Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
496 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 144 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 |
|---|---|---|
| 9. C4×#1039 | C4 | semidirect |
| 10. #87781 | C4 | semidirect |
| 36. #1039 | C42 | semidirect |
| 37. #1039 | C4⋊C4 | semidirect |
| 83. C52 | C4×C4⋊C4 | semidirect |
| 131. C5 | #64938 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#1039 | 2 |
| C2×#87781 | 2 |
| C2×Dic52 | 2 |
| C5×#3963 | 2 |
| #64938 | 5 |