Finite Group DatabasebetaFinite Group DatabasebetaOrder 1200.
184 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 80 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×C5 | D3×D5 |
| commutator, cosocle | C2×C3×C5 | C23×C5 |
| Frattini | C2 | C2×C5×D3×D5 |
| Fitting, socle, prime radical | C22×C3×C52 | C22 |
| hypocenter | C3×C5 | C2×C5×Q8 |
| LCS | G ▷ C2×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C22×C5 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C5×#1204 | C2 | direct (N × H) |
| 11. C2×#1204 | C5 | direct (N × H) |
| 16. C2×C3×C52 | Q8 | semidirect |
| 26. #1204 | C2×C5 | direct (N × H) |
| 33. C3×C52 | C2×Q8 | semidirect |
| 44. C2×C52 | Dic6 | semidirect |
| 58. C2×C3×C5 | Dic10 | semidirect |
| 59. C2×C3×C5 | C5×Q8 | semidirect |
| 62. C52 | C2×Dic6 | semidirect |
| 79. C3×C5 | C2×Dic10 | semidirect |
| 80. C3×C5 | C2×C5×Q8 | semidirect |
| 87. C2×C5 | #1204 | direct (N × H) |
| 88. C2×C5 | C5×Dic6 | semidirect |
| 95. C2×C3 | C5×Dic10 | semidirect |
| 98. C5 | C2×#1204 | direct (N × H) |
| 99. C5 | C2×C5×Dic6 | semidirect |
| 104. C3 | C2×C5×Dic10 | semidirect |
| 105. C2 | C5×#1204 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×Dic15 | 2 |
| C2×C52×Dic3 | 2 |
| C2×C3×C5×Dic5 | 2 |
| C5×#1204 | 2 |
| C2×C5×Dic10 | 3 |
| C2×C5×Dic6 | 5 |
| C2×#1204 | 5 |