Finite Group Databasebeta

← C2×C3×C3⋊(C5⋊D35) #20263162

Subgroups — C2×C3×C3⋊(C5⋊D35) #20263162

Order 6300.

352 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 134 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×C3⋊(C5⋊D35)C212yesmaximal, direct product factor
2C2×C32×C52×C7C211yesmaximal, characteristic, complemented
3C2×C3⋊(C5⋊D35)C311yesmaximal, characteristic, direct product factor
4C2×C3×C5⋊D35—31nomaximal
5C32×C52×C7C2211yescharacteristic, complemented, Hall
6C2×C3×D105—56nomaximal
7C2×C3×C52×C7—21no—
8C2×C3×C52×C7D311yescharacteristic, complemented
9C2×C3×C52×C7C2×C311yescharacteristic, complemented
10C3⋊(C5⋊D35)C2×C312yesdirect product factor
11C3×C5⋊D35—32no—
12C2×C3×C3⋊(C5⋊D5)—71nomaximal, Hall
13C2×C5⋊D35—31noHall
14C2×C32×C5×C7D516yescomplemented
15C3×D105—512no—
16C3×C52×C7—21no—
17C3×C52×C7C2×D311yescharacteristic, complemented
18C3×C52×C7C22×C311yescharacteristic, complemented
19C2×C32×C52D711yescharacteristic, complemented
20C3×C3⋊(C5⋊D5)—72no—
21C2×D105—56no—
22C2×C3×D35—156no—
23C2×C52×C7C3×D311yescharacteristic, complemented
24C5⋊D35—32no—
25C32×C5×C7C2×D516yescomplemented
26C2×C3⋊(C5⋊D5)—71no—
27C2×C3×C5⋊D5—211no—
28C2×C3×D21—251noHall
29C32×C52C2×D711yescharacteristic, complemented, Hall
30C2×C3×C5×C7—26no—
31C2×C3×C5×C7C3×D516yescomplemented
32C2×C3×C5×C7D1516yescomplemented
33D105—512no—
34C3×D35—1512no—
35C2×C3×D15—356no—
36C52×C7C2×C3×D311yescharacteristic, complemented, Hall
37C2×C3×C52—21no—
38C2×C3×C52C3×D711yescharacteristic, complemented
39C2×C3×C52D2111yescharacteristic, complemented
40C3⋊(C5⋊D5)—72no—
41C3×C5⋊D5—212no—
42C2×D35—156no—
43C2×C32×C7C5⋊D511yescharacteristic, complemented
44C3×D21—252no—
45C3×C5×C7—26no—
46C3×C5×C7C2×C3×D516yescomplemented
47C3×C5×C7C2×D1516yescomplemented
48C2×C5⋊D5—211noHall
49C2×C32×C5D3516yescomplemented
50C3×D15—3512no—
51C2×D21—251no—
52C2×C3×D7—751no—
53C3×C52—21no—
54C3×C52C2×C3×D711yescharacteristic, complemented
55C3×C52C2×D2111yescharacteristic, complemented
56C2×C5×C7C3×D1516yescomplemented
57D35—1512no—
58C32×C7C2×C5⋊D511yescharacteristic, complemented, Hall
59C2×D15—356no—
60C2×C3×D5—1056no—
61C2×C52C3×D2111yescharacteristic, complemented
62C5⋊D5—212no—
63C32×C5C2×D3516yescomplemented
64C2×C3×C7—21no—
65C2×C3×C7C3×C5⋊D511yescharacteristic, complemented
66C2×C3×C7C3⋊(C5⋊D5)11yescharacteristic, complemented
67D21—252no—
68C3×D7—752no—
69C2×C3×D3—1751noHall
70C5×C7C2×C3×D1516yescomplemented
71C2×C3×C5—26no—
72C2×C3×C5C3×D3516yescomplemented
73C2×C3×C5D10516yescomplemented
74D15—3512no—
75C3×D5—10512no—
76C2×D7—751noHall
77C52C2×C3×D2111yescharacteristic, complemented, Sylow
78C3×C7—21no—
79C3×C7C2×C3×C5⋊D511yescharacteristic, complemented
80C3×C7C2×C3⋊(C5⋊D5)11yescharacteristic, complemented
81C2×D5—1056no—
82C2×C32C5⋊D3511yescharacteristic, complemented
83C3×D3—1752no—
84C3×C5—26no—
85C3×C5C2×C3×D3516yescomplemented
86C3×C5C2×D10516yescomplemented
87C2×C7C3×C3⋊(C5⋊D5)11yescharacteristic, complemented
88D7—752no—
89C22×C3—5251no—
90C2×D3—1751no—
91C2×C5C3×D10516yescomplemented
92D5—10512no—
93C32C2×C5⋊D3511yescharacteristic, complemented, Sylow
94C7C2×C3×C3⋊(C5⋊D5)11yescharacteristic, complemented, Sylow
95C2×C3—21no—
96C2×C3—5252no—
97C2×C3C3×C5⋊D3511yescharacteristic, complemented
98C2×C3C3⋊(C5⋊D35)11yescharacteristic, direct product factor
99D3—1752no—
100C5C2×C3×D10516yescomplemented
101C22—5251noSylow
102C3—21no—
103C3C2×C3×C5⋊D3511yescharacteristic, complemented
104C3C2×C3⋊(C5⋊D35)11yescharacteristic, direct product factor
105C2—5252no—
106C2C3×C3⋊(C5⋊D35)11yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3C3⋊(C5⋊D35)
commutator, hypocenterC3×C52×C7C22×C3
FrattiniC1G
Fitting, socleC2×C32×C52×C7C2
LCSG ▷ C3×C52×C7
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
1. C3×C3⋊(C5⋊D35)C2direct (N × H)
2. C2×C32×C52×C7C2semidirect
3. C2×C3⋊(C5⋊D35)C3direct (N × H)
5. C32×C52×C7C22semidirect
8. C2×C3×C52×C7D3semidirect
9. C2×C3×C52×C7C2×C3semidirect
10. C3⋊(C5⋊D35)C2×C3direct (N × H)
14. C2×C32×C5×C7D5semidirect
17. C3×C52×C7C2×D3semidirect
18. C3×C52×C7C22×C3semidirect
19. C2×C32×C52D7semidirect
23. C2×C52×C7C3×D3semidirect
25. C32×C5×C7C2×D5semidirect
29. C32×C52C2×D7semidirect
31. C2×C3×C5×C7C3×D5semidirect
32. C2×C3×C5×C7D15semidirect
36. C52×C7C2×C3×D3semidirect
38. C2×C3×C52C3×D7semidirect
39. C2×C3×C52D21semidirect
43. C2×C32×C7C5⋊D5semidirect
46. C3×C5×C7C2×C3×D5semidirect
47. C3×C5×C7C2×D15semidirect
49. C2×C32×C5D35semidirect
54. C3×C52C2×C3×D7semidirect
55. C3×C52C2×D21semidirect
56. C2×C5×C7C3×D15semidirect
58. C32×C7C2×C5⋊D5semidirect
61. C2×C52C3×D21semidirect
63. C32×C5C2×D35semidirect
65. C2×C3×C7C3×C5⋊D5semidirect
66. C2×C3×C7C3⋊(C5⋊D5)semidirect
70. C5×C7C2×C3×D15semidirect
72. C2×C3×C5C3×D35semidirect
73. C2×C3×C5D105semidirect
77. C52C2×C3×D21semidirect
79. C3×C7C2×C3×C5⋊D5semidirect
80. C3×C7C2×C3⋊(C5⋊D5)semidirect
82. C2×C32C5⋊D35semidirect
85. C3×C5C2×C3×D35semidirect
86. C3×C5C2×D105semidirect
87. C2×C7C3×C3⋊(C5⋊D5)semidirect
91. C2×C5C3×D105semidirect
93. C32C2×C5⋊D35semidirect
94. C7C2×C3×C3⋊(C5⋊D5)semidirect
97. C2×C3C3×C5⋊D35semidirect
98. C2×C3C3⋊(C5⋊D35)direct (N × H)
100. C5C2×C3×D105semidirect
103. C3C2×C3×C5⋊D35semidirect
104. C3C2×C3⋊(C5⋊D35)direct (N × H)
106. C2C3×C3⋊(C5⋊D35)direct (N × H)