Finite Group Databasebeta

← C3⋊(C5⋊(C17⋊AGL(1,𝔽11))) #43242513

Subgroups — C3⋊(C5⋊(C17⋊AGL(1,𝔽11))) #43242513

Order 28050.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×C17×C11⋊C5C211yesmaximal, characteristic, complemented, Hall
2C5⋊(C17⋊AGL(1,𝔽11))—31nomaximal, Hall
3C3⋊(C17⋊AGL(1,𝔽11))—51nomaximal
4D2805C511yesmaximal, characteristic, complemented
5C5×C17×C11⋊C5D311yescharacteristic, complemented, Hall
6C3×C17×C11⋊C5—22no—
7C3×C17×C11⋊C5D511yescharacteristic, complemented
8C3×C5×C11×C17C2×C511yescharacteristic, complemented
9C5×D255—111nomaximal, Hall
10D935—31no—
11C17⋊AGL(1,𝔽11)—151no—
12C3⋊(C5⋊AGL(1,𝔽11))—171nomaximal, Hall
13C3×C52×C17—221noHall
14D561—51noHall
15C5×C11×C17C5×D311yescharacteristic, complemented
16C17×C11⋊C5—22no—
17C17×C11⋊C5D1511yescharacteristic, complemented
18C5×D85—331noHall
19C3×C5×C11⋊C5D1711yescharacteristic, complemented, Hall
20C3×C11×C17C5×D511yescharacteristic, complemented, Hall
21C5⋊AGL(1,𝔽11)—511noHall
22D255—111no—
23C5×D51—551no—
24C52×C17—221noHall
25D187—151noHall
26D165—171no—
27C3⋊AGL(1,𝔽11)—851no—
28C5×C11⋊C5D5111yescharacteristic, complemented, Hall
29C3×C5×C17—222no—
30C3×C5×C17—221no—
31C3×C5×C17AGL(1,𝔽11)11yescharacteristic, complemented
32C11×C17C5×D1511yescharacteristic, complemented, Hall
33D85—331no—
34C5×D17—1651no—
35C3×C5×C11C5×D1711yescharacteristic, complemented
36C3×C11⋊C5—22no—
37C3×C11⋊C5D8511yescharacteristic, complemented
38C5×D15—1871noHall
39D55—511no—
40AGL(1,𝔽11)—2551no—
41D51—551noHall
42C5×C17—222no—
43C5×C17—221no—
44C5×C17C3⋊AGL(1,𝔽11)11yescharacteristic, complemented
45C3×C52—221noHall
46D33—851noHall
47C5×C11C5×D5111yescharacteristic, complemented
48C11⋊C5—22no—
49C11⋊C5D25511yescharacteristic, complemented
50C3×C17C5⋊AGL(1,𝔽11)11yescharacteristic, complemented, Hall
51C5×D5—5611noHall
52D17—1651noHall
53C3×C11C5×D8511yescharacteristic, complemented, Hall
54D15—1871no—
55C5×D3—9351no—
56C52—221noSylow
57D11—2551noHall
58C17C3⋊(C5⋊AGL(1,𝔽11))11yescharacteristic, complemented, Sylow
59C3×C5—221no—
60C3×C5—222no—
61C3×C5C17⋊AGL(1,𝔽11)11yescharacteristic, complemented
62C11C5×D25511yescharacteristic, complemented, Sylow
63C2×C5—28051no—
64D5—5611no—
65D3—9351noHall
66C5—221no—
67C5—222no—
68C5C3⋊(C17⋊AGL(1,𝔽11))11yescharacteristic, complemented
69C3C5⋊(C17⋊AGL(1,𝔽11))11yescharacteristic, complemented, Sylow
70C2—28051noSylow
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C11×C17C2×C5
LCSG ▷ C3×C5×C11×C17
UCSC1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C3×C5×C17×C11⋊C5C2semidirect
4. D2805C5semidirect
5. C5×C17×C11⋊C5D3semidirect
7. C3×C17×C11⋊C5D5semidirect
8. C3×C5×C11×C17C2×C5semidirect
15. C5×C11×C17C5×D3semidirect
17. C17×C11⋊C5D15semidirect
19. C3×C5×C11⋊C5D17semidirect
20. C3×C11×C17C5×D5semidirect
28. C5×C11⋊C5D51semidirect
31. C3×C5×C17AGL(1,𝔽11)semidirect
32. C11×C17C5×D15semidirect
35. C3×C5×C11C5×D17semidirect
37. C3×C11⋊C5D85semidirect
44. C5×C17C3⋊AGL(1,𝔽11)semidirect
47. C5×C11C5×D51semidirect
49. C11⋊C5D255semidirect
50. C3×C17C5⋊AGL(1,𝔽11)semidirect
53. C3×C11C5×D85semidirect
58. C17C3⋊(C5⋊AGL(1,𝔽11))semidirect
61. C3×C5C17⋊AGL(1,𝔽11)semidirect
62. C11C5×D255semidirect
68. C5C3⋊(C17⋊AGL(1,𝔽11))semidirect
69. C3C5⋊(C17⋊AGL(1,𝔽11))semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C3×C5×C17×C11⋊C52
C5⋊(C17⋊AGL(1,𝔽11))3
C3⋊(C17⋊AGL(1,𝔽11))5
D28055
C5×D25511
C3⋊(C5⋊AGL(1,𝔽11))17