Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
391 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 391 conjugacy classes of subgroups — too many to draw. Only its 113 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×#1042 |
| commutator, socle | C22×C52 | C22×C4 |
| Fitting | C2×C52×Q8 | C4 |
| prime radical, cosocle | C22×C5×D5 | C23 |
| hypercenter | C2×Q8 | #1042 |
| 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×C5×Dic10 | C4 | semidirect |
| 13. C2×C5×Dic10 | C4 | semidirect |
| 23. C2×#1042 | Q8 | semidirect |
| 61. C2×C5×Q8 | Dic5 | semidirect |
| 62. C2×C5×Q8 | AGL(1,𝔽5) | semidirect |
| 71. C2×Dic10 | Dic5 | semidirect |
| 72. C2×Dic10 | Dic5 | semidirect |
| 124. C52 | #391 | semidirect |
| 154. C2×Q8 | #1042 | semidirect |
| 191. C5 | #65519 | semidirect |
| 192. 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×C5×Q8×D5 | 2 |
| C2×C4⋊#1042 | 2 |
| C2×C4×#1042 | 2 |
| #11716849 | 2 |
| (C2×AGL(1,𝔽5))⋊Q8 | 5 |
| #65519 | 5 |