Finite Group DatabasebetaFinite Group DatabasebetaOrder 2400.
864 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 864 conjugacy classes of subgroups — too many to draw. Only its 156 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 | C23×C3×C52 | C22 |
| hypercenter | C23 | D3×C5⋊D5 |
| hypocenter | C3×C52 | #127 |
| LCS | G ▷ C22×C3×C52 ▷ C3×C52 | |
| UCS | C1 ◁ C22 ◁ C23 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#10597159 | C2 | semidirect |
| 2. C2×C52×#67 | C2 | semidirect |
| 3. C2×C3×C22⋊(C5⋊D5) | C2 | semidirect |
| 4. C2×#10597116 | C2 | semidirect |
| 5. C2×#10597115 | C2 | semidirect |
| 6. C2×#10597114 | C2 | semidirect |
| 7. Dic3×#1039 | C2 | semidirect |
| 27. C2×C22⋊(C5⋊D5) | D3 | semidirect |
| 43. C3⋊#1039 | D4 | semidirect |
| 44. C52×Dic3 | D4 | semidirect |
| 45. C3×#1039 | D4 | semidirect |
| 47. C2×C5×#67 | D5 | semidirect |
| 102. #1039 | #67 | semidirect |
| 111. C3×C52 | #127 | semidirect |
| 127. C5×Dic3 | C22⋊D5 | semidirect |
| 139. C2×#67 | C5⋊D5 | semidirect |
| 163. C52 | #940 | semidirect |
| 200. C3×C5 | #4086 | semidirect |
| 216. Dic3 | C22⋊(C5⋊D5) | semidirect |
| 244. C5 | #91567 | semidirect |
| 261. C3 | #11717260 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597159 | 2 |
| C2×C52×#67 | 2 |
| C2×C3×C22⋊(C5⋊D5) | 2 |
| C2×#10597116 | 2 |
| C2×#10597115 | 2 |
| C2×#10597114 | 2 |
| Dic3×#1039 | 2 |
| #11717260 | 3 |
| #91567 | 5 |