Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
648 conjugacy classes of subgroups; only the 195 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 195 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 |
|---|---|---|
| 2. C2×C52×M16 | C2 | semidirect |
| 3. C2×C4⋊#1039 | C2 | semidirect |
| 4. #11716688 | C2 | semidirect |
| 5. #11716683 | C2 | semidirect |
| 10. #87900 | C4 | semidirect |
| 30. C4⋊(C5⋊D5) | C2×C4 | semidirect |
| 33. #6045 | C2×C4 | semidirect |
| 36. C2×C5×M16 | D5 | semidirect |
| 87. C2×M16 | C5⋊D5 | semidirect |
| 91. C52 | #417 | semidirect |
| 137. C5 | #65422 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87900 | 2 |
| C2×C52×M16 | 2 |
| C2×C4⋊#1039 | 2 |
| #11716688 | 2 |
| #11716683 | 2 |
| #65422 | 5 |