Finite Group Databasebeta

← C3×C5⋊(ΓL(1,𝔽8)⋊D31) #34086243

Subgroups — C3×C5⋊(ΓL(1,𝔽8)⋊D31) #34086243

Order 19530.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×ΓL(1,𝔽8)×C31C211yesmaximal, characteristic, complemented, Hall
2C5⋊(ΓL(1,𝔽8)⋊D31)C313yesmaximal, direct product factor
3C3×D1085C311yesmaximal, characteristic, complemented
4C3×ΓL(1,𝔽8)⋊D31—51nomaximal, Hall
5C5×ΓL(1,𝔽8)×C31C2×C313yescomplemented
6C3×C5×C7×C31C2×C311yescharacteristic, complemented
7C32×D155—71nomaximal, Hall
8D1085C3211yescharacteristic, complemented, Hall
9C3×ΓL(1,𝔽8)×C31D511yescharacteristic, complemented, Hall
10C32×C5×C31—71noHall
11C3×D217—51no—
12ΓL(1,𝔽8)⋊D31—53no—
13C5×C7×C31C2×C3211yescharacteristic, complemented, Hall
14C3×D155—73no—
15C3×D155—211no—
16C3×C7×C31C3×D511yescharacteristic, complemented
17ΓL(1,𝔽8)×C31C3×D513yescomplemented
18C3×C5⋊AGL(1,𝔽7)—311nomaximal, Hall
19C32×D31—351noHall
20C3×C5×C31—73no—
21C3×C5×C31AGL(1,𝔽7)11yescharacteristic, complemented
22D217—51noHall
23C3×C5×ΓL(1,𝔽8)D3111yescharacteristic, complemented, Hall
24D155—211noHall
25C32×C31—71noHall
26C7×C31C32×D511yescharacteristic, complemented, Hall
27C3×D35—311no—
28C5⋊AGL(1,𝔽7)—313no—
29C3×D31—353no—
30C3×D31—351no—
31C5×C31C3×AGL(1,𝔽7)11yescharacteristic, complemented, Hall
32C3×AGL(1,𝔽7)—1551noHall
33C3×C5×C7C3×D3111yescharacteristic, complemented
34C5×ΓL(1,𝔽8)C3×D3113yescomplemented
35C3×C31—73no—
36C3×C31C5⋊AGL(1,𝔽7)11yescharacteristic, complemented
37C32×D5—2171noHall
38D35—311noHall
39C3×ΓL(1,𝔽8)D15511yescharacteristic, complemented, Hall
40D31—351noHall
41C32×C5—71noHall
42C3×D7—1551no—
43AGL(1,𝔽7)—1553no—
44C5×C7C32×D3111yescharacteristic, complemented, Hall
45C31C3×C5⋊AGL(1,𝔽7)11yescharacteristic, complemented, Sylow
46C3×D5—6511no—
47C3×D5—2173no—
48C3×C7C3×D15511yescharacteristic, complemented
49ΓL(1,𝔽8)C3×D15513yescomplemented
50C2×C32—10851noHall
51C3×C5—73no—
52C3×C5ΓL(1,𝔽8)⋊D3111yescharacteristic, complemented
53D7—1551noHall
54D5—6511noHall
55C32—71noSylow
56C7C32×D15511yescharacteristic, complemented, Sylow
57C2×C3—10853no—
58C2×C3—32551no—
59C5C3×ΓL(1,𝔽8)⋊D3111yescharacteristic, complemented, Sylow
60C3—73no—
61C3C5⋊(ΓL(1,𝔽8)⋊D31)11yescharacteristic, direct product factor
62C2—32551noSylow
subgroupG/H
center, hypercenterC3C5⋊(ΓL(1,𝔽8)⋊D31)
commutator, cosocle, hypocenterC5×C7×C31C2×C32
FrattiniC1G
Fitting, socleC3×C5×C7×C31C2×C3
LCSG ▷ C5×C7×C31
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×C5×ΓL(1,𝔽8)×C31C2semidirect
2. C5⋊(ΓL(1,𝔽8)⋊D31)C3direct (N × H)
3. C3×D1085C3semidirect
5. C5×ΓL(1,𝔽8)×C31C2×C3semidirect
6. C3×C5×C7×C31C2×C3semidirect
8. D1085C32semidirect
9. C3×ΓL(1,𝔽8)×C31D5semidirect
13. C5×C7×C31C2×C32semidirect
16. C3×C7×C31C3×D5semidirect
17. ΓL(1,𝔽8)×C31C3×D5semidirect
21. C3×C5×C31AGL(1,𝔽7)semidirect
23. C3×C5×ΓL(1,𝔽8)D31semidirect
26. C7×C31C32×D5semidirect
31. C5×C31C3×AGL(1,𝔽7)semidirect
33. C3×C5×C7C3×D31semidirect
34. C5×ΓL(1,𝔽8)C3×D31semidirect
36. C3×C31C5⋊AGL(1,𝔽7)semidirect
39. C3×ΓL(1,𝔽8)D155semidirect
44. C5×C7C32×D31semidirect
45. C31C3×C5⋊AGL(1,𝔽7)semidirect
48. C3×C7C3×D155semidirect
49. ΓL(1,𝔽8)C3×D155semidirect
52. C3×C5ΓL(1,𝔽8)⋊D31semidirect
56. C7C32×D155semidirect
59. C5C3×ΓL(1,𝔽8)⋊D31semidirect
61. C3C5⋊(ΓL(1,𝔽8)⋊D31)direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×ΓL(1,𝔽8)×C312
C5⋊(ΓL(1,𝔽8)⋊D31)3
C3×D10853
C3×ΓL(1,𝔽8)⋊D315
C32×D1557
C3×C5⋊AGL(1,𝔽7)31