Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
568 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 131 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×C52×SD16 | C2 | semidirect |
| 2. #11717264 | C2 | semidirect |
| 3. C2×#87811 | C2 | semidirect |
| 5. C2×#87810 | C2 | semidirect |
| 6. C2×#87800 | C2 | semidirect |
| 7. C8×#1039 | C2 | semidirect |
| 37. C52×C8 | D4 | semidirect |
| 38. #6029 | D4 | semidirect |
| 39. C2×C5×SD16 | D5 | semidirect |
| 55. #1039 | SD16 | semidirect |
| 89. C5×C8 | C22⋊D5 | semidirect |
| 94. C2×SD16 | C5⋊D5 | semidirect |
| 98. C52 | #492 | semidirect |
| 142. C8 | C22⋊(C5⋊D5) | semidirect |
| 143. C5 | #65464 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C52×SD16 | 2 |
| #11717264 | 2 |
| C2×#87811 | 2 |
| #11717260 | 2 |
| C2×#87810 | 2 |
| C2×#87800 | 2 |
| C8×#1039 | 2 |
| #65464 | 5 |