Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
488 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 191 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. Q8×#1039 | C2 | semidirect |
| 4. #11716702 | C2 | semidirect |
| 6. #11716684 | C2 | semidirect |
| 7. C8×#1039 | C2 | semidirect |
| 11. C52×SD16 | C4 | semidirect |
| 23. C52×Q8 | C2×C4 | semidirect |
| 33. C52×C8 | C2×C4 | semidirect |
| 52. #1039 | SD16 | direct (N × H) |
| 56. C5×SD16 | Dic5 | semidirect |
| 72. C5×Q8 | C2×Dic5 | semidirect |
| 82. C5×C8 | C2×Dic5 | semidirect |
| 91. C52 | C4×SD16 | semidirect |
| 106. SD16 | #1039 | direct (N × H) |
| 121. Q8 | C2×#1039 | semidirect |
| 132. C8 | C2×#1039 | semidirect |
| 133. C5 | SD16×Dic5 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C52×SD16 | 2 |
| Q8×#1039 | 2 |
| D4×#1039 | 2 |
| #11716702 | 2 |
| #11716699 | 2 |
| #11716684 | 2 |
| C8×#1039 | 2 |
| SD16×Dic5 | 5 |