Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
322 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 322 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 |
|---|---|---|
| 2. C5×#4090 | C2 | semidirect |
| 3. C5×#4055 | C2 | semidirect |
| 4. C52×#101 | C2 | semidirect |
| 5. C5×#3957 | C2 | semidirect |
| 18. #65041 | C5 | direct (N × H) |
| 37. #4090 | C2×C5 | semidirect |
| 38. #4055 | C2×C5 | semidirect |
| 41. C5×#101 | D5 | semidirect |
| 42. C5×#101 | C2×C5 | semidirect |
| 43. #3957 | C2×C5 | semidirect |
| 115. #101 | C5×D5 | semidirect |
| 116. C52 | #456 | semidirect |
| 168. C5 | #65041 | direct (N × H) |
| 169. C5 | C5×#456 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4147 | 2 |
| C5×#4090 | 2 |
| C5×#4055 | 2 |
| C52×#101 | 2 |
| C5×#3957 | 2 |
| C5×#456 | 5 |
| #65041 | 5 |