Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
258 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 68 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 |
|---|---|---|
| 61. C5×Dic5 | Q16 | semidirect |
| 138. C52 | #462 | semidirect |
| 161. Dic5 | #689 | semidirect |
| 200. C5 | #65082 | semidirect |
| 201. C5 | #65320 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4033 | 2 |
| #11716983 | 2 |
| C2×#87776 | 2 |
| C2×#87775 | 2 |
| #11716677 | 2 |
| C5×#3942 | 2 |
| #11716612 | 2 |
| #65320 | 5 |
| #65082 | 5 |