Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
496 conjugacy classes of subgroups; only the 180 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 180 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4 | D52 |
| commutator | C2×C52 | C2×C42 |
| Frattini | C23 | C2×D52 |
| Fitting | C22×C4×C52 | C22 |
| socle, prime radical, cosocle | C23×C52 | C23 |
| hypocenter | C52 | C4×C4⋊C4 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C22×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 13. C4×C5×Dic5 | C4 | semidirect |
| 14. #87780 | C4 | direct (N × H) |
| 47. C4×C52 | C4⋊C4 | semidirect |
| 51. C5×Dic5 | C42 | semidirect |
| 72. C4×Dic5 | Dic5 | semidirect |
| 119. C52 | C4×C4⋊C4 | semidirect |
| 139. C4×C5 | #683 | semidirect |
| 140. C4×C5 | C4⋊Dic5 | semidirect |
| 146. Dic5 | C4×Dic5 | semidirect |
| 186. C5 | C4×#683 | semidirect |
| 187. C5 | C4×C4⋊Dic5 | semidirect |
| 197. C4 | #87780 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#1039 | 2 |
| C2×C4×C5×Dic5 | 2 |
| C2×#87780 | 2 |
| #11716620 | 2 |
| C4×C4⋊Dic5 | 5 |
| C4×#683 | 5 |