Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
440 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 440 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 |
|---|---|---|
| 7. C52×Q16 | C4 | semidirect |
| 35. #1039 | Q16 | direct (N × H) |
| 37. C5×Q16 | Dic5 | semidirect |
| 62. C52 | C4×Q16 | semidirect |
| 71. Q16 | #1039 | direct (N × H) |
| 90. C5 | Q16×Dic5 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C52×Q16 | 2 |
| Q8×#1039 | 2 |
| #11716702 | 2 |
| #11716685 | 2 |
| C8×#1039 | 2 |
| Q16×Dic5 | 5 |