Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
624 conjugacy classes of subgroups; only the 264 normal subgroups are shown.
This group has 624 conjugacy classes of subgroups — too many to draw. Only its 264 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, hypocenter | C52 | C43 |
| Frattini | C23 | C2×D52 |
| Fitting | C22×C4×C52 | C22 |
| socle, prime radical, cosocle | C23×C52 | C23 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C22×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 7. C4×#1039 | C4 | semidirect |
| 8. C4×C5×Dic5 | C4 | semidirect |
| 9. Dic52 | C4 | direct (N × H) |
| 26. C4×C52 | C42 | semidirect |
| 27. #1039 | C42 | semidirect |
| 28. C5×Dic5 | C42 | semidirect |
| 39. C4×Dic5 | Dic5 | direct (N × H) |
| 62. C52 | C43 | semidirect |
| 72. C4×C5 | C4×Dic5 | semidirect |
| 75. Dic5 | C4×Dic5 | direct (N × H) |
| 97. C5 | C42×Dic5 | semidirect |
| 103. C4 | Dic52 | 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×Dic52 | 2 |
| C42×Dic5 | 5 |