Finite Group DatabasebetaFinite Group DatabasebetaOrder 1200.
280 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 63 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 | D15⋊D5 |
| commutator, cosocle | C2×C3×C52 | C23 |
| Frattini | C2 | C2×D15⋊D5 |
| Fitting, socle | C22×C3×C52 | C22 |
| hypocenter | C3×C52 | C2×D4 |
| LCS | G ▷ C2×C3×C52 ▷ C3×C52 | |
| UCS | C1 ◁ C22 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C5×D15 | C2 | semidirect |
| 2. C22×C3×C5⋊D5 | C2 | semidirect |
| 3. C2×C5×Dic15 | C2 | semidirect |
| 4. #10597127 | C2 | direct (N × H) |
| 8. C2×C5×D15 | C22 | semidirect |
| 10. C2×C3×C5⋊D5 | C22 | semidirect |
| 11. C5×Dic15 | C22 | semidirect |
| 14. C22×C5⋊D5 | D3 | semidirect |
| 18. C2×C3×C52 | D4 | semidirect |
| 22. C22×D15 | D5 | semidirect |
| 27. C2×Dic15 | D5 | semidirect |
| 33. C2×C5⋊D5 | C2×D3 | semidirect |
| 39. C3×C52 | C2×D4 | semidirect |
| 44. C2×D15 | C2×D5 | semidirect |
| 53. Dic15 | C2×D5 | semidirect |
| 55. C2×C52 | #67 | semidirect |
| 71. C2×C3×C5 | D20 | semidirect |
| 72. C2×C3×C5 | C22⋊D5 | semidirect |
| 80. C52 | C2×#67 | semidirect |
| 102. C3×C5 | C2×D20 | semidirect |
| 103. C3×C5 | C2×C22⋊D5 | semidirect |
| 113. C2×C5 | #1201 | semidirect |
| 114. C2×C5 | #1202 | semidirect |
| 126. C2×C3 | #6038 | semidirect |
| 130. C5 | C2×#1201 | semidirect |
| 131. C5 | C2×#1202 | semidirect |
| 138. C3 | C2×#6038 | semidirect |
| 141. C2 | #10597127 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×D15 | 2 |
| C22×C3×C5⋊D5 | 2 |
| C2×C5×Dic15 | 2 |
| #10597127 | 2 |
| C2×#6038 | 3 |
| C2×#1202 | 5 |
| C2×#1201 | 5 |