Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
222 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 60 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 |
|---|---|---|
| 126. C52 | #491 | semidirect |
| 184. C5 | #65086 | semidirect |
| 185. C5 | #65358 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4036 | 2 |
| #11716983 | 2 |
| #11716677 | 2 |
| C5×#3942 | 2 |
| #11716608 | 2 |
| #11716606 | 2 |
| #11716595 | 2 |
| #65358 | 5 |
| #65086 | 5 |