Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
528 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 86 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 | C22×#1044 |
| commutator, socle | C22×C52 | C22×C4 |
| Fitting | C2×C52×Q8 | C4 |
| prime radical, cosocle | C22×C5⋊D5 | C23 |
| hypercenter | C2×Q8 | #1044 |
| hypocenter | C52 | #391 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 7. C2×C52×Q8 | C4 | semidirect |
| 12. C2×#6045 | C4 | semidirect |
| 13. C2×#6045 | C4 | semidirect |
| 22. C2×#1044 | Q8 | semidirect |
| 53. C2×C5×Q8 | AGL(1,𝔽5) | semidirect |
| 107. C52 | #391 | semidirect |
| 132. C2×Q8 | #1044 | semidirect |
| 167. C5 | (C2×AGL(1,𝔽5))⋊Q8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×C5⋊D5 | 2 |
| C2×C4⋊#1044 | 2 |
| C2×C4×#1044 | 2 |
| #11716899 | 2 |
| (C2×AGL(1,𝔽5))⋊Q8 | 5 |