Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
275 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 275 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 |
|---|---|---|
| 1. C2×C5×#704 | C2 | semidirect |
| 2. C2×#87827 | C2 | semidirect |
| 4. C22⋊#6032 | C2 | semidirect |
| 5. #11716759 | C2 | semidirect |
| 6. #11716754 | C2 | semidirect |
| 7. #11716752 | C2 | semidirect |
| 38. C5×#170 | D4 | semidirect |
| 39. C2×#704 | D5 | semidirect |
| 59. C2×C5⋊D5 | M16 | semidirect |
| 130. #170 | C22⋊D5 | semidirect |
| 142. C52 | #435 | semidirect |
| 222. C5 | #65416 | semidirect |
| 223. C5 | #65694 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#704 | 2 |
| C2×#87827 | 2 |
| #11717070 | 2 |
| C22⋊#6032 | 2 |
| #11716759 | 2 |
| #11716754 | 2 |
| #11716752 | 2 |
| #65694 | 5 |
| #65416 | 5 |