Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
526 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 152 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×D52 |
| commutator, socle, cosocle | C22×C52 | C24 |
| Fitting | C42×C52 | C22 |
| prime radical | C2×C5×D20 | C22 |
| hypercenter | C42 | D52 |
| hypocenter | C52 | #554 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C4×#6045 | C2 | semidirect |
| 3. C5×#4015 | C2 | semidirect |
| 5. D5×C4⋊Dic5 | C2 | semidirect |
| 6. #11717006 | C2 | semidirect |
| 7. #11716991 | C2 | semidirect |
| 8. #11716975 | C2 | semidirect |
| 36. C5×D20 | Q8 | semidirect |
| 53. #4015 | D5 | semidirect |
| 135. D20 | Dic10 | semidirect |
| 150. C52 | #554 | semidirect |
| 220. C5 | #65877 | semidirect |
| 221. C5 | #66064 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#6045 | 2 |
| C4×C5×D20 | 2 |
| C5×#4015 | 2 |
| #11717017 | 2 |
| D5×C4⋊Dic5 | 2 |
| #11717006 | 2 |
| #11716991 | 2 |
| #11716975 | 2 |
| #66064 | 5 |
| #65877 | 5 |