Finite Group DatabasebetaFinite Group DatabasebetaOrder 38220.
208 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 37 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⋊#16838459 | C2 | semidirect |
| 2. C5×#16838449 | C2 | semidirect |
| 3. C13×D35⋊D7 | C3 | semidirect |
| 4. C5×#14274262 | C22 | semidirect |
| 6. C7×C13×D35 | C2×C3 | semidirect |
| 7. C5×C13×C7⋊D7 | C2×C3 | semidirect |
| 10. #16838449 | D5 | semidirect |
| 11. C5×C72×C13 | C22×C3 | semidirect |
| 18. #14274262 | C2×D5 | semidirect |
| 24. C13×C7⋊D7 | C3×D5 | semidirect |
| 27. D35⋊D7 | C13⋊C3 | semidirect |
| 28. C13×D35 | AGL(1,𝔽7) | semidirect |
| 34. C72×C13 | C2×C3×D5 | semidirect |
| 40. C7×D35 | C2×C13⋊C3 | semidirect |
| 41. C5×C7⋊D7 | C2×C13⋊C3 | semidirect |
| 43. C5×C7×C13 | C2×AGL(1,𝔽7) | semidirect |
| 53. C5×C72 | C22×C13⋊C3 | semidirect |
| 71. C7⋊D7 | D5×C13⋊C3 | semidirect |
| 74. C7×C13 | D5×AGL(1,𝔽7) | semidirect |
| 78. D35 | #10587721 | semidirect |
| 82. C5×C13 | #64423⋊C2 | semidirect |
| 85. C72 | C2×D5×C13⋊C3 | semidirect |
| 92. C5×C7 | C2×#10587721 | semidirect |
| 106. C13 | #64424⋊D5 | semidirect |
| 111. C7 | D5×#10587721 | semidirect |
| 114. C5 | #21439613 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5⋊#16838459 | 2 |
| C5×#16838449 | 2 |
| C13×D35⋊D7 | 3 |
| #21439613 | 5 |
| D5×#10587721 | 7 |
| #64424⋊D5 | 13 |