Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
568 conjugacy classes of subgroups; only the 271 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 271 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 |
|---|---|---|
| 4. #11716682 | C2 | semidirect |
| 5. C8×#1039 | C2 | semidirect |
| 8. C52×M16 | C4 | semidirect |
| 13. #87804 | C4 | semidirect |
| 24. C52×C8 | C2×C4 | semidirect |
| 25. #6029 | C2×C4 | semidirect |
| 38. #1039 | M16 | direct (N × H) |
| 41. C5×M16 | Dic5 | semidirect |
| 60. C5×C8 | C2×Dic5 | semidirect |
| 67. C52 | C4×M16 | semidirect |
| 79. M16 | #1039 | direct (N × H) |
| 97. C8 | C2×#1039 | semidirect |
| 98. C5 | M16×Dic5 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C52×M16 | 2 |
| C2×C4×#1039 | 2 |
| C2×#87804 | 2 |
| #11716682 | 2 |
| C8×#1039 | 2 |
| M16×Dic5 | 5 |