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 | C52×C22⋊Q8 | C2 |
| hypercenter | C22⋊Q8 | C5⋊D5 |
| hypocenter | C52 | #546 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#87904 | C2 | semidirect |
| 2. C22×C4⋊(C5⋊D5) | C2 | semidirect |
| 3. C52×C22⋊Q8 | C2 | semidirect |
| 4. #11717267 | C2 | semidirect |
| 5. C4×C22⋊(C5⋊D5) | C2 | semidirect |
| 6. #11717215 | C2 | semidirect |
| 7. #11717215 | C2 | semidirect |
| 8. #11717214 | C2 | semidirect |
| 9. #11717213 | C2 | semidirect |
| 10. #11717202 | C2 | semidirect |
| 11. C22⋊C4×C5⋊D5 | C2 | semidirect |
| 13. C2×C52×Q8 | C22 | semidirect |
| 21. C2×C4⋊(C5⋊D5) | C22 | semidirect |
| 22. C2×C4⋊(C5⋊D5) | C22 | semidirect |
| 23. C2×C4×C5⋊D5 | C22 | semidirect |
| 24. C2×C4×C5⋊D5 | C22 | semidirect |
| 25. C2×C4×C5⋊D5 | C22 | semidirect |
| 26. C52×C4⋊C4 | C22 | semidirect |
| 27. C52×C4⋊C4 | C22 | semidirect |
| 30. #87808 | C22 | semidirect |
| 31. #87808 | C22 | semidirect |
| 32. #87808 | C22 | semidirect |
| 33. #87808 | C22 | semidirect |
| 34. #87808 | C22 | semidirect |
| 35. #87806 | C22 | semidirect |
| 36. C4×#1039 | C22 | semidirect |
| 59. C4⋊(C5⋊D5) | D4 | semidirect |
| 65. C5×C22⋊Q8 | D5 | semidirect |
| 76. C22×C52 | #41 | semidirect |
| 96. C2×C5×Q8 | C2×D5 | semidirect |
| 109. C5×C4⋊C4 | C2×D5 | semidirect |
| 110. C5×C4⋊C4 | C2×D5 | semidirect |
| 157. C22⋊Q8 | C5⋊D5 | semidirect |
| 164. C52 | #546 | semidirect |
| 167. C22×C5 | #713 | semidirect |
| 188. C2×Q8 | C2×C5⋊D5 | semidirect |
| 201. C4⋊C4 | C2×C5⋊D5 | semidirect |
| 202. C4⋊C4 | C2×C5⋊D5 | semidirect |
| 243. C5 | #65964 | semidirect |
| 256. C22 | #87904 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87904 | 2 |
| C22×C4⋊(C5⋊D5) | 2 |
| C52×C22⋊Q8 | 2 |
| #11717267 | 2 |
| C4×C22⋊(C5⋊D5) | 2 |
| #11717215 | 2 |
| #11717214 | 2 |
| #11717213 | 2 |
| #11717202 | 2 |
| C22⋊C4×C5⋊D5 | 2 |
| #65964 | 5 |