Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
328 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | C22×D35 |
| commutator, socle, cosocle | C2×C5×C7 | C24 |
| Frattini | C2 | C23×D35 |
| Fitting | C5×C7×#41 | C2 |
| hypercenter | #41 | D35 |
| hypocenter | C5×C7 | C2×#41 |
| LCS | G ▷ C2×C5×C7 ▷ C5×C7 | |
| UCS | C1 ◁ C4 ◁ #41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×C7×#41 | C2 | semidirect |
| 2. #10587991 | C2 | semidirect |
| 3. Q8×D35 | C2 | semidirect |
| 4. #10587989 | C2 | semidirect |
| 5. D4×D35 | C2 | semidirect |
| 6. #10587987 | C2 | semidirect |
| 7. C2×C4×D35 | C2 | semidirect |
| 9. C5×C7×Q8 | C22 | semidirect |
| 10. C5×C7×D4 | C22 | semidirect |
| 11. C2×C4×C5×C7 | C22 | semidirect |
| 12. C22⋊D35 | C22 | semidirect |
| 13. C2×Dic35 | C22 | semidirect |
| 14. D140 | C22 | semidirect |
| 17. C4×D35 | C22 | semidirect |
| 18. C4×D35 | C22 | semidirect |
| 19. Dic70 | C22 | semidirect |
| 30. C7×#41 | D5 | semidirect |
| 37. C5×#41 | D7 | semidirect |
| 47. D35 | #41 | direct (N × H) |
| 49. C7×Q8 | C2×D5 | semidirect |
| 50. C7×D4 | C2×D5 | semidirect |
| 51. C2×C4×C7 | C2×D5 | semidirect |
| 61. C5×Q8 | C2×D7 | semidirect |
| 62. C5×D4 | C2×D7 | semidirect |
| 63. C2×C4×C5 | C2×D7 | semidirect |
| 72. C5×C7 | C2×#41 | semidirect |
| 93. #41 | D35 | direct (N × H) |
| 107. Q8 | C2×D35 | semidirect |
| 110. D4 | C2×D35 | semidirect |
| 116. C2×C4 | C2×D35 | semidirect |
| 117. C7 | D5×#41 | semidirect |
| 118. C5 | D7×#41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×C7×#41 | 2 |
| #10587991 | 2 |
| Q8×D35 | 2 |
| #10587989 | 2 |
| D4×D35 | 2 |
| #10587987 | 2 |
| C2×C4×D35 | 2 |
| D7×#41 | 5 |
| D5×#41 | 7 |