Finite Group DatabasebetaFinite Group DatabasebetaOrder 1200.
192 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D15⋊D5 |
| commutator, socle, cosocle | C2×C3×C52 | C23 |
| Fitting | C3×C4×C52 | C22 |
| hypercenter | C4 | D15⋊D5 |
| hypocenter | C3×C52 | #41 |
| LCS | G ▷ C2×C3×C52 ▷ C3×C52 | |
| UCS | C1 ◁ C2 ◁ C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C4×C5×D15 | C2 | semidirect |
| 2. C5×Dic30 | C2 | semidirect |
| 3. C3×C4⋊(C5⋊D5) | C2 | semidirect |
| 4. #10597127 | C2 | semidirect |
| 5. #10597126 | C2 | semidirect |
| 14. C4⋊(C5⋊D5) | D3 | semidirect |
| 22. C4×D15 | D5 | semidirect |
| 23. Dic30 | D5 | semidirect |
| 40. C3×C52 | #41 | semidirect |
| 76. C52 | #237 | semidirect |
| 96. C3×C5 | #709 | semidirect |
| 97. C3×C5 | #713 | semidirect |
| 120. C5 | #6765 | semidirect |
| 121. C5 | #6766 | semidirect |
| 127. C3 | #87874 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C5×D15 | 2 |
| C5×Dic30 | 2 |
| C3×C4⋊(C5⋊D5) | 2 |
| #10597127 | 2 |
| #10597126 | 2 |
| #87874 | 3 |
| #6766 | 5 |
| #6765 | 5 |