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, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C52×C9×C37 | C22 |
| Frattini | C3 | D15×D185 |
| socle | C3×C52×C37 | C2×D3 |
| LCS | G ▷ C52×C9×C37 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5⋊D1665 | C2 | semidirect |
| 2. C5×C37×D45 | C2 | semidirect |
| 3. C5×C9×D185 | C2 | semidirect |
| 5. C52×C9×C37 | C22 | semidirect |
| 15. C37×D45 | D5 | semidirect |
| 17. C9×D185 | D5 | semidirect |
| 23. C5×D185 | D9 | semidirect |
| 26. C5×C9×C37 | C2×D5 | semidirect |
| 27. C5×C9×C37 | C2×D5 | semidirect |
| 36. C52×C37 | C2×D9 | semidirect |
| 47. C5×D45 | D37 | semidirect |
| 54. D185 | D45 | direct (N × H) |
| 57. C9×C37 | D52 | semidirect |
| 59. C52×C9 | C2×D37 | semidirect |
| 64. C5×C37 | D5×D9 | semidirect |
| 65. C5×C37 | C2×D45 | semidirect |
| 78. D45 | D185 | direct (N × H) |
| 91. C5×C9 | D5×D37 | semidirect |
| 92. C5×C9 | C2×D185 | semidirect |
| 93. C37 | D5×D45 | semidirect |
| 102. C52 | D9×D37 | semidirect |
| 119. C9 | D5×D185 | semidirect |
| 124. C5 | D37×D45 | semidirect |
| 125. C5 | D9×D185 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5⋊D1665 | 2 |
| C5×C37×D45 | 2 |
| C5×C9×D185 | 2 |
| D15×D185 | 3 |
| D9×D185 | 5 |
| D37×D45 | 5 |
| D5×D45 | 37 |