Finite Group DatabasebetaFinite Group DatabasebetaOrder 33300.
144 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 36 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 | C52×C37 | C22×C9 |
| prime radical | D5×C5⋊(D37⋊C3) | C3 |
| cosocle | C52×C37⋊C3 | C22×C3 |
| LCS | G ▷ C52×C37 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5⋊(C5⋊(#66526⋊C2)) | C2 | semidirect |
| 2. C5×D5×#66526 | C2 | semidirect |
| 3. C5×C5⋊(#66526⋊C2) | C2 | semidirect |
| 5. C52×#66526 | C22 | semidirect |
| 11. D5×D185 | C9 | semidirect |
| 13. D5×#66526 | D5 | semidirect |
| 17. C5⋊(#66526⋊C2) | D5 | direct (N × H) |
| 22. C5⋊D185 | C2×C9 | semidirect |
| 23. C5×D185 | C2×C9 | semidirect |
| 24. C5×D5×C37 | C2×C9 | semidirect |
| 26. C5×#66526 | C2×D5 | semidirect |
| 27. C5×#66526 | C2×D5 | semidirect |
| 36. C52×C37 | C22×C9 | semidirect |
| 54. D185 | C9×D5 | semidirect |
| 56. D5×C37 | C9×D5 | semidirect |
| 57. #66526 | D52 | semidirect |
| 64. C5×C37 | C2×C9×D5 | semidirect |
| 65. C5×C37 | C2×C9×D5 | semidirect |
| 89. C5×D5 | #66526⋊C2 | semidirect |
| 93. C37 | C9×D52 | semidirect |
| 102. C52 | C2×#66526⋊C2 | semidirect |
| 118. D5 | C5⋊(#66526⋊C2) | direct (N × H) |
| 124. C5 | D5×#66526⋊C2 | semidirect |
| 125. C5 | C2×C5⋊(#66526⋊C2) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5⋊(C5⋊(#66526⋊C2)) | 2 |
| C5×D5×#66526 | 2 |
| C5×C5⋊(#66526⋊C2) | 2 |
| D5×C5⋊(D37⋊C3) | 3 |
| C2×C5⋊(#66526⋊C2) | 5 |
| D5×#66526⋊C2 | 5 |
| C9×D52 | 37 |