Finite Group DatabasebetaFinite Group DatabasebetaOrder 38220.
200 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 35 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. D65×#3862 | C2 | semidirect |
| 2. C13×C5⋊#64425 | C2 | semidirect |
| 3. C5×#16838454 | C2 | semidirect |
| 4. D65⋊(C7⋊D7) | C3 | semidirect |
| 5. C5×C13×#3862 | C22 | semidirect |
| 7. C13×C5⋊(C7⋊D7) | C2×C3 | semidirect |
| 8. C72×D65 | C2×C3 | semidirect |
| 9. C5×C7⋊D91 | C2×C3 | semidirect |
| 12. #16838454 | D5 | semidirect |
| 14. C5×C72×C13 | C22×C3 | semidirect |
| 20. C13×#3862 | C2×D5 | semidirect |
| 24. C5⋊#64425 | D13 | semidirect |
| 27. C7⋊D91 | C3×D5 | semidirect |
| 35. C7×D65 | AGL(1,𝔽7) | semidirect |
| 39. C5×#3862 | C2×D13 | semidirect |
| 40. C72×C13 | C2×C3×D5 | semidirect |
| 45. C5⋊(C7⋊D7) | C3×D13 | semidirect |
| 49. C5×C7×C13 | C2×AGL(1,𝔽7) | semidirect |
| 61. C5×C72 | C2×C3×D13 | semidirect |
| 74. #3862 | D5×D13 | semidirect |
| 77. D65 | #64425 | semidirect |
| 85. C7×C13 | D5×AGL(1,𝔽7) | semidirect |
| 96. C5×C13 | C2×#64425 | semidirect |
| 99. C72 | C3×D5×D13 | semidirect |
| 105. C5×C7 | D13×AGL(1,𝔽7) | semidirect |
| 123. C13 | D5×#64425 | semidirect |
| 129. C7 | (C5⋊AGL(1,𝔽7))⋊D13 | semidirect |
| 133. C5 | D13×#64425 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D65×#3862 | 2 |
| C13×C5⋊#64425 | 2 |
| C5×#16838454 | 2 |
| D65⋊(C7⋊D7) | 3 |
| D13×#64425 | 5 |
| (C5⋊AGL(1,𝔽7))⋊D13 | 7 |
| D5×#64425 | 13 |