Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
328 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 174 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C5 | C22×D7 |
| commutator, cosocle | C2×C7 | C24×C5 |
| Frattini | C2 | C23×C5×D7 |
| Fitting | C5×C7×#41 | C2 |
| socle | C2×C5×C7 | C24 |
| hypercenter | C5×#41 | D7 |
| hypocenter | C7 | C2×C5×#41 |
| LCS | G ▷ C2×C7 ▷ C7 | |
| UCS | C1 ◁ C4×C5 ◁ C5×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×C7×#41 | C2 | semidirect |
| 2. C5×#1161 | C2 | semidirect |
| 3. C5×Q8×D7 | C2 | semidirect |
| 4. C5×#1159 | C2 | semidirect |
| 5. C5×D4×D7 | C2 | semidirect |
| 6. C5×#1157 | C2 | semidirect |
| 7. C2×C4×C5×D7 | C2 | semidirect |
| 9. C5×C7×Q8 | C22 | semidirect |
| 10. C5×C7×D4 | C22 | semidirect |
| 11. C2×C4×C5×C7 | C22 | semidirect |
| 12. C5×C22⋊D7 | C22 | semidirect |
| 13. C2×C5×Dic7 | C22 | semidirect |
| 14. C5×D28 | C22 | semidirect |
| 17. C4×C5×D7 | C22 | semidirect |
| 18. C4×C5×D7 | C22 | semidirect |
| 19. C5×Dic14 | C22 | semidirect |
| 20. D7×#41 | C5 | direct (N × H) |
| 30. C7×#41 | C2×C5 | semidirect |
| 31. #1161 | C2×C5 | semidirect |
| 32. Q8×D7 | C2×C5 | semidirect |
| 33. #1159 | C2×C5 | semidirect |
| 34. D4×D7 | C2×C5 | semidirect |
| 35. #1157 | C2×C5 | semidirect |
| 36. C2×C4×D7 | C2×C5 | semidirect |
| 40. C5×#41 | D7 | direct (N × H) |
| 47. C5×D7 | #41 | direct (N × H) |
| 49. C7×Q8 | C22×C5 | semidirect |
| 50. C7×D4 | C22×C5 | semidirect |
| 51. C2×C4×C7 | C22×C5 | semidirect |
| 52. C22⋊D7 | C22×C5 | semidirect |
| 53. C2×Dic7 | C22×C5 | semidirect |
| 54. D28 | C22×C5 | semidirect |
| 57. C4×D7 | C22×C5 | semidirect |
| 58. C4×D7 | C22×C5 | semidirect |
| 59. Dic14 | C22×C5 | semidirect |
| 62. C5×Q8 | C2×D7 | semidirect |
| 65. C5×D4 | C2×D7 | semidirect |
| 71. C2×C4×C5 | C2×D7 | semidirect |
| 72. C5×C7 | C2×#41 | semidirect |
| 93. #41 | C5×D7 | direct (N × H) |
| 100. D7 | C5×#41 | direct (N × H) |
| 107. Q8 | C2×C5×D7 | semidirect |
| 110. D4 | C2×C5×D7 | semidirect |
| 116. C2×C4 | C2×C5×D7 | semidirect |
| 117. C7 | C2×C5×#41 | semidirect |
| 118. C5 | D7×#41 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×C7×#41 | 2 |
| C5×#1161 | 2 |
| C5×Q8×D7 | 2 |
| C5×#1159 | 2 |
| C5×D4×D7 | 2 |
| C5×#1157 | 2 |
| C2×C4×C5×D7 | 2 |
| D7×#41 | 5 |
| C2×C5×#41 | 7 |