Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
247 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 247 conjugacy classes of subgroups — too many to draw. Only its 72 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 |
|---|---|---|
| 2. C4⋊#6032 | C2 | semidirect |
| 3. C5×C4⋊#170 | C2 | semidirect |
| 5. #11716752 | C2 | semidirect |
| 35. C4⋊#170 | D5 | semidirect |
| 110. C52 | #432 | semidirect |
| 174. C5 | #65124 | semidirect |
| 175. C5 | #65683 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#6036 | 2 |
| C4⋊#6032 | 2 |
| C5×C4⋊#170 | 2 |
| #11716754 | 2 |
| #11716752 | 2 |
| #65683 | 5 |
| #65124 | 5 |