Finite Group DatabasebetaFinite Group DatabasebetaOrder 38220.
144 conjugacy classes of subgroups; only the 33 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 33 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, hypocenter | C5×C72×C13 | C3×C4 |
| prime radical | D5×C13×#3861 | C2 |
| cosocle | C72×D5×C13 | C2×C3 |
| LCS | G ▷ C5×C72×C13 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C7×C7⋊#63120 | C3 | semidirect |
| 3. C5×C13×#3861 | C4 | semidirect |
| 9. C5×C72×C13 | C3×C4 | semidirect |
| 15. C13×#3861 | AGL(1,𝔽5) | semidirect |
| 16. C7⋊#63120 | ΓL(1,𝔽8) | semidirect |
| 30. C5×#3861 | Dic13 | semidirect |
| 31. C72×C13 | C3×AGL(1,𝔽5) | semidirect |
| 38. C5×C7×C13 | ΓL(1,𝔽8)⋊C4 | semidirect |
| 39. C5×C7×C13 | C4×ΓL(1,𝔽8) | semidirect |
| 50. C5×C72 | C3×Dic13 | semidirect |
| 60. #3861 | #63120 | semidirect |
| 69. C7×C13 | AGL(1,𝔽5)×ΓL(1,𝔽8) | semidirect |
| 70. C7×C13 | ΓL(1,𝔽8)⋊AGL(1,𝔽5) | semidirect |
| 77. C5×C13 | #10596873 | semidirect |
| 80. C72 | C3×#63120 | semidirect |
| 86. C5×C7 | ΓL(1,𝔽8)×Dic13 | semidirect |
| 87. C5×C7 | ΓL(1,𝔽8)⋊Dic13 | semidirect |
| 100. C13 | #15668767 | semidirect |
| 104. C7 | ΓL(1,𝔽8)⋊#63120 | semidirect |
| 105. C7 | ΓL(1,𝔽8)×#63120 | semidirect |
| 107. C5 | #21439536 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×C13×#3861 | 2 |
| C7×C7⋊#63120 | 3 |
| #21439536 | 5 |
| ΓL(1,𝔽8)×#63120 | 7 |
| ΓL(1,𝔽8)⋊#63120 | 7 |
| #15668767 | 13 |