Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
328 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 112 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D5×D11 |
| commutator, socle, cosocle | C2×C5×C11 | C24 |
| Fitting | C5×Q8×C11 | C22 |
| hypercenter | Q8 | D5×D11 |
| hypocenter | C5×C11 | C2×#41 |
| LCS | G ▷ C2×C5×C11 ▷ C5×C11 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11725035 | C2 | semidirect |
| 2. C11×#713 | C2 | semidirect |
| 3. C5×Q8×D11 | C2 | semidirect |
| 4. D11×D20 | C2 | semidirect |
| 5. C4×D5×D11 | C2 | semidirect |
| 6. #11724986 | C2 | semidirect |
| 7. #11724985 | C2 | semidirect |
| 9. C5×Q8×C11 | C22 | semidirect |
| 10. D220 | C22 | semidirect |
| 11. C4×D55 | C22 | semidirect |
| 12. C11×D20 | C22 | semidirect |
| 13. C4×D5×C11 | C22 | semidirect |
| 15. C5×Dic22 | C22 | semidirect |
| 16. #89169 | C22 | semidirect |
| 17. #89166 | C22 | semidirect |
| 18. D5×Dic11 | C22 | semidirect |
| 31. Q8×D11 | D5 | semidirect |
| 39. C5×D11 | #41 | semidirect |
| 42. Q8×C11 | C2×D5 | semidirect |
| 52. Dic22 | C2×D5 | semidirect |
| 57. #713 | D11 | direct (N × H) |
| 60. C5×C11 | C2×#41 | semidirect |
| 71. C5×Q8 | C2×D11 | semidirect |
| 76. D20 | C2×D11 | semidirect |
| 80. C4×D5 | C2×D11 | semidirect |
| 85. D11 | #713 | direct (N × H) |
| 101. C11 | C2×#713 | semidirect |
| 108. Q8 | D5×D11 | semidirect |
| 118. C5 | #41×D11 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11725035 | 2 |
| C11×#713 | 2 |
| C5×Q8×D11 | 2 |
| D11×D20 | 2 |
| C4×D5×D11 | 2 |
| #11724986 | 2 |
| #11724985 | 2 |
| #41×D11 | 5 |
| C2×#713 | 11 |