Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
195 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 195 conjugacy classes of subgroups — too many to draw. Only its 51 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. #11716500 | C2 | semidirect |
| 2. C2×#87722 | C2 | semidirect |
| 3. C2×#87712 | C2 | semidirect |
| 4. #11716457 | C2 | semidirect |
| 5. C25×#102 | C2 | semidirect |
| 6. #11716369 | C2 | semidirect |
| 7. #11716356 | C2 | semidirect |
| 38. #6014 | D4 | semidirect |
| 104. #102 | D25 | semidirect |
| 105. C25 | #469 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11716500 | 2 |
| C2×#87722 | 2 |
| C2×#87712 | 2 |
| #11716457 | 2 |
| C25×#102 | 2 |
| #11716369 | 2 |
| #11716356 | 2 |
| #65071 | 5 |