 | C2 | semidirect |
| 7. C5×#3939 | C2 | semidirect |
| 22. #65101 | C5 | direct (N × H) |
| 38. C5×#168 | D4 | semidirect |
| 43. #4092 | C2×C5 | semidirect |
| 44. C2×#688 | C2×C5 | semidirect |
| 45. C2×#676 | C2×C5 | semidirect |
| 49. C5×#103 | D5 | semidirect |
| 50. C5×#103 | C2×C5 | semidirect |
| 52. #3953 | C2×C5 | semidirect |
| 53. #3939 | C2×C5 | semidirect |
| 139. #168 | C5×D4 | semidirect |
| 145. #103 | C5×D5 | semidirect |
| 147. C52 | #468 | semidirect |
| 222. C5 | #65101 | direct (N × H) |
| 223. C5 | C5×#468 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4092 | 2 |
| C2×C5×#688 | 2 |
| C2×C5×#676 | 2 |
| C5×#4041 | 2 |
| C52×#103 | 2 |
| C5×#3953 | 2 |
| C5×#3939 | 2 |
| C5×#468 | 5 |
| #65101 | 5 |