Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
600 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 130 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 | C22×D52 | C22 |
| hypercenter | C42 | D52 |
| hypocenter | C52 | C2×#126 |
| 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. C42×C5⋊D5 | C2 | semidirect |
| 2. C5×#4022 | C2 | semidirect |
| 4. #11717001 | C2 | semidirect |
| 5. #11716980 | C2 | semidirect |
| 9. C42×C52 | C22 | semidirect |
| 10. C4×#1039 | C22 | semidirect |
| 12. C5×#683 | C22 | semidirect |
| 13. #87780 | C22 | semidirect |
| 29. #4022 | D5 | semidirect |
| 46. C42×C5 | C2×D5 | semidirect |
| 52. #683 | C2×D5 | semidirect |
| 57. C5⋊D5 | #126 | semidirect |
| 78. C52 | C2×#126 | semidirect |
| 100. C42 | D52 | semidirect |
| 116. C5 | D5×#126 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C42×C5⋊D5 | 2 |
| C5×#4022 | 2 |
| #11717039 | 2 |
| #11717001 | 2 |
| #11716980 | 2 |
| D5×#126 | 5 |