Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
328 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 127 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D55 |
| commutator, cosocle | C2×C5×C11 | C24 |
| Frattini | C2 | C23×D55 |
| Fitting | C2×C5×D4×C11 | C2 |
| socle | C22×C5×C11 | C23 |
| hypercenter | C2×D4 | D55 |
| hypocenter | C5×C11 | C2×#41 |
| LCS | G ▷ C2×C5×C11 ▷ C5×C11 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C5×D4×C11 | C2 | semidirect |
| 2. C2×C22⋊D55 | C2 | semidirect |
| 3. C22×Dic55 | C2 | semidirect |
| 4. #11725033 | C2 | direct (N × H) |
| 5. C2×C4×D55 | C2 | semidirect |
| 6. C2×Dic110 | C2 | semidirect |
| 9. C5×D4×C11 | C22 | semidirect |
| 11. C22⋊D55 | C22 | semidirect |
| 14. C2×Dic55 | C22 | semidirect |
| 15. C4×D55 | C22 | semidirect |
| 16. Dic110 | C22 | semidirect |
| 26. C2×D4×C11 | D5 | semidirect |
| 34. C2×C5×C11 | #41 | semidirect |
| 39. D4×C11 | C2×D5 | semidirect |
| 47. C2×C5×D4 | D11 | semidirect |
| 53. C5×C11 | C2×#41 | semidirect |
| 64. C5×D4 | C2×D11 | semidirect |
| 74. C2×C11 | #711 | semidirect |
| 88. C2×D4 | D55 | semidirect |
| 91. C11 | C2×#711 | semidirect |
| 93. C2×C5 | #4341 | semidirect |
| 100. D4 | C2×D55 | semidirect |
| 106. C5 | C2×#4341 | semidirect |
| 117. C2 | #11725033 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×D4×C11 | 2 |
| C2×C22⋊D55 | 2 |
| C22×Dic55 | 2 |
| #11725033 | 2 |
| C2×C4×D55 | 2 |
| C2×Dic110 | 2 |
| C2×#4341 | 5 |
| C2×#711 | 11 |