Finite Group DatabasebetaFinite Group DatabasebetaOrder 38220.
208 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 36 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⋊#16838460 | C2 | semidirect |
| 2. C5×C13×#64424 | C2 | semidirect |
| 3. (C7⋊D7)⋊D65 | C3 | semidirect |
| 4. C5×C13×#3861 | C22 | semidirect |
| 6. C7×D455 | C2×C3 | semidirect |
| 7. C5×C13×C7⋊D7 | C2×C3 | semidirect |
| 10. C13×#64424 | D5 | semidirect |
| 11. C5×C72×C13 | C22×C3 | semidirect |
| 18. C13×#3861 | C2×D5 | semidirect |
| 21. C5×#64424 | D13 | semidirect |
| 24. C13×C7⋊D7 | C3×D5 | semidirect |
| 28. D455 | AGL(1,𝔽7) | semidirect |
| 33. C5×#3861 | C2×D13 | semidirect |
| 34. C72×C13 | C2×C3×D5 | semidirect |
| 41. C5×C7⋊D7 | C3×D13 | semidirect |
| 43. C5×C7×C13 | C2×AGL(1,𝔽7) | semidirect |
| 48. #64424 | D65 | semidirect |
| 53. C5×C72 | C2×C3×D13 | semidirect |
| 65. #3861 | C2×D65 | semidirect |
| 71. C7⋊D7 | C3×D65 | semidirect |
| 74. C7×C13 | D5×AGL(1,𝔽7) | semidirect |
| 82. C5×C13 | #64423⋊C2 | semidirect |
| 85. C72 | C2×C3×D65 | semidirect |
| 92. C5×C7 | D13×AGL(1,𝔽7) | semidirect |
| 106. C13 | #64424⋊D5 | semidirect |
| 111. C7 | AGL(1,𝔽7)×D65 | semidirect |
| 114. C5 | #64424⋊D13 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5⋊#16838460 | 2 |
| C5×C13×#64424 | 2 |
| (C7⋊D7)⋊D65 | 3 |
| #64424⋊D13 | 5 |
| AGL(1,𝔽7)×D65 | 7 |
| #64424⋊D5 | 13 |