Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
162 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 49 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×AGL(1,ℤ/8) | C2 | semidirect |
| 2. #11716512 | C2 | semidirect |
| 3. #11716510 | C2 | semidirect |
| 4. C2×#87722 | C2 | semidirect |
| 5. #11716380 | C2 | semidirect |
| 6. #11716372 | C2 | semidirect |
| 7. #11716370 | C2 | semidirect |
| 94. AGL(1,ℤ/8) | D25 | semidirect |
| 100. C25 | #472 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×AGL(1,ℤ/8) | 2 |
| #11716512 | 2 |
| #11716510 | 2 |
| C2×#87722 | 2 |
| #11716380 | 2 |
| #11716372 | 2 |
| #11716370 | 2 |
| #65488 | 5 |