Finite Group DatabasebetaFinite Group DatabasebetaOrder 38220.
208 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C72×C13 | C22×C3 |
| LCS | G ▷ C5×C72×C13 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5⋊((C13⋊C3)⋊(C7⋊D7)) | C2 | semidirect |
| 2. C7×C13⋊C3×D35 | C2 | semidirect |
| 3. C5×C7×(C13⋊C3)⋊D7 | C2 | semidirect |
| 4. D35×D91 | C3 | semidirect |
| 5. C5×C72×C13⋊C3 | C22 | semidirect |
| 7. C5⋊(C7⋊D91) | C2×C3 | semidirect |
| 8. C7×C13×D35 | C2×C3 | semidirect |
| 9. C5×C7×D91 | C2×C3 | semidirect |
| 14. C7×(C13⋊C3)⋊D7 | D5 | semidirect |
| 15. C5×C72×C13 | C22×C3 | semidirect |
| 20. C13⋊C3×D35 | D7 | semidirect |
| 22. C5×(C13⋊C3)⋊D7 | D7 | semidirect |
| 25. C72×C13⋊C3 | C2×D5 | semidirect |
| 32. C5×C7×C13⋊C3 | C2×D7 | semidirect |
| 33. C5×C7×C13⋊C3 | C2×D7 | semidirect |
| 35. C7×D91 | C3×D5 | semidirect |
| 43. C13×D35 | C3×D7 | semidirect |
| 45. C5×D91 | C3×D7 | semidirect |
| 49. C72×C13 | C2×C3×D5 | semidirect |
| 55. (C13⋊C3)⋊D7 | D35 | direct (N × H) |
| 59. C7×D35 | D13⋊C3 | semidirect |
| 62. C5×C7×C13 | C2×C3×D7 | semidirect |
| 63. C5×C7×C13 | C2×C3×D7 | semidirect |
| 75. C7×C13⋊C3 | D5×D7 | semidirect |
| 76. C7×C13⋊C3 | C2×D35 | semidirect |
| 78. C5×C72 | C2×D13⋊C3 | semidirect |
| 87. C5×C13⋊C3 | D72 | semidirect |
| 92. D91 | C3×D35 | semidirect |
| 109. C7×C13 | C3×D5×D7 | semidirect |
| 110. C7×C13 | C2×C3×D35 | semidirect |
| 120. D35 | (C13⋊C3)⋊D7 | direct (N × H) |
| 123. C5×C13 | C3×D72 | semidirect |
| 126. C72 | D5×D13⋊C3 | semidirect |
| 134. C13⋊C3 | D7×D35 | semidirect |
| 136. C5×C7 | D7×D13⋊C3 | semidirect |
| 137. C5×C7 | C2×(C13⋊C3)⋊D7 | semidirect |
| 158. C13 | C3×D7×D35 | semidirect |
| 164. C7 | D35×D13⋊C3 | semidirect |
| 165. C7 | D5×(C13⋊C3)⋊D7 | semidirect |
| 169. C5 | D7×(C13⋊C3)⋊D7 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5⋊((C13⋊C3)⋊(C7⋊D7)) | 2 |
| C7×C13⋊C3×D35 | 2 |
| C5×C7×(C13⋊C3)⋊D7 | 2 |
| D35×D91 | 3 |
| D7×(C13⋊C3)⋊D7 | 5 |
| D5×(C13⋊C3)⋊D7 | 7 |
| D35×D13⋊C3 | 7 |
| C3×D7×D35 | 13 |