Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
364 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 66 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. #11717256 | C2 | semidirect |
| 2. C2×C5×#686 | C2 | semidirect |
| 3. #11717032 | C2 | semidirect |
| 4. C2×#87773 | C2 | semidirect |
| 5. #11716596 | C2 | semidirect |
| 26. C5×#168 | D4 | semidirect |
| 32. C2×#686 | D5 | semidirect |
| 87. #168 | C22⋊D5 | semidirect |
| 93. C52 | #496 | semidirect |
| 140. C5 | #65443 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717256 | 2 |
| C2×C5×#686 | 2 |
| #11717032 | 2 |
| C2×#87773 | 2 |
| #11716596 | 2 |
| #65443 | 5 |