Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1032 conjugacy classes of subgroups; only the 315 normal subgroups are shown.
This group has 1032 conjugacy classes of subgroups — too many to draw. Only its 315 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×#87804 | C2 | semidirect |
| 4. #11717227 | C2 | semidirect |
| 5. M16×C5⋊D5 | C2 | semidirect |
| 6. #11717221 | C2 | semidirect |
| 17. C52×M16 | C22 | semidirect |
| 18. C2×C52×C8 | C22 | semidirect |
| 20. #87804 | C22 | semidirect |
| 21. C2×#6029 | C22 | semidirect |
| 22. #87799 | C22 | semidirect |
| 23. C8×C5⋊D5 | C22 | semidirect |
| 45. C2×C5×M16 | D5 | semidirect |
| 71. C5×M16 | C2×D5 | semidirect |
| 72. C2×C5×C8 | C2×D5 | semidirect |
| 108. C2×M16 | C5⋊D5 | semidirect |
| 109. C52 | #568 | semidirect |
| 134. M16 | C2×C5⋊D5 | semidirect |
| 137. C2×C8 | C2×C5⋊D5 | semidirect |
| 162. C5 | #66079 | 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×#87804 | 2 |
| #11717227 | 2 |
| M16×C5⋊D5 | 2 |
| #11717221 | 2 |
| #66079 | 5 |