Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
334 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 334 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 |
|---|---|---|
| 2. C5×#4015 | C2 | semidirect |
| 4. C5×C4⋊#168 | C2 | semidirect |
| 5. #11716607 | C2 | semidirect |
| 36. #4015 | D5 | semidirect |
| 40. C4⋊#168 | D5 | semidirect |
| 46. C4×C52 | SD16 | semidirect |
| 118. C52 | #461 | semidirect |
| 138. C4×C5 | #677 | semidirect |
| 139. C4×C5 | #688 | semidirect |
| 183. C5 | #65130 | semidirect |
| 184. C5 | #65372 | semidirect |
| 192. C4 | #87774 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C4⋊(C5⋊D5) | 2 |
| C5×#4015 | 2 |
| C2×#87774 | 2 |
| C5×C4⋊#168 | 2 |
| #11716607 | 2 |
| #65372 | 5 |
| #65130 | 5 |