Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
222 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 222 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 |
|---|---|---|
| 120. C52 | #479 | semidirect |
| 176. C5 | #65088 | semidirect |
| 177. C5 | #65311 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×Q8×Dic5 | 2 |
| #11716988 | 2 |
| #11716702 | 2 |
| C5×#3967 | 2 |
| #11716617 | 2 |
| #11716614 | 2 |
| #11716612 | 2 |
| #65311 | 5 |
| #65088 | 5 |