Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
616 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 126 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×#1043 |
| commutator, socle | C22×C52 | C22×C4 |
| Fitting | C42×C52 | C4 |
| prime radical, cosocle | C22×C5⋊D5 | C23 |
| hypercenter | C42 | #1043 |
| hypocenter | C52 | #382 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 8. C42×C52 | C4 | semidirect |
| 9. C4×#1039 | C4 | semidirect |
| 10. C4×#1039 | C4 | semidirect |
| 38. C42×C5 | AGL(1,𝔽5) | semidirect |
| 59. C52 | #382 | semidirect |
| 75. C42 | #1043 | semidirect |
| 90. C5 | #65689 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊#1043 | 2 |
| C42×C5⋊D5 | 2 |
| #11716874 | 2 |
| #65689 | 5 |