Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
252 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 74 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 |
|---|---|---|
| 19. #87775 | C4 | semidirect |
| 127. C52 | #441 | semidirect |
| 186. C5 | #65078 | semidirect |
| 187. C5 | #65319 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4033 | 2 |
| Dic5×Dic10 | 2 |
| C2×#87775 | 2 |
| #11716675 | 2 |
| C5×#3942 | 2 |
| #11716607 | 2 |
| #11716595 | 2 |
| #65319 | 5 |
| #65078 | 5 |