Finite Group DatabasebetaFinite Group DatabasebetaOrder 38220.
136 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 30 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | C13⋊#64418 |
| commutator, cosocle, hypocenter | C13×#3862 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C72×C13 | D3 |
| LCS | G ▷ C13×#3862 | |
| UCS | C1 ◁ C2×C5 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C5×C13×#3862 | C2 | semidirect |
| 2. C5×C13⋊#64418 | C2 | direct (N × H) |
| 4. C5×C13×#3862 | C22 | semidirect |
| 5. C2×C13⋊#64418 | C5 | direct (N × H) |
| 7. C2×C5×C72×C13 | D3 | semidirect |
| 8. C2×C13×#3862 | C2×C5 | semidirect |
| 9. C13⋊#64418 | C2×C5 | direct (N × H) |
| 10. C5×C72×C13 | C2×D3 | semidirect |
| 14. C13×#3862 | C22×C5 | semidirect |
| 17. C2×C5×#3862 | D13 | semidirect |
| 20. C2×C72×C13 | C5×D3 | semidirect |
| 29. C5×#3862 | C2×D13 | semidirect |
| 30. C72×C13 | C2×C5×D3 | semidirect |
| 33. C2×C5×C72 | D39 | semidirect |
| 42. C2×#3862 | C5×D13 | semidirect |
| 46. C5×C72 | C2×D39 | semidirect |
| 56. #3862 | C2×C5×D13 | semidirect |
| 59. C2×C5×C13 | #64418 | semidirect |
| 62. C2×C72 | C5×D39 | semidirect |
| 74. C5×C13 | C2×#64418 | semidirect |
| 77. C72 | C2×C5×D39 | semidirect |
| 87. C2×C13 | C5×#64418 | semidirect |
| 97. C13 | C2×C5×#64418 | semidirect |
| 100. C2×C5 | C13⋊#64418 | direct (N × H) |
| 106. C5 | C2×C13⋊#64418 | direct (N × H) |
| 110. C2 | C5×C13⋊#64418 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×C13×#3862 | 2 |
| C5×C13⋊#64418 | 2 |
| C2×C5×C7×D91 | 3 |
| C2×C13⋊#64418 | 5 |
| C2×C5×#64418 | 13 |
| C2×C5×D39 | 49 |