Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
276 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 114 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. #65473 | C5 | direct (N × H) |
| 45. C5×Q16 | Dic5 | semidirect |
| 46. C5×Q16 | C4×C5 | semidirect |
| 89. C52 | #441 | semidirect |
| 107. Q16 | C5×Dic5 | semidirect |
| 129. C5 | #65473 | direct (N × H) |
| 130. C5 | C5×#441 | 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×#3949 | 2 |
| C5×#3947 | 2 |
| C5×#441 | 5 |
| #65473 | 5 |