Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
328 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 110 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | C2×D5×D11 |
| commutator, socle, cosocle | C2×C5×C11 | C24 |
| Frattini | C2 | C22×D5×D11 |
| Fitting | C2×C4×C5×C11 | C22 |
| hypercenter | C2×C4 | D5×D11 |
| hypocenter | C5×C11 | C2×#41 |
| LCS | G ▷ C2×C5×C11 ▷ C5×C11 | |
| UCS | C1 ◁ C4 ◁ C2×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C4×D55 | C2 | semidirect |
| 2. C11×#709 | C2 | semidirect |
| 3. C5×#4339 | C2 | semidirect |
| 4. #11725007 | C2 | semidirect |
| 5. #11724997 | C2 | semidirect |
| 6. #11724994 | C2 | semidirect |
| 7. C4×D5×D11 | C2 | semidirect |
| 8. #11724988 | C2 | semidirect |
| 9. D55⋊Q8 | C2 | semidirect |
| 10. #11724985 | C2 | semidirect |
| 11. #11724983 | C2 | semidirect |
| 14. C2×C4×C5×C11 | C22 | semidirect |
| 15. C2×Dic55 | C22 | semidirect |
| 18. C4×D55 | C22 | semidirect |
| 19. C4×D55 | C22 | semidirect |
| 20. C11×C22⋊D5 | C22 | semidirect |
| 21. C11×D20 | C22 | semidirect |
| 22. C4×D5×C11 | C22 | semidirect |
| 23. C11×Dic10 | C22 | semidirect |
| 24. C5×C22⋊D11 | C22 | semidirect |
| 25. C5×D44 | C22 | semidirect |
| 26. C4×C5×D11 | C22 | semidirect |
| 27. C5×Dic22 | C22 | semidirect |
| 28. #89170 | C22 | semidirect |
| 29. #89169 | C22 | semidirect |
| 30. #89168 | C22 | semidirect |
| 31. #89167 | C22 | semidirect |
| 33. D5×Dic11 | C22 | semidirect |
| 34. Dic5×D11 | C22 | semidirect |
| 57. #4339 | D5 | semidirect |
| 64. D55 | #41 | semidirect |
| 73. C2×C4×C11 | C2×D5 | semidirect |
| 76. C22⋊D11 | C2×D5 | semidirect |
| 80. D44 | C2×D5 | semidirect |
| 87. C4×D11 | C2×D5 | semidirect |
| 89. Dic22 | C2×D5 | semidirect |
| 98. #709 | D11 | semidirect |
| 101. C5×C11 | C2×#41 | semidirect |
| 121. C2×C4×C5 | C2×D11 | semidirect |
| 124. C22⋊D5 | C2×D11 | semidirect |
| 128. D20 | C2×D11 | semidirect |
| 135. C4×D5 | C2×D11 | semidirect |
| 137. Dic10 | C2×D11 | semidirect |
| 169. C11 | D5×#41 | semidirect |
| 198. C2×C4 | D5×D11 | semidirect |
| 199. C5 | #41×D11 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D55 | 2 |
| C11×#709 | 2 |
| C5×#4339 | 2 |
| #11725007 | 2 |
| #11724997 | 2 |
| #11724994 | 2 |
| C4×D5×D11 | 2 |
| #11724988 | 2 |
| D55⋊Q8 | 2 |
| #11724985 | 2 |
| #11724983 | 2 |
| #41×D11 | 5 |
| D5×#41 | 11 |