Finite Group DatabasebetaFinite Group DatabasebetaOrder 2400.
864 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 864 conjugacy classes of subgroups — too many to draw. Only its 174 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×D3×C5⋊D5 |
| commutator, socle, cosocle | C22×C3×C52 | C23 |
| Fitting | C2×C3×C4×C52 | C22 |
| hypercenter | C2×C4 | D3×C5⋊D5 |
| hypocenter | C3×C52 | #127 |
| LCS | G ▷ C22×C3×C52 ▷ C3×C52 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C4⋊(C3⋊(C5⋊D5)) | C2 | semidirect |
| 2. C2×C52×D12 | C2 | semidirect |
| 3. C2×#10597116 | C2 | semidirect |
| 4. C3×C4×#1039 | C2 | semidirect |
| 17. C4×#1039 | D3 | semidirect |
| 23. C3×C4×C52 | D4 | semidirect |
| 24. C3×#1039 | D4 | semidirect |
| 26. C2×C5×D12 | D5 | semidirect |
| 53. C4×C52 | D12 | semidirect |
| 54. #1039 | D12 | semidirect |
| 60. C3×C52 | #127 | semidirect |
| 66. C3×C4×C5 | C22⋊D5 | semidirect |
| 74. C2×D12 | C5⋊D5 | semidirect |
| 88. C52 | #874 | semidirect |
| 101. C4×C5 | #1203 | semidirect |
| 107. C3×C5 | #4086 | semidirect |
| 114. C3×C4 | C22⋊(C5⋊D5) | semidirect |
| 130. C5 | #91451 | semidirect |
| 137. C4 | #10597116 | semidirect |
| 138. C3 | #11717260 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊(C3⋊(C5⋊D5)) | 2 |
| C2×C52×D12 | 2 |
| C2×#10597116 | 2 |
| C3×C4×#1039 | 2 |
| #11717260 | 3 |
| #91451 | 5 |