Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
235 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 235 conjugacy classes of subgroups — too many to draw. Only its 96 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. C5×#4002 | C2 | semidirect |
| 4. C5×C4⋊#170 | C2 | semidirect |
| 13. #65683 | C5 | direct (N × H) |
| 29. #4002 | C2×C5 | semidirect |
| 30. C4⋊#170 | C2×C5 | semidirect |
| 95. C52 | #432 | semidirect |
| 151. C5 | C5×#432 | semidirect |
| 152. C5 | #65683 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C42×C5×D5 | 2 |
| C5×#4003 | 2 |
| C5×#4002 | 2 |
| C5×C4⋊#170 | 2 |
| #65683 | 5 |
| C5×#432 | 5 |