Finite Group DatabasebetaFinite Group DatabasebetaOrder 38220.
136 conjugacy classes of subgroups; only the 24 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 24 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 | #64418⋊D5 |
| 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. C13×C5⋊#64425 | C2 | semidirect |
| 3. C5×C13×#64418 | C2 | semidirect |
| 5. C5×C13×#3862 | C22 | semidirect |
| 7. C13×C5⋊(C7⋊D7) | D3 | semidirect |
| 11. C13×#64418 | D5 | semidirect |
| 13. C5×C72×C13 | C2×D3 | semidirect |
| 14. #64418⋊D5 | C13 | direct (N × H) |
| 17. C13×#3862 | C2×D5 | semidirect |
| 20. C5⋊#64425 | C2×C13 | semidirect |
| 21. C5⋊#64418 | C2×C13 | semidirect |
| 22. C5×#64418 | C2×C13 | semidirect |
| 36. C5×#3862 | C22×C13 | semidirect |
| 37. C72×C13 | D3×D5 | semidirect |
| 40. C5⋊(C7⋊D7) | D3×C13 | semidirect |
| 53. #64418 | D5×C13 | semidirect |
| 56. C5×C72 | C2×D3×C13 | semidirect |
| 68. #3862 | C2×D5×C13 | semidirect |
| 91. C5×C13 | #64418⋊C2 | semidirect |
| 94. C72 | D3×D5×C13 | semidirect |
| 118. C13 | #64418⋊D5 | direct (N × H) |
| 129. 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 |
| C13×C5⋊#64425 | 2 |
| C5×C13×#64418 | 2 |
| C13×D7×D35 | 3 |
| C13×#64418⋊C2 | 5 |
| #64418⋊D5 | 13 |
| D3×D5×C13 | 49 |