Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1336 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 1336 conjugacy classes of subgroups — too many to draw. Only its 251 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 | C23×C5⋊D5 |
| commutator, socle, cosocle | C22×C52 | C24 |
| Fitting | C4×C52×D4 | C2 |
| hypercenter | C4×D4 | C5⋊D5 |
| hypocenter | C52 | #546 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#87900 | C2 | semidirect |
| 2. C22×C4⋊(C5⋊D5) | C2 | semidirect |
| 3. C4×C52×D4 | C2 | semidirect |
| 4. #11717257 | C2 | semidirect |
| 5. #11717250 | C2 | semidirect |
| 6. #11717244 | C2 | semidirect |
| 7. #11717214 | C2 | semidirect |
| 8. #11717204 | C2 | semidirect |
| 9. C22⋊C4×C5⋊D5 | C2 | semidirect |
| 10. #11717195 | C2 | semidirect |
| 11. C4×C4⋊(C5⋊D5) | C2 | semidirect |
| 15. C22×C4×C52 | C22 | semidirect |
| 16. C2×C22⋊(C5⋊D5) | C22 | semidirect |
| 17. C2×C22⋊(C5⋊D5) | C22 | semidirect |
| 23. C2×C4×C5⋊D5 | C22 | semidirect |
| 24. C2×C4×C5⋊D5 | C22 | semidirect |
| 25. C2×#6045 | C22 | semidirect |
| 26. C52×C4⋊C4 | C22 | semidirect |
| 28. C52×C22⋊C4 | C22 | semidirect |
| 29. C42×C52 | C22 | semidirect |
| 31. #87808 | C22 | semidirect |
| 32. #87808 | C22 | semidirect |
| 33. #87808 | C22 | semidirect |
| 34. #87808 | C22 | semidirect |
| 35. C4⋊#1039 | C22 | semidirect |
| 36. #87806 | C22 | semidirect |
| 59. C4⋊(C5⋊D5) | D4 | semidirect |
| 65. C4×C5×D4 | D5 | semidirect |
| 79. C22×C52 | #41 | semidirect |
| 98. C22×C4×C5 | C2×D5 | semidirect |
| 109. C5×C4⋊C4 | C2×D5 | semidirect |
| 111. C5×C22⋊C4 | C2×D5 | semidirect |
| 112. C42×C5 | C2×D5 | semidirect |
| 162. C4×D4 | C5⋊D5 | semidirect |
| 164. C52 | #546 | semidirect |
| 170. C22×C5 | #709 | semidirect |
| 199. C22×C4 | C2×C5⋊D5 | semidirect |
| 202. C4⋊C4 | C2×C5⋊D5 | semidirect |
| 209. C22⋊C4 | C2×C5⋊D5 | semidirect |
| 210. C42 | C2×C5⋊D5 | semidirect |
| 243. C5 | #65884 | semidirect |
| 256. C22 | #87900 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87900 | 2 |
| C22×C4⋊(C5⋊D5) | 2 |
| C4×C52×D4 | 2 |
| #11717257 | 2 |
| #11717250 | 2 |
| #11717244 | 2 |
| #11717214 | 2 |
| #11717204 | 2 |
| C22⋊C4×C5⋊D5 | 2 |
| #11717195 | 2 |
| C4×C4⋊(C5⋊D5) | 2 |
| #65884 | 5 |