Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
464 conjugacy classes of subgroups; only the 164 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 164 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C2×D52 |
| commutator | C2×C52 | C2×C42 |
| Fitting | C22×C4×C52 | C22 |
| socle, prime radical, cosocle | C23×C52 | C23 |
| hypercenter | C22×C4 | D52 |
| hypocenter | C52 | C4×C4⋊C4 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C23 ◁ C22×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 11. C4×C5×Dic5 | C4 | semidirect |
| 12. #87780 | C4 | semidirect |
| 49. C5×Dic5 | C42 | semidirect |
| 50. C5×Dic5 | C4⋊C4 | semidirect |
| 68. C4×Dic5 | Dic5 | semidirect |
| 114. C52 | C4×C4⋊C4 | semidirect |
| 140. Dic5 | C4×Dic5 | semidirect |
| 141. Dic5 | C4⋊Dic5 | semidirect |
| 180. C5 | #64938 | semidirect |
| 181. C5 | C4×C4⋊Dic5 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C5×Dic5 | 2 |
| C2×#87780 | 2 |
| C2×Dic52 | 2 |
| #11716698 | 2 |
| C5×#3963 | 2 |
| C4×C4⋊Dic5 | 5 |
| #64938 | 5 |