Finite Group DatabasebetaFinite Group DatabasebetaOrder 38220.
136 conjugacy classes of subgroups; only the 26 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 26 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | #15668791 |
| commutator, cosocle, hypocenter | C5×#3862 | C22×C13 |
| Frattini | C1 | G |
| Fitting, socle | C5×C72×C13 | C2×D3 |
| LCS | G ▷ C5×#3862 | |
| UCS | C1 ◁ C13 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C13×C5⋊#64418 | C2 | semidirect |
| 2. C5×C13×#64425 | C2 | semidirect |
| 4. C5×C13×#3862 | C22 | semidirect |
| 7. C5×C13×C7⋊D7 | D3 | semidirect |
| 9. C13×#64425 | D5 | semidirect |
| 10. C5×C72×C13 | C2×D3 | semidirect |
| 11. #15668791 | C13 | direct (N × H) |
| 14. C13×#3862 | C2×D5 | semidirect |
| 16. C5×#64425 | C2×C13 | semidirect |
| 17. C5⋊#64418 | C2×C13 | semidirect |
| 19. C13×C7⋊D7 | D15 | semidirect |
| 27. C5×#3862 | C22×C13 | semidirect |
| 28. C72×C13 | C2×D15 | semidirect |
| 32. C5×C7⋊D7 | D3×C13 | semidirect |
| 38. #64425 | D5×C13 | semidirect |
| 42. C5×C72 | C2×D3×C13 | semidirect |
| 51. #3862 | C2×D5×C13 | semidirect |
| 56. C7⋊D7 | C13×D15 | semidirect |
| 66. C5×C13 | #64418⋊C2 | semidirect |
| 69. C72 | C2×C13×D15 | semidirect |
| 86. C13 | #15668791 | direct (N × H) |
| 94. C5 | C13×#64418⋊C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×C5⋊#64418 | 2 |
| C5×C13×#64425 | 2 |
| C13×D35⋊D7 | 3 |
| C13×#64418⋊C2 | 5 |
| #15668791 | 13 |
| C2×C13×D15 | 49 |