Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
744 conjugacy classes of subgroups; only the 164 normal subgroups are shown.
This group has 744 conjugacy classes of subgroups — too many to draw. Only its 164 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×D52 |
| commutator, socle, cosocle | C22×C52 | C24 |
| Fitting | C2×C52×Q8 | C22 |
| hypercenter | C2×Q8 | D52 |
| hypocenter | C52 | #548 |
| 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 |
|---|---|---|
| 1. C2×#87904 | C2 | semidirect |
| 2. C2×C5×Q8×D5 | C2 | semidirect |
| 3. C5×Q8×Dic5 | C2 | semidirect |
| 4. #11717027 | C2 | semidirect |
| 5. C4×#6038 | C2 | semidirect |
| 6. #11716990 | C2 | semidirect |
| 7. #11716982 | C2 | semidirect |
| 26. C52×Q8 | D4 | semidirect |
| 41. C2×Q8×D5 | D5 | semidirect |
| 45. Q8×Dic5 | D5 | semidirect |
| 58. C2×C5×D5 | #41 | semidirect |
| 109. C5×Q8 | D20 | semidirect |
| 110. C5×Q8 | C22⋊D5 | semidirect |
| 141. C52 | #548 | semidirect |
| 159. C2×D5 | #713 | semidirect |
| 203. Q8 | #6038 | semidirect |
| 214. C5 | #65910 | semidirect |
| 215. C5 | #66151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87904 | 2 |
| C2×C5×Q8×D5 | 2 |
| C5×Q8×Dic5 | 2 |
| #11717027 | 2 |
| C4×#6038 | 2 |
| #11716990 | 2 |
| #11716982 | 2 |
| #66151 | 5 |
| #65910 | 5 |