Finite Group DatabasebetaFinite Group DatabasebetaOrder 38220.
208 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 40 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. C7×C5⋊((C13⋊C3)⋊D7) | C2 | semidirect |
| 2. C5×C13⋊C3×C7⋊D7 | C2 | semidirect |
| 3. (C7⋊D7)⋊D65 | C3 | semidirect |
| 4. C5×C72×C13⋊C3 | C22 | semidirect |
| 6. C7×D455 | C2×C3 | semidirect |
| 7. C5×C13×C7⋊D7 | C2×C3 | semidirect |
| 9. C13⋊C3×C7⋊D7 | D5 | semidirect |
| 11. C5×C72×C13 | C22×C3 | semidirect |
| 13. C5⋊((C13⋊C3)⋊D7) | D7 | semidirect |
| 18. C72×C13⋊C3 | C2×D5 | semidirect |
| 23. C5×C7×C13⋊C3 | C2×D7 | semidirect |
| 24. C13×C7⋊D7 | C3×D5 | semidirect |
| 28. D455 | C3×D7 | semidirect |
| 34. C72×C13 | C2×C3×D5 | semidirect |
| 41. C5×C7⋊D7 | D13⋊C3 | semidirect |
| 43. C5×C7×C13 | C2×C3×D7 | semidirect |
| 51. C7×C13⋊C3 | D5×D7 | semidirect |
| 53. C5×C72 | C2×D13⋊C3 | semidirect |
| 59. C5×C13⋊C3 | D72 | semidirect |
| 71. C7⋊D7 | C5⋊(D13⋊C3) | semidirect |
| 74. C7×C13 | C3×D5×D7 | semidirect |
| 82. C5×C13 | C3×D72 | semidirect |
| 85. C72 | C2×C5⋊(D13⋊C3) | semidirect |
| 90. C13⋊C3 | D35⋊D7 | semidirect |
| 92. C5×C7 | D7×D13⋊C3 | semidirect |
| 106. C13 | C3×D35⋊D7 | semidirect |
| 111. C7 | D7×C5⋊(D13⋊C3) | semidirect |
| 114. C5 | ((C13⋊C3)⋊D7)⋊D7 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×C5⋊((C13⋊C3)⋊D7) | 2 |
| C5×C13⋊C3×C7⋊D7 | 2 |
| (C7⋊D7)⋊D65 | 3 |
| ((C13⋊C3)⋊D7)⋊D7 | 5 |
| D7×C5⋊(D13⋊C3) | 7 |
| C3×D35⋊D7 | 13 |