Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
178 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 74 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. C2×#87763 | C2 | semidirect |
| 3. C5×#3998 | C2 | semidirect |
| 4. #11716748 | C2 | semidirect |
| 5. D5×#674 | C2 | semidirect |
| 27. #3998 | D5 | semidirect |
| 83. C52 | #504 | semidirect |
| 122. C5 | #65196 | semidirect |
| 123. C5 | #65791 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11716932 | 2 |
| C2×#87763 | 2 |
| C5×#3998 | 2 |
| #11716748 | 2 |
| D5×#674 | 2 |
| #65791 | 5 |
| #65196 | 5 |