Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
285 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 285 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 |
|---|---|---|
| 1. C2×#87827 | C2 | semidirect |
| 2. C2×D5×#170 | C2 | semidirect |
| 4. C4×#6032 | C2 | semidirect |
| 5. C5×#4004 | C2 | semidirect |
| 6. #11716754 | C2 | semidirect |
| 7. #11716753 | C2 | semidirect |
| 30. #6038 | C8 | semidirect |
| 36. #6032 | D4 | semidirect |
| 46. #4004 | D5 | semidirect |
| 56. C2×C5⋊D5 | C2×C8 | semidirect |
| 59. C2×C5×D5 | C2×C8 | semidirect |
| 63. C5×Dic5 | C2×C8 | semidirect |
| 141. C52 | C8×D4 | semidirect |
| 159. C2×D5 | D5⋊C8 | semidirect |
| 171. Dic5 | C8×D5 | semidirect |
| 218. C5 | #65123 | semidirect |
| 219. C5 | #65692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87827 | 2 |
| C2×D5×#170 | 2 |
| #11716998 | 2 |
| C4×#6032 | 2 |
| C5×#4004 | 2 |
| #11716754 | 2 |
| #11716753 | 2 |
| #65692 | 5 |
| #65123 | 5 |