Finite Group DatabasebetaFinite Group DatabasebetaOrder 38220.
120 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 120 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 | C2 | C5⋊#16838469 |
| commutator, hypocenter | C5×C72×C13 | C3×C4 |
| Fitting, socle, cosocle | C2×C5×C72×C13 | C2×C3 |
| prime radical | C2×C5×C7×#63271 | C2 |
| LCS | G ▷ C5×C72×C13 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C7⋊Dic455 | C3 | semidirect |
| 3. C5×C7×#63271 | C4 | semidirect |
| 9. C5×C72×C13 | C3×C4 | semidirect |
| 14. C7×#63271 | Dic5 | semidirect |
| 19. C5×#63271 | Dic7 | semidirect |
| 30. C72×C13 | C3×Dic5 | semidirect |
| 36. C5×C7×C13 | ΓL(1,𝔽8)⋊C4 | semidirect |
| 37. C5×C7×C13 | C3×Dic7 | semidirect |
| 45. #63271 | Dic35 | semidirect |
| 48. C5×C72 | Dic13⋊C3 | semidirect |
| 66. C7×C13 | ΓL(1,𝔽8)⋊Dic5 | semidirect |
| 67. C7×C13 | C3×Dic35 | semidirect |
| 74. C5×C13 | ΓL(1,𝔽8)⋊Dic7 | semidirect |
| 77. C72 | Dic65⋊C3 | semidirect |
| 82. C5×C7 | #11763955 | semidirect |
| 83. C5×C7 | #11763964 | semidirect |
| 96. C13 | ΓL(1,𝔽8)⋊Dic35 | semidirect |
| 100. C7 | #19129703 | semidirect |
| 101. C7 | #19129706 | semidirect |
| 103. C5 | #21439545 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×C7×#63271 | 2 |
| C7⋊Dic455 | 3 |
| #21439545 | 5 |
| #19129706 | 7 |
| #19129703 | 7 |
| ΓL(1,𝔽8)⋊Dic35 | 13 |