Finite Group Databasebeta

← C29×C3⋊(ΓL(1,𝔽8)⋊AGL(1,𝔽5)) #49141466

Subgroups — C29×C3⋊(ΓL(1,𝔽8)⋊AGL(1,𝔽5)) #49141466

Order 36540.

112 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D5×ΓL(1,𝔽8)×C29C211yesmaximal, characteristic
2C29×C3⋊(C7⋊AGL(1,𝔽5))C311yesmaximal, characteristic, complemented
3C29×ΓL(1,𝔽8)⋊AGL(1,𝔽5)—31nomaximal
4C3×C5×ΓL(1,𝔽8)×C29C411yescharacteristic, complemented, Hall
5C29×C3⋊(ΓL(1,𝔽8)⋊C4)—51nomaximal, Hall
6D5×ΓL(1,𝔽8)×C29—21no—
7D5×ΓL(1,𝔽8)×C29D311yescharacteristic
8C3×C7×D5×C29C2×C311yescharacteristic
9C3×C29×ΓL(1,𝔽16)—71nomaximal, Hall
10C29×C7⋊AGL(1,𝔽5)—31noHall
11C2×C3×ΓL(1,𝔽8)×C29—51no—
12C5×ΓL(1,𝔽8)×C29—21no—
13C5×ΓL(1,𝔽8)×C29Dic311yescharacteristic, complemented
14C3×C5×C7×C29C3×C411yescharacteristic, complemented
15C32×D5×C29—71no—
16C29×Dic21—51no—
17C29×ΓL(1,𝔽8)⋊C4—151no—
18C7×D5×C29C3×D311yescharacteristic
19C3×ΓL(1,𝔽8)×C29AGL(1,𝔽5)11yescharacteristic, complemented, Hall
20C29×ΓL(1,𝔽16)—71no—
21C3×AGL(1,𝔽5)×C29—211no—
22C32×C5×C29—71noHall
23C3⋊(ΓL(1,𝔽8)⋊AGL(1,𝔽5))C2911yesmaximal, characteristic, direct product factor, Hall
24C2×C3×C7×C29—51no—
25C2×ΓL(1,𝔽8)×C29—51no—
26C2×ΓL(1,𝔽8)×C29—101no—
27C3×Dic3×C29—351noHall
28C5×C7×C29C3×Dic311yescharacteristic, complemented, Hall
29C3×D5×C29—71no—
30C3×D5×C29—141no—
31C3×D5×C29AGL(1,𝔽7)11yescharacteristic
32Dic7×C29—151noHall
33C3×D5×ΓL(1,𝔽8)C2×C2911yescharacteristic
34C3×C7×C29C3×AGL(1,𝔽5)11yescharacteristic, complemented
35ΓL(1,𝔽8)×C29—21no—
36ΓL(1,𝔽8)×C29ΓL(1,𝔽16)11yescharacteristic, complemented
37AGL(1,𝔽5)×C29—211noHall
38C2×C32×C29—351no—
39C3×C5×C29—71no—
40C3×C5×C29—141no—
41C3×C5×C29ΓL(1,𝔽8)⋊C411yescharacteristic, complemented
42C3⋊(C7⋊AGL(1,𝔽5))C3×C2911yescharacteristic, complemented
43ΓL(1,𝔽8)⋊AGL(1,𝔽5)—31no—
44C2×C7×C29—51no—
45C3×C4×C29—1051no—
46Dic3×C29—351no—
47C3×C5×ΓL(1,𝔽8)C4×C2911yescharacteristic, complemented, Hall
48D5×C29C3⋊AGL(1,𝔽7)11yescharacteristic
49C32×C29—71noHall
50C3⋊(ΓL(1,𝔽8)⋊C4)—51noHall
51C3×C7×D5C2×C3×C2911yescharacteristic
52D5×ΓL(1,𝔽8)—21no—
53D5×ΓL(1,𝔽8)D3×C2911yescharacteristic
54C7×C29C3×ΓL(1,𝔽16)11yescharacteristic, complemented, Hall
55C3×ΓL(1,𝔽16)—71noHall
56C2×C3×C29—51no—
57C2×C3×C29—351no—
58C2×C3×C29—701no—
59C5×C29C3⋊(ΓL(1,𝔽8)⋊C4)11yescharacteristic, complemented, Hall
60C7⋊AGL(1,𝔽5)—31noHall
61C2×C3×ΓL(1,𝔽8)—51no—
62C4×C29—1051noHall
63C3×C5×C7C3×C4×C2911yescharacteristic, complemented
64C5×ΓL(1,𝔽8)—21no—
65C5×ΓL(1,𝔽8)Dic3×C2911yescharacteristic, complemented
66C32×D5—71no—
67C3×C29—71no—
68C3×C29—141no—
69C3×C29ΓL(1,𝔽8)⋊AGL(1,𝔽5)11yescharacteristic, complemented
70Dic21—51no—
71ΓL(1,𝔽8)⋊C4—151no—
72C7×D5C3×D3×C2911yescharacteristic
73C3×ΓL(1,𝔽8)AGL(1,𝔽5)×C2911yescharacteristic, complemented, Hall
74ΓL(1,𝔽16)—71no—
75C3×AGL(1,𝔽5)—211no—
76C2×C29—51no—
77C32×C5—71noHall
78C2×C3×C7—51no—
79C2×ΓL(1,𝔽8)—51no—
80C2×ΓL(1,𝔽8)—101no—
81C3×Dic3—351noHall
82C5×C7C3×Dic3×C2911yescharacteristic, complemented, Hall
83C3×D5—71no—
84C3×D5—141no—
85C3×D5C29×AGL(1,𝔽7)11yescharacteristic
86C29C3⋊(ΓL(1,𝔽8)⋊AGL(1,𝔽5))11yescharacteristic, direct product factor, Sylow
87Dic7—151noHall
88C3×C7C3×AGL(1,𝔽5)×C2911yescharacteristic, complemented
89ΓL(1,𝔽8)—21no—
90ΓL(1,𝔽8)C29×ΓL(1,𝔽16)11yescharacteristic, complemented
91AGL(1,𝔽5)—211noHall
92C2×C32—351no—
93C3×C5—71no—
94C3×C5—141no—
95C3×C5C29×ΓL(1,𝔽8)⋊C411yescharacteristic, complemented
96C2×C7—51no—
97C3×C4—1051no—
98Dic3—351no—
99D5C29×C3⋊AGL(1,𝔽7)11yescharacteristic
100C32—71noSylow
101C7C3×C29×ΓL(1,𝔽16)11yescharacteristic, complemented, Sylow
102C2×C3—51no—
103C2×C3—351no—
104C2×C3—701no—
105C5C29×C3⋊(ΓL(1,𝔽8)⋊C4)11yescharacteristic, complemented, Sylow
106C4—1051noSylow
107C3—71no—
108C3—141no—
109C3C29×ΓL(1,𝔽8)⋊AGL(1,𝔽5)11yescharacteristic, complemented
110C2—51no—
subgroupG/H
center, hypercenterC29C3⋊(ΓL(1,𝔽8)⋊AGL(1,𝔽5))
commutator, hypocenterC3×C5×C7C3×C4×C29
FrattiniC1G
Fitting, socleC3×C5×C7×C29C3×C4
prime radicalC3×D5×ΓL(1,𝔽8)×C29C2
cosocleC3×C7×D5C2×C3×C29
LCSG ▷ C3×C5×C7
UCSC1 ◁ C29

Complements

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

NH ≅ G/Ntype
2. C29×C3⋊(C7⋊AGL(1,𝔽5))C3semidirect
4. C3×C5×ΓL(1,𝔽8)×C29C4semidirect
13. C5×ΓL(1,𝔽8)×C29Dic3semidirect
14. C3×C5×C7×C29C3×C4semidirect
19. C3×ΓL(1,𝔽8)×C29AGL(1,𝔽5)semidirect
23. C3⋊(ΓL(1,𝔽8)⋊AGL(1,𝔽5))C29direct (N × H)
28. C5×C7×C29C3×Dic3semidirect
34. C3×C7×C29C3×AGL(1,𝔽5)semidirect
36. ΓL(1,𝔽8)×C29ΓL(1,𝔽16)semidirect
41. C3×C5×C29ΓL(1,𝔽8)⋊C4semidirect
42. C3⋊(C7⋊AGL(1,𝔽5))C3×C29semidirect
47. C3×C5×ΓL(1,𝔽8)C4×C29semidirect
54. C7×C29C3×ΓL(1,𝔽16)semidirect
59. C5×C29C3⋊(ΓL(1,𝔽8)⋊C4)semidirect
63. C3×C5×C7C3×C4×C29semidirect
65. C5×ΓL(1,𝔽8)Dic3×C29semidirect
69. C3×C29ΓL(1,𝔽8)⋊AGL(1,𝔽5)semidirect
73. C3×ΓL(1,𝔽8)AGL(1,𝔽5)×C29semidirect
82. C5×C7C3×Dic3×C29semidirect
86. C29C3⋊(ΓL(1,𝔽8)⋊AGL(1,𝔽5))direct (N × H)
88. C3×C7C3×AGL(1,𝔽5)×C29semidirect
90. ΓL(1,𝔽8)C29×ΓL(1,𝔽16)semidirect
95. C3×C5C29×ΓL(1,𝔽8)⋊C4semidirect
101. C7C3×C29×ΓL(1,𝔽16)semidirect
105. C5C29×C3⋊(ΓL(1,𝔽8)⋊C4)semidirect
109. C3C29×ΓL(1,𝔽8)⋊AGL(1,𝔽5)semidirect

Maximal subgroups

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

subgroupindex
C3×D5×ΓL(1,𝔽8)×C292
C29×C3⋊(C7⋊AGL(1,𝔽5))3
C29×ΓL(1,𝔽8)⋊AGL(1,𝔽5)3
C29×C3⋊(ΓL(1,𝔽8)⋊C4)5
C3×C29×ΓL(1,𝔽16)7
C3⋊(ΓL(1,𝔽8)⋊AGL(1,𝔽5))29