Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
258 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 106 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. C52×C4⋊C8 | C2 | semidirect |
| 4. C5×#3947 | C2 | semidirect |
| 5. C5×C4⋊#168 | C2 | semidirect |
| 16. #65124 | C5 | direct (N × H) |
| 34. C5×C4⋊C8 | D5 | semidirect |
| 35. C5×C4⋊C8 | C2×C5 | semidirect |
| 39. #3947 | C2×C5 | semidirect |
| 40. C4⋊#168 | C2×C5 | semidirect |
| 109. C4⋊C8 | C5×D5 | semidirect |
| 112. C52 | #432 | semidirect |
| 174. C5 | #65124 | direct (N × H) |
| 175. C5 | C5×#432 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C42×C5×D5 | 2 |
| C52×C4⋊C8 | 2 |
| C5×#3952 | 2 |
| C5×#3947 | 2 |
| C5×C4⋊#168 | 2 |
| C5×#432 | 5 |
| #65124 | 5 |