Finite Group DatabasebetaFinite Group DatabasebetaOrder 1200.
192 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 46 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D3×D52 |
| commutator, Fitting, socle, cosocle | C2×C3×C52 | C23 |
| hypocenter | C3×C52 | #41 |
| LCS | G ▷ C2×C3×C52 ▷ C3×C52 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10597129 | C2 | semidirect |
| 2. #10597123 | C2 | semidirect |
| 3. #10597113 | C2 | semidirect |
| 4. C5×D5×Dic3 | C2 | semidirect |
| 5. C3×#6037 | C2 | semidirect |
| 17. #6037 | D3 | semidirect |
| 28. D5×Dic3 | D5 | semidirect |
| 35. C3×C52 | #41 | semidirect |
| 64. C52 | #237 | semidirect |
| 82. C3×C5 | #709 | semidirect |
| 103. C5 | #6779 | semidirect |
| 109. C3 | #87873 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10597129 | 2 |
| #10597123 | 2 |
| #10597113 | 2 |
| C5×D5×Dic3 | 2 |
| C3×#6037 | 2 |
| #87873 | 3 |
| #6779 | 5 |