Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
262 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 102 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 |
|---|---|---|
| 12. C5×#689 | C4 | semidirect |
| 21. #65079 | C5 | direct (N × H) |
| 58. C5×Dic5 | Q16 | semidirect |
| 78. #689 | C4×C5 | semidirect |
| 129. C52 | C4×Q16 | semidirect |
| 152. Dic5 | C5×Q16 | semidirect |
| 188. C5 | #65079 | direct (N × H) |
| 189. C5 | C4×C5×Q16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×Q8×Dic5 | 2 |
| C2×C5×#689 | 2 |
| C5×#4033 | 2 |
| C52×#103 | 2 |
| C5×#3948 | 2 |
| C5×C8×Dic5 | 2 |
| C5×#3939 | 2 |
| C4×C5×Q16 | 5 |
| #65079 | 5 |