Finite Group DatabasebetaFinite Group DatabasebetaOrder 26100.
124 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C3⋊#15668533 |
| commutator, hypocenter | C3×C52×C29 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C32×C52×C29 | C4 |
| prime radical | C32×C5×D145 | C2 |
| cosocle | C3×C5×D145 | C2×C3 |
| LCS | G ▷ C3×C52×C29 | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3⋊#15668533 | C3 | direct (N × H) |
| 4. C32×C52×C29 | C4 | semidirect |
| 14. C3×C52×C29 | Dic3 | semidirect |
| 15. C3×C52×C29 | C3×C4 | semidirect |
| 22. C32×C5×C29 | Dic5 | semidirect |
| 23. C32×C5×C29 | AGL(1,𝔽5) | semidirect |
| 32. C52×C29 | C3×Dic3 | semidirect |
| 42. C3×C5×C29 | C3×Dic5 | semidirect |
| 43. C3×C5×C29 | Dic15 | semidirect |
| 44. C3×C5×C29 | C3×AGL(1,𝔽5) | semidirect |
| 45. C3×C5×C29 | ΓL(1,𝔽16) | semidirect |
| 52. C32×C29 | #1042 | semidirect |
| 53. C32×C52 | #1181 | semidirect |
| 63. C5×C29 | C3×Dic15 | semidirect |
| 64. C5×C29 | C3×ΓL(1,𝔽16) | semidirect |
| 70. C3×C29 | C3×#1042 | semidirect |
| 71. C3×C29 | C3⋊#1042 | semidirect |
| 73. C3×C52 | C3×#1181 | semidirect |
| 74. C3×C52 | C3⋊#1181 | semidirect |
| 82. C32×C5 | #10596815 | semidirect |
| 83. C32×C5 | #10596817 | semidirect |
| 91. C29 | C3×C3⋊#1042 | semidirect |
| 92. C52 | C3×C3⋊#1181 | semidirect |
| 101. C3×C5 | C3×#10596815 | semidirect |
| 102. C3×C5 | C3×#10596817 | semidirect |
| 103. C3×C5 | C3⋊#10596815 | semidirect |
| 104. C3×C5 | C3⋊#10596817 | semidirect |
| 109. C32 | #15668533 | semidirect |
| 114. C5 | C3×C3⋊#10596815 | semidirect |
| 115. C5 | C3×C3⋊#10596817 | semidirect |
| 118. C3 | C3×#15668533 | semidirect |
| 119. C3 | C3⋊#15668533 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C5×D145 | 2 |
| C3⋊#15668533 | 3 |
| C3×#15668533 | 3 |
| C3×C3⋊#10596817 | 5 |
| C3×C3⋊#10596815 | 5 |
| C3×C3⋊#1042 | 29 |