Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
624 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 624 conjugacy classes of subgroups — too many to draw. Only its 179 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 | C23×D15 |
| commutator, socle, cosocle | C22×C3×C5 | C24 |
| Fitting | C3×C4×C5×Q8 | C2 |
| hypercenter | C4×Q8 | D15 |
| hypocenter | C3×C5 | #550 |
| LCS | G ▷ C22×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C22 ◁ C4×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#6821 | C2 | semidirect |
| 2. C3×C4×C5×Q8 | C2 | semidirect |
| 3. #91784 | C2 | semidirect |
| 4. #91763 | C2 | semidirect |
| 5. C4×D60 | C2 | semidirect |
| 19. C4×C5×Q8 | D3 | semidirect |
| 24. C3×C5×Q8 | D4 | semidirect |
| 34. C3×C4×Q8 | D5 | semidirect |
| 55. C3×C4×C5 | #41 | semidirect |
| 68. C5×Q8 | D12 | semidirect |
| 80. C4×Q8 | D15 | semidirect |
| 87. C3×Q8 | D20 | semidirect |
| 102. C4×C5 | #239 | semidirect |
| 114. C3×C5 | #550 | semidirect |
| 121. C3×C4 | #713 | semidirect |
| 128. Q8 | D60 | semidirect |
| 141. C5 | #5577 | semidirect |
| 149. C4 | #6821 | semidirect |
| 150. C3 | #65911 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6821 | 2 |
| C3×C4×C5×Q8 | 2 |
| #91784 | 2 |
| #91763 | 2 |
| C4×D60 | 2 |
| #65911 | 3 |
| #5577 | 5 |