Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
279 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 279 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 4. #11716760 | C2 | semidirect |
| 5. #11716759 | C2 | semidirect |
| 47. #1039 | M16 | semidirect |
| 50. C5×Dic5 | M16 | semidirect |
| 116. C52 | #423 | semidirect |
| 142. Dic5 | #704 | semidirect |
| 182. C5 | #65407 | semidirect |
| 183. C5 | #65758 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87853 | 2 |
| C2×C5×#704 | 2 |
| C2×Dic52 | 2 |
| #11716760 | 2 |
| #11716759 | 2 |
| #65758 | 5 |
| #65407 | 5 |