Finite Group DatabasebetaFinite Group DatabasebetaOrder 30420.
116 conjugacy classes of subgroups; only the 33 normal subgroups are shown.
This group has 116 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 | C3×C5×C132 | C3×C4 |
| prime radical | C3×C13⋊C3×D65 | C2 |
| cosocle | C3×C13×D65 | C2×C3 |
| LCS | G ▷ C3×C5×C132 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C13×C3⋊#63122 | C3 | semidirect |
| 4. C3×C5×C13×C13⋊C3 | C4 | semidirect |
| 12. C5×C13×C13⋊C3 | Dic3 | semidirect |
| 13. C3×C5×C132 | C3×C4 | semidirect |
| 19. C3×C13×C13⋊C3 | AGL(1,𝔽5) | semidirect |
| 25. C5×C132 | C3×Dic3 | semidirect |
| 26. C3⋊#63122 | C13⋊C3 | direct (N × H) |
| 32. C3×C5×C13⋊C3 | #261 | semidirect |
| 33. C3×C132 | C3×AGL(1,𝔽5) | semidirect |
| 35. C13×C13⋊C3 | ΓL(1,𝔽16) | semidirect |
| 52. C3×C5×C13 | C4×C13⋊C3 | semidirect |
| 53. C3×C5×C13 | C3×#261 | semidirect |
| 55. C5×C13⋊C3 | C3⋊#261 | semidirect |
| 57. C132 | C3×ΓL(1,𝔽16) | semidirect |
| 65. C3×C13⋊C3 | #63122 | semidirect |
| 74. C5×C13 | Dic3×C13⋊C3 | semidirect |
| 75. C5×C13 | C3×C3⋊#261 | semidirect |
| 84. C3×C13 | AGL(1,𝔽5)×C13⋊C3 | semidirect |
| 85. C3×C13 | C3×#63122 | semidirect |
| 87. C13⋊C3 | C3⋊#63122 | direct (N × H) |
| 98. C3×C5 | C13⋊C3×#261 | semidirect |
| 100. C13 | C13⋊C3×ΓL(1,𝔽16) | semidirect |
| 101. C13 | C3×C3⋊#63122 | semidirect |
| 109. C5 | C13⋊C3×C3⋊#261 | semidirect |
| 113. C3 | C13⋊C3×#63122 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C13⋊C3×D65 | 2 |
| C13×C3⋊#63122 | 3 |
| C13⋊C3×#63122 | 3 |
| C13⋊C3×C3⋊#261 | 5 |
| C3×C3⋊#63122 | 13 |
| C13⋊C3×ΓL(1,𝔽16) | 13 |