Finite Group DatabasebetaFinite Group DatabasebetaOrder 38220.
120 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 45 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 | C2 | D5×C13⋊#3862 |
| commutator, hypocenter | C5×C72×C13 | C3×C4 |
| Fitting, socle, cosocle | C2×C5×C72×C13 | C2×C3 |
| prime radical | C2×C5×C13⋊#3862 | C2 |
| LCS | G ▷ C5×C72×C13 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C72×C13×Dic5 | C3 | semidirect |
| 3. C5×C13⋊#3862 | C4 | semidirect |
| 9. C5×C72×C13 | C3×C4 | semidirect |
| 14. C13⋊#3862 | Dic5 | direct (N × H) |
| 16. C7×C13×Dic5 | ΓL(1,𝔽8) | semidirect |
| 17. C7×C13×Dic5 | ΓL(1,𝔽8) | semidirect |
| 24. C72×Dic5 | C13⋊C3 | semidirect |
| 30. C72×C13 | C3×Dic5 | semidirect |
| 36. C5×C7×C13 | C4×ΓL(1,𝔽8) | semidirect |
| 37. C5×C7×C13 | C4×ΓL(1,𝔽8) | semidirect |
| 47. C13×Dic5 | #3862 | semidirect |
| 48. C5×C72 | C4×C13⋊C3 | semidirect |
| 59. C7×Dic5 | #63270 | semidirect |
| 60. C7×Dic5 | #63271 | semidirect |
| 66. C7×C13 | Dic5×ΓL(1,𝔽8) | semidirect |
| 67. C7×C13 | Dic5×ΓL(1,𝔽8) | semidirect |
| 74. C5×C13 | C4×#3862 | semidirect |
| 77. C72 | Dic5×C13⋊C3 | semidirect |
| 82. C5×C7 | C4×#63270 | semidirect |
| 83. C5×C7 | C4×#63271 | semidirect |
| 91. Dic5 | C13⋊#3862 | direct (N × H) |
| 96. C13 | Dic5×#3862 | semidirect |
| 100. C7 | Dic5×#63270 | semidirect |
| 101. C7 | Dic5×#63271 | semidirect |
| 103. C5 | C4×C13⋊#3862 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×C13⋊#3862 | 2 |
| C72×C13×Dic5 | 3 |
| C4×C13⋊#3862 | 5 |
| Dic5×#63271 | 7 |
| Dic5×#63270 | 7 |
| Dic5×#3862 | 13 |