Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
243 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 243 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. C2×#87748 | C2 | semidirect |
| 2. C2×SD16×C25 | C2 | semidirect |
| 3. #11716500 | C2 | semidirect |
| 4. C2×#87722 | C2 | semidirect |
| 5. #11716384 | C2 | semidirect |
| 6. #11716369 | C2 | semidirect |
| 7. #11716368 | C2 | semidirect |
| 28. Q8×C25 | D4 | semidirect |
| 38. D100 | D4 | semidirect |
| 109. C2×SD16 | D25 | semidirect |
| 115. C25 | #449 | semidirect |
| 156. Q8 | C22⋊D25 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87748 | 2 |
| C2×SD16×C25 | 2 |
| #11716500 | 2 |
| C2×#87722 | 2 |
| #11716384 | 2 |
| #11716369 | 2 |
| #11716368 | 2 |
| #65461 | 5 |