Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
216 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 20. #65146 | C5 | direct (N × H) |
| 118. C52 | #479 | semidirect |
| 174. C5 | #65146 | direct (N × H) |
| 175. C5 | C5×#479 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4036 | 2 |
| C5×#4033 | 2 |
| C52×#106 | 2 |
| C5×#3948 | 2 |
| C5×#3946 | 2 |
| C5×#3942 | 2 |
| C5×#3939 | 2 |
| C5×#479 | 5 |
| #65146 | 5 |