Finite Group Databasebeta

← C5×C3⋊(ΓL(1,𝔽8)⋊D31) #34086259

Subgroups — C5×C3⋊(ΓL(1,𝔽8)⋊D31) #34086259

Order 19530.

72 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—31nomaximal
3C5×D651C311yesmaximal, characteristic, complemented
4C3⋊(ΓL(1,𝔽8)⋊D31)C511yesmaximal, characteristic, direct product factor, Hall
5C5×ΓL(1,𝔽8)×C31—21no—
6C5×ΓL(1,𝔽8)×C31D311yescharacteristic, complemented
7C3×C5×C7×C31C2×C311yescharacteristic, complemented
8C3×C5×D93—71nomaximal, Hall
9C5×D217—31noHall
10C3×ΓL(1,𝔽8)×C31C2×C511yescharacteristic, complemented, Hall
11C32×C5×C31—71noHall
12D651C3×C511yescharacteristic, complemented
13ΓL(1,𝔽8)⋊D31—31no—
14C5×C7×C31C3×D311yescharacteristic, complemented, Hall
15C5×D93—71no—
16C3×C5×D31—211no—
17C3×C7×C31C2×C3×C511yescharacteristic, complemented
18ΓL(1,𝔽8)×C31—21no—
19ΓL(1,𝔽8)×C31C5×D311yescharacteristic, complemented
20C5×C3⋊AGL(1,𝔽7)—311nomaximal, Hall
21C3×D93—71noHall
22C3×C5×C31—71no—
23C3×C5×C31—141no—
24C3×C5×C31AGL(1,𝔽7)11yescharacteristic, complemented
25D217—31noHall
26C3×C5×ΓL(1,𝔽8)D3111yescharacteristic, complemented, Hall
27C5×D31—211noHall
28C32×C31—71noHall
29C7×C31C3×C5×D311yescharacteristic, complemented, Hall
30C5×D21—311no—
31C5×AGL(1,𝔽7)—931no—
32D93—71no—
33C3×D31—211no—
34C5×C31C3⋊AGL(1,𝔽7)11yescharacteristic, complemented, Hall
35C3⋊AGL(1,𝔽7)—311noHall
36C3×C5×C7C3×D3111yescharacteristic, complemented
37C5×ΓL(1,𝔽8)—21no—
38C5×ΓL(1,𝔽8)D9311yescharacteristic, complemented
39C3×C31—71no—
40C3×C31—141no—
41C3×C31C5×AGL(1,𝔽7)11yescharacteristic, complemented
42C3×C5×D3—2171noHall
43C5×D7—931noHall
44C3×ΓL(1,𝔽8)C5×D3111yescharacteristic, complemented, Hall
45D31—211noHall
46C32×C5—71noHall
47D21—311no—
48AGL(1,𝔽7)—931no—
49C5×C7C3×D9311yescharacteristic, complemented, Hall
50C31C5×C3⋊AGL(1,𝔽7)11yescharacteristic, complemented, Sylow
51C2×C3×C5—6511no—
52C5×D3—2171no—
53C3×C7C3×C5×D3111yescharacteristic, complemented
54ΓL(1,𝔽8)—21no—
55ΓL(1,𝔽8)C5×D9311yescharacteristic, complemented
56C3×D3—2171noHall
57C3×C5—71no—
58C3×C5—141no—
59C3×C5ΓL(1,𝔽8)⋊D3111yescharacteristic, complemented
60D7—931noHall
61C2×C5—6511noHall
62C32—71noSylow
63C7C3×C5×D9311yescharacteristic, complemented, Sylow
64C2×C3—6511no—
65D3—2171no—
66C5C3⋊(ΓL(1,𝔽8)⋊D31)11yescharacteristic, direct product factor, Sylow
67C3—71no—
68C3—141no—
69C3C5×ΓL(1,𝔽8)⋊D3111yescharacteristic, complemented
70C2—6511noSylow
subgroupG/H
center, hypercenterC5C3⋊(ΓL(1,𝔽8)⋊D31)
commutator, cosocle, hypocenterC3×C7×C31C2×C3×C5
FrattiniC1G
Fitting, socleC3×C5×C7×C31C2×C3
LCSG ▷ C3×C7×C31
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
1. C3×C5×ΓL(1,𝔽8)×C31C2semidirect
3. C5×D651C3semidirect
4. C3⋊(ΓL(1,𝔽8)⋊D31)C5direct (N × H)
6. C5×ΓL(1,𝔽8)×C31D3semidirect
7. C3×C5×C7×C31C2×C3semidirect
10. C3×ΓL(1,𝔽8)×C31C2×C5semidirect
12. D651C3×C5semidirect
14. C5×C7×C31C3×D3semidirect
17. C3×C7×C31C2×C3×C5semidirect
19. ΓL(1,𝔽8)×C31C5×D3semidirect
24. C3×C5×C31AGL(1,𝔽7)semidirect
26. C3×C5×ΓL(1,𝔽8)D31semidirect
29. C7×C31C3×C5×D3semidirect
34. C5×C31C3⋊AGL(1,𝔽7)semidirect
36. C3×C5×C7C3×D31semidirect
38. C5×ΓL(1,𝔽8)D93semidirect
41. C3×C31C5×AGL(1,𝔽7)semidirect
44. C3×ΓL(1,𝔽8)C5×D31semidirect
49. C5×C7C3×D93semidirect
50. C31C5×C3⋊AGL(1,𝔽7)semidirect
53. C3×C7C3×C5×D31semidirect
55. ΓL(1,𝔽8)C5×D93semidirect
59. C3×C5ΓL(1,𝔽8)⋊D31semidirect
63. C7C3×C5×D93semidirect
66. C5C3⋊(ΓL(1,𝔽8)⋊D31)direct (N × H)
69. C3C5×ΓL(1,𝔽8)⋊D31semidirect

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)⋊D313
C5×D6513
C3⋊(ΓL(1,𝔽8)⋊D31)5
C3×C5×D937
C5×C3⋊AGL(1,𝔽7)31