Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
702 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 702 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 | C2 | C22×#6038 |
| commutator, cosocle | C4×C52 | C24 |
| Frattini | C4 | C22×D52 |
| Fitting | C52×#41 | C22 |
| socle | C2×C52 | C22×D4 |
| hypercenter | #41 | D52 |
| hypocenter | C52 | #576 |
| LCS | G ▷ C4×C52 ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C2 ◁ #41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11717522 | C2 | semidirect |
| 2. C5×#4149 | C2 | semidirect |
| 3. C5×#4094 | C2 | semidirect |
| 4. #11716948 | C2 | semidirect |
| 5. #11716947 | C2 | semidirect |
| 6. #11716943 | C2 | semidirect |
| 7. C2×#87771 | C2 | semidirect |
| 11. #87900 | C22 | semidirect |
| 12. C2×C4⋊(C5⋊D5) | C22 | semidirect |
| 15. C5×#709 | C22 | semidirect |
| 16. C2×C5×D20 | C22 | semidirect |
| 17. C5×#681 | C22 | semidirect |
| 18. C2×C5×#168 | C22 | semidirect |
| 19. #87776 | C22 | semidirect |
| 20. #87774 | C22 | semidirect |
| 21. #87773 | C22 | semidirect |
| 22. #87771 | C22 | semidirect |
| 23. #87771 | C22 | semidirect |
| 47. #4149 | D5 | semidirect |
| 51. #4094 | D5 | semidirect |
| 85. #709 | C2×D5 | semidirect |
| 89. C2×D20 | C2×D5 | semidirect |
| 97. #681 | C2×D5 | semidirect |
| 98. C2×#168 | C2×D5 | semidirect |
| 159. C52 | #576 | semidirect |
| 229. C5 | #66086 | semidirect |
| 230. C5 | #66169 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717522 | 2 |
| C5×#4149 | 2 |
| C5×#4094 | 2 |
| #11716948 | 2 |
| #11716947 | 2 |
| #11716943 | 2 |
| C2×#87771 | 2 |
| #66169 | 5 |
| #66086 | 5 |