Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
216 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 57 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. C25×#124 | C2 | semidirect |
| 2. C2×#87724 | C2 | semidirect |
| 3. C2×#87722 | C2 | semidirect |
| 4. #11716436 | C2 | semidirect |
| 5. #11716351 | C2 | semidirect |
| 26. #6014 | D4 | semidirect |
| 68. #124 | D25 | semidirect |
| 70. C25 | #496 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×#124 | 2 |
| C2×#87724 | 2 |
| C2×#87722 | 2 |
| #11716436 | 2 |
| #11716351 | 2 |
| #65347 | 5 |