Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
143 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 143 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C4 | D5×AGL(1,𝔽5) |
| commutator | C2×C52 | C4×C8 |
| Fitting | C2×C4×C52 | C2×C4 |
| socle, prime radical | C22×C52 | C42 |
| cosocle | C4×C5×Dic5 | C22 |
| hypocenter | C52 | #322 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C2×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 14. #6032 | C8 | semidirect |
| 63. C52 | #322 | semidirect |
| 99. C5 | #64674 | semidirect |
| 100. C5 | #170⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#6032 | 2 |
| C4×C5×#170 | 2 |
| Dic5×#168 | 2 |
| #170⋊C8 | 5 |
| #64674 | 5 |