Finite Group Databasebeta

← C5×C3⋊(ΓL(1,𝔽8)⋊D37) #37552098

Subgroups — C5×C3⋊(ΓL(1,𝔽8)⋊D37) #37552098

Order 23310.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×ΓL(1,𝔽8)×C37C211yesmaximal, characteristic, complemented, Hall
2C5×ΓL(1,𝔽8)⋊D37—31nomaximal
3C5×D777C311yesmaximal, characteristic, complemented
4C3⋊(ΓL(1,𝔽8)⋊D37)C511yesmaximal, characteristic, direct product factor, Hall
5C5×ΓL(1,𝔽8)×C37—21no—
6C5×ΓL(1,𝔽8)×C37D311yescharacteristic, complemented
7C3×C5×C7×C37C2×C311yescharacteristic, complemented
8C3×C5×D111—71nomaximal, Hall
9C5×D259—31noHall
10C3×ΓL(1,𝔽8)×C37C2×C511yescharacteristic, complemented, Hall
11C32×C5×C37—71noHall
12D777C3×C511yescharacteristic, complemented
13ΓL(1,𝔽8)⋊D37—31no—
14C5×C7×C37C3×D311yescharacteristic, complemented, Hall
15C5×D111—71no—
16C3×C5×D37—211no—
17C3×C7×C37C2×C3×C511yescharacteristic, complemented
18ΓL(1,𝔽8)×C37—21no—
19ΓL(1,𝔽8)×C37C5×D311yescharacteristic, complemented
20C3×D111—71noHall
21C5×C3⋊AGL(1,𝔽7)—371nomaximal, Hall
22C3×C5×C37—71no—
23C3×C5×C37—141no—
24C3×C5×C37AGL(1,𝔽7)11yescharacteristic, complemented
25D259—31noHall
26C5×D37—211noHall
27C32×C37—71noHall
28C3×C5×ΓL(1,𝔽8)D3711yescharacteristic, complemented, Hall
29C7×C37C3×C5×D311yescharacteristic, complemented, Hall
30D111—71no—
31C3×D37—211no—
32C5×D21—371no—
33C5×AGL(1,𝔽7)—1111no—
34C5×C37C3⋊AGL(1,𝔽7)11yescharacteristic, complemented, Hall
35C3⋊AGL(1,𝔽7)—371noHall
36C3×C37—71no—
37C3×C37—141no—
38C3×C37C5×AGL(1,𝔽7)11yescharacteristic, complemented
39C3×C5×C7C3×D3711yescharacteristic, complemented
40C5×ΓL(1,𝔽8)—21no—
41C5×ΓL(1,𝔽8)D11111yescharacteristic, complemented
42C3×C5×D3—2591noHall
43D37—211noHall
44C5×D7—1111noHall
45C3×ΓL(1,𝔽8)C5×D3711yescharacteristic, complemented, Hall
46C32×C5—71noHall
47D21—371no—
48AGL(1,𝔽7)—1111no—
49C37C5×C3⋊AGL(1,𝔽7)11yescharacteristic, complemented, Sylow
50C5×C7C3×D11111yescharacteristic, complemented, Hall
51C2×C3×C5—7771no—
52C5×D3—2591no—
53C3×C7C3×C5×D3711yescharacteristic, complemented
54ΓL(1,𝔽8)—21no—
55ΓL(1,𝔽8)C5×D11111yescharacteristic, complemented
56C3×D3—2591noHall
57C3×C5—71no—
58C3×C5—141no—
59C3×C5ΓL(1,𝔽8)⋊D3711yescharacteristic, complemented
60D7—1111noHall
61C2×C5—7771noHall
62C32—71noSylow
63C7C3×C5×D11111yescharacteristic, complemented, Sylow
64C2×C3—7771no—
65D3—2591no—
66C5C3⋊(ΓL(1,𝔽8)⋊D37)11yescharacteristic, direct product factor, Sylow
67C3—71no—
68C3—141no—
69C3C5×ΓL(1,𝔽8)⋊D3711yescharacteristic, complemented
70C2—7771noSylow
subgroupG/H
center, hypercenterC5C3⋊(ΓL(1,𝔽8)⋊D37)
commutator, cosocle, hypocenterC3×C7×C37C2×C3×C5
FrattiniC1G
Fitting, socleC3×C5×C7×C37C2×C3
LCSG ▷ C3×C7×C37
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
1. C3×C5×ΓL(1,𝔽8)×C37C2semidirect
3. C5×D777C3semidirect
4. C3⋊(ΓL(1,𝔽8)⋊D37)C5direct (N × H)
6. C5×ΓL(1,𝔽8)×C37D3semidirect
7. C3×C5×C7×C37C2×C3semidirect
10. C3×ΓL(1,𝔽8)×C37C2×C5semidirect
12. D777C3×C5semidirect
14. C5×C7×C37C3×D3semidirect
17. C3×C7×C37C2×C3×C5semidirect
19. ΓL(1,𝔽8)×C37C5×D3semidirect
24. C3×C5×C37AGL(1,𝔽7)semidirect
28. C3×C5×ΓL(1,𝔽8)D37semidirect
29. C7×C37C3×C5×D3semidirect
34. C5×C37C3⋊AGL(1,𝔽7)semidirect
38. C3×C37C5×AGL(1,𝔽7)semidirect
39. C3×C5×C7C3×D37semidirect
41. C5×ΓL(1,𝔽8)D111semidirect
45. C3×ΓL(1,𝔽8)C5×D37semidirect
49. C37C5×C3⋊AGL(1,𝔽7)semidirect
50. C5×C7C3×D111semidirect
53. C3×C7C3×C5×D37semidirect
55. ΓL(1,𝔽8)C5×D111semidirect
59. C3×C5ΓL(1,𝔽8)⋊D37semidirect
63. C7C3×C5×D111semidirect
66. C5C3⋊(ΓL(1,𝔽8)⋊D37)direct (N × H)
69. C3C5×ΓL(1,𝔽8)⋊D37semidirect

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)×C372
C5×ΓL(1,𝔽8)⋊D373
C5×D7773
C3⋊(ΓL(1,𝔽8)⋊D37)5
C3×C5×D1117
C5×C3⋊AGL(1,𝔽7)37