Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
213 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 213 conjugacy classes of subgroups — too many to draw. Only its 61 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×SD16×C25 | C2 | semidirect |
| 2. #11716506 | C2 | semidirect |
| 3. C2×#87724 | C2 | semidirect |
| 5. C2×#87721 | C2 | semidirect |
| 6. C2×#87713 | C2 | semidirect |
| 7. C8×Dic25 | C2 | semidirect |
| 37. C8×C25 | D4 | semidirect |
| 38. #6014 | D4 | semidirect |
| 55. Dic25 | SD16 | semidirect |
| 94. C2×SD16 | D25 | semidirect |
| 98. C25 | #492 | semidirect |
| 142. C8 | C22⋊D25 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×SD16×C25 | 2 |
| #11716506 | 2 |
| C2×#87724 | 2 |
| #11716502 | 2 |
| C2×#87721 | 2 |
| C2×#87713 | 2 |
| C8×Dic25 | 2 |
| #65464 | 5 |