Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1160 conjugacy classes of subgroups; only the 307 normal subgroups are shown.
This group has 1160 conjugacy classes of subgroups — too many to draw. Only its 307 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×C5⋊D5 |
| commutator, socle, cosocle | C22×C52 | C24 |
| Fitting | C22×C52×Q8 | C2 |
| hypercenter | C22×Q8 | C5⋊D5 |
| hypocenter | C52 | #548 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C22×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C52×Q8 | C2 | semidirect |
| 2. C2×#87904 | C2 | semidirect |
| 3. #11717267 | C2 | semidirect |
| 4. #11717266 | C2 | semidirect |
| 5. Q8×#1039 | C2 | semidirect |
| 6. #11717250 | C2 | semidirect |
| 7. C4×C22⋊(C5⋊D5) | C2 | semidirect |
| 26. C52×Q8 | D4 | semidirect |
| 36. C22×C5×Q8 | D5 | semidirect |
| 45. C22×C52 | #41 | semidirect |
| 78. C5×Q8 | C22⋊D5 | semidirect |
| 89. C22×Q8 | C5⋊D5 | semidirect |
| 95. C52 | #548 | semidirect |
| 98. C22×C5 | #713 | semidirect |
| 130. Q8 | C22⋊(C5⋊D5) | semidirect |
| 140. C5 | #66151 | semidirect |
| 146. C22 | #87904 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C52×Q8 | 2 |
| C2×#87904 | 2 |
| #11717267 | 2 |
| #11717266 | 2 |
| Q8×#1039 | 2 |
| #11717250 | 2 |
| C4×C22⋊(C5⋊D5) | 2 |
| #66151 | 5 |