Finite Group Databasebeta

← C3×C7×C3⋊(C5⋊D35) #36348075

Subgroups — C3×C7×C3⋊(C5⋊D35) #36348075

Order 22050.

432 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 132 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
1C32×C52×C72C211yesmaximal, characteristic, complemented, Hall
2C7×C3⋊(C5⋊D35)C311yesmaximal, characteristic, direct product factor
3C3×C7×C5⋊D35—31nomaximal
4C3×C7×D105—56nomaximal
5C3×C52×C72—21no—
6C3×C52×C72D311yescharacteristic, complemented
7C3×C52×C72C2×C311yescharacteristic, complemented
8C3×C3⋊(C5⋊D35)C711yesmaximal, characteristic, direct product factor
9C3×C7×C3⋊(C5⋊D5)—71nomaximal
10C7×C5⋊D35—31noHall
11C32×C5×C72D516yescomplemented
12C32×C52×C7—23no—
13C32×C52×C7D711yescharacteristic, complemented
14C32×C52×C7C2×C711yescharacteristic, complemented
15C7×D105—56no—
16C3×C7×D35—156no—
17C52×C72C3×D311yescharacteristic, complemented, Hall
18C3⋊(C5⋊D35)C3×C711yescharacteristic, direct product factor
19C7×C3⋊(C5⋊D5)—71no—
20C3×C5⋊D35—31no—
21C3×C7×C5⋊D5—211no—
22C3×C7×D21—251noHall
23C3×C5×C72—26no—
24C3×C5×C72C3×D516yescomplemented
25C3×C5×C72D1516yescomplemented
26C3×D105—56no—
27C3×C7×D15—356no—
28C3×C52×C7—26no—
29C3×C52×C7—21no—
30C3×C52×C7—21no—
31C3×C52×C7—23no—
32C3×C52×C7—23no—
33C3×C52×C7D3×C711yescharacteristic, complemented
34C3×C52×C7C3×D711yescharacteristic, complemented
35C3×C52×C7D2111yescharacteristic, complemented
36C3×C52×C7C2×C3×C711yescharacteristic, complemented
37C7×D35—156no—
38C3×C3⋊(C5⋊D5)—71noHall
39C32×C72C5⋊D511yescharacteristic, complemented, Hall
40C5⋊D35—31no—
41C7×C5⋊D5—211no—
42C32×C5×C7—218no—
43C32×C5×C7C7×D516yescomplemented
44C32×C5×C7D3516yescomplemented
45C7×D21—251no—
46C3×C7×D7—751no—
47C5×C72C3×D1516yescomplemented
48C32×C52C7×D711yescharacteristic, complemented, Hall
49D105—56no—
50C7×D15—356no—
51C3×D35—156no—
52C3×C7×D5—1056no—
53C52×C7—23no—
54C52×C7C3×D3×C711yescharacteristic, complemented
55C52×C7C3×D2111yescharacteristic, complemented
56C3⋊(C5⋊D5)—71no—
57C3×C5⋊D5—211no—
58C3×C72—21no—
59C3×C72C3×C5⋊D511yescharacteristic, complemented
60C3×C72C3⋊(C5⋊D5)11yescharacteristic, complemented
61C3×D21—251no—
62C3×D3×C7—1751no—
63C3×C5×C7—236no—
64C3×C5×C7—26no—
65C3×C5×C7—26no—
66C3×C5×C7—218no—
67C3×C5×C7—218no—
68C3×C5×C7C3×C7×D516yescomplemented
69C3×C5×C7C3×D3516yescomplemented
70C3×C5×C7C7×D1516yescomplemented
71C3×C5×C7D10516yescomplemented
72C7×D7—751noHall
73C3×D15—356no—
74C3×C52—21no—
75C3×C52C3×C7×D711yescharacteristic, complemented
76C3×C52C7×D2111yescharacteristic, complemented
77D35—156no—
78C7×D5—1056no—
79C32×C7—23no—
80C32×C7C7×C5⋊D511yescharacteristic, complemented
81C32×C7C5⋊D3511yescharacteristic, complemented
82C5⋊D5—211noHall
83C72C3×C3⋊(C5⋊D5)11yescharacteristic, complemented, Sylow
84C32×C5C7×D3516yescomplemented
85C2×C3×C7—5251no—
86D21—251no—
87C3×D7—751no—
88D3×C7—1751no—
89C5×C7—218no—
90C5×C7C3×C7×D1516yescomplemented
91C5×C7C3×D10516yescomplemented
92D15—356no—
93C3×D5—1056no—
94C52C3×C7×D2111yescharacteristic, complemented, Sylow
95C3×C7—26no—
96C3×C7—21no—
97C3×C7—21no—
98C3×C7—23no—
99C3×C7—23no—
100C3×C7C3×C7×C5⋊D511yescharacteristic, complemented
101C3×C7C3×C5⋊D3511yescharacteristic, complemented
102C3×C7C7×C3⋊(C5⋊D5)11yescharacteristic, complemented
103C3×C7C3⋊(C5⋊D35)11yescharacteristic, direct product factor
104C3×D3—1751noHall
105C3×C5—26no—
106C3×C5C3×C7×D3516yescomplemented
107C3×C5C7×D10516yescomplemented
108C2×C7—5251no—
109D7—751no—
110D5—1056no—
111C32C7×C5⋊D3511yescharacteristic, complemented, Sylow
112C7—23no—
113C7C3×C7×C3⋊(C5⋊D5)11yescharacteristic, complemented
114C7C3×C3⋊(C5⋊D35)11yescharacteristic, direct product factor
115C2×C3—5251no—
116D3—1751no—
117C5C3×C7×D10516yescomplemented
118C3—21no—
119C3C3×C7×C5⋊D3511yescharacteristic, complemented
120C3C7×C3⋊(C5⋊D35)11yescharacteristic, direct product factor
121C2—5251noSylow
subgroupG/H
center, hypercenterC3×C7C3⋊(C5⋊D35)
commutator, cosocle, hypocenterC3×C52×C7C2×C3×C7
FrattiniC1G
Fitting, socleC32×C52×C72C2
LCSG ▷ C3×C52×C7
UCSC1 ◁ C3×C7

Complements

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

NH ≅ G/Ntype
1. C32×C52×C72C2semidirect
2. C7×C3⋊(C5⋊D35)C3direct (N × H)
6. C3×C52×C72D3semidirect
7. C3×C52×C72C2×C3semidirect
8. C3×C3⋊(C5⋊D35)C7direct (N × H)
11. C32×C5×C72D5semidirect
13. C32×C52×C7D7semidirect
14. C32×C52×C7C2×C7semidirect
17. C52×C72C3×D3semidirect
18. C3⋊(C5⋊D35)C3×C7direct (N × H)
24. C3×C5×C72C3×D5semidirect
25. C3×C5×C72D15semidirect
33. C3×C52×C7D3×C7semidirect
34. C3×C52×C7C3×D7semidirect
35. C3×C52×C7D21semidirect
36. C3×C52×C7C2×C3×C7semidirect
39. C32×C72C5⋊D5semidirect
43. C32×C5×C7C7×D5semidirect
44. C32×C5×C7D35semidirect
47. C5×C72C3×D15semidirect
48. C32×C52C7×D7semidirect
54. C52×C7C3×D3×C7semidirect
55. C52×C7C3×D21semidirect
59. C3×C72C3×C5⋊D5semidirect
60. C3×C72C3⋊(C5⋊D5)semidirect
68. C3×C5×C7C3×C7×D5semidirect
69. C3×C5×C7C3×D35semidirect
70. C3×C5×C7C7×D15semidirect
71. C3×C5×C7D105semidirect
75. C3×C52C3×C7×D7semidirect
76. C3×C52C7×D21semidirect
80. C32×C7C7×C5⋊D5semidirect
81. C32×C7C5⋊D35semidirect
83. C72C3×C3⋊(C5⋊D5)semidirect
84. C32×C5C7×D35semidirect
90. C5×C7C3×C7×D15semidirect
91. C5×C7C3×D105semidirect
94. C52C3×C7×D21semidirect
100. C3×C7C3×C7×C5⋊D5semidirect
101. C3×C7C3×C5⋊D35semidirect
102. C3×C7C7×C3⋊(C5⋊D5)semidirect
103. C3×C7C3⋊(C5⋊D35)direct (N × H)
106. C3×C5C3×C7×D35semidirect
107. C3×C5C7×D105semidirect
111. C32C7×C5⋊D35semidirect
113. C7C3×C7×C3⋊(C5⋊D5)semidirect
114. C7C3×C3⋊(C5⋊D35)direct (N × H)
117. C5C3×C7×D105semidirect
119. C3C3×C7×C5⋊D35semidirect
120. C3C7×C3⋊(C5⋊D35)direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C52×C722
C7×C3⋊(C5⋊D35)3
C3×C7×C5⋊D353
C3×C7×D1055
C3×C3⋊(C5⋊D35)7
C3×C7×C3⋊(C5⋊D5)7