Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
496 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 141 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. C52×C22⋊Q8 | C2 | semidirect |
| 2. C2×#87811 | C2 | semidirect |
| 4. C22×#6029 | C2 | semidirect |
| 5. #11716702 | C2 | semidirect |
| 6. #11716676 | C2 | semidirect |
| 7. #11716675 | C2 | semidirect |
| 37. #6029 | D4 | semidirect |
| 38. C5×C22⋊Q8 | D5 | semidirect |
| 47. C22×C52 | SD16 | semidirect |
| 95. C22⋊Q8 | C5⋊D5 | semidirect |
| 100. C52 | #465 | semidirect |
| 103. C22×C5 | #688 | semidirect |
| 148. C5 | #65337 | semidirect |
| 154. C22 | #87811 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×C22⋊Q8 | 2 |
| C2×#87811 | 2 |
| #11717250 | 2 |
| C22×#6029 | 2 |
| #11716702 | 2 |
| #11716676 | 2 |
| #11716675 | 2 |
| #65337 | 5 |