Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
258 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 98 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. #65078 | C5 | direct (N × H) |
| 78. #689 | C4×C5 | semidirect |
| 129. C52 | #441 | semidirect |
| 188. C5 | #65078 | direct (N × H) |
| 189. C5 | C5×#441 | 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×#3947 | 2 |
| C5×#3940 | 2 |
| C5×#441 | 5 |
| #65078 | 5 |