Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
280 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 118 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 |
| 15. Q16×Dic5 | C5 | direct (N × H) |
| 42. C5×Dic5 | Q16 | direct (N × H) |
| 47. C5×Q16 | Dic5 | direct (N × H) |
| 48. C5×Q16 | C4×C5 | semidirect |
| 94. C52 | C4×Q16 | semidirect |
| 112. Dic5 | C5×Q16 | direct (N × H) |
| 114. Q16 | C5×Dic5 | direct (N × H) |
| 140. C5 | Q16×Dic5 | direct (N × H) |
| 141. C5 | C4×C5×Q16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C52×Q16 | 2 |
| C5×Q8×Dic5 | 2 |
| C5×#3967 | 2 |
| C5×#3950 | 2 |
| C5×C8×Dic5 | 2 |
| C4×C5×Q16 | 5 |
| Q16×Dic5 | 5 |