Finite Group DatabasebetaFinite Group DatabasebetaOrder 3600.
992 conjugacy classes of subgroups; only the 201 normal subgroups are shown.
This group has 992 conjugacy classes of subgroups — too many to draw. Only its 201 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | (C3⋊D3)⋊(C5⋊D5) |
| commutator, cosocle | C2×C32×C52 | C23 |
| Frattini | C2 | C2×(C3⋊D3)⋊(C5⋊D5) |
| Fitting, socle | C22×C32×C52 | C22 |
| hypocenter | C32×C52 | C2×D4 |
| LCS | G ▷ C2×C32×C52 ▷ C32×C52 | |
| UCS | C1 ◁ C22 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C3×C3⋊(C5⋊D5) | C2 | semidirect |
| 2. C22×C52×C3⋊D3 | C2 | semidirect |
| 3. C2×C3×C3⋊#1039 | C2 | semidirect |
| 4. #14268298 | C2 | direct (N × H) |
| 9. C2×C52×C3⋊D3 | C22 | semidirect |
| 11. C2×C3×C3⋊(C5⋊D5) | C22 | semidirect |
| 12. C3×C3⋊#1039 | C22 | semidirect |
| 14. C22×C3⋊(C5⋊D5) | D3 | semidirect |
| 19. C2×C3⋊#1039 | D3 | semidirect |
| 23. C2×C32×C52 | D4 | semidirect |
| 28. C22×C5×C3⋊D3 | D5 | semidirect |
| 36. C2×C3⋊(C5⋊D5) | C2×D3 | semidirect |
| 46. C3⋊#1039 | C2×D3 | semidirect |
| 50. C32×C52 | C2×D4 | semidirect |
| 57. C2×C5×C3⋊D3 | C2×D5 | semidirect |
| 63. C2×C3×C52 | D12 | semidirect |
| 64. C2×C3×C52 | #67 | semidirect |
| 89. C2×C32×C5 | C22⋊D5 | semidirect |
| 95. C3×C52 | C2×D12 | semidirect |
| 96. C3×C52 | C2×#67 | semidirect |
| 97. C22×C3⋊D3 | C5⋊D5 | semidirect |
| 118. C2×C52 | #626 | semidirect |
| 123. C32×C5 | C2×C22⋊D5 | semidirect |
| 130. C2×C3⋊D3 | C2×C5⋊D5 | semidirect |
| 136. C2×C3×C5 | #1201 | semidirect |
| 137. C2×C3×C5 | #1203 | semidirect |
| 146. C52 | C2×#626 | semidirect |
| 162. C2×C32 | C22⋊(C5⋊D5) | semidirect |
| 168. C3×C5 | C2×#1201 | semidirect |
| 169. C3×C5 | C2×#1203 | semidirect |
| 187. C2×C5 | #67156 | semidirect |
| 190. C32 | C2×C22⋊(C5⋊D5) | semidirect |
| 198. C2×C3 | #10597114 | semidirect |
| 199. C2×C3 | #10597116 | semidirect |
| 207. C5 | C2×#67156 | semidirect |
| 215. C3 | C2×#10597114 | semidirect |
| 216. C3 | C2×#10597116 | semidirect |
| 219. C2 | #14268298 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C3⋊(C5⋊D5) | 2 |
| C22×C52×C3⋊D3 | 2 |
| C2×C3×C3⋊#1039 | 2 |
| #14268298 | 2 |
| C2×#10597116 | 3 |
| C2×#10597114 | 3 |
| C2×#67156 | 5 |