Finite Group Databasebeta

← D51⋊(C5⋊D35) #49088014

Subgroups — D51⋊(C5⋊D35) #49088014

Order 35700.

320 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 85 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×C5⋊D595C211yesmaximal, characteristic, complemented
2C52×C7×D51C211yesmaximal, characteristic, complemented
3C17×C3⋊(C5⋊D35)C211yesmaximal, characteristic, complemented
4D17×C5⋊D35—31nomaximal, Hall
5C3×C52×C7×C17C2211yescharacteristic, complemented, Hall
6D51⋊D35—56nomaximal
7C5⋊D595D311yescharacteristic, complemented
8C17×C5⋊D35—31no—
9C52×C7×D17—31no—
10D51⋊(C5⋊D5)—71nomaximal, Hall
11C17×D105—56no—
12C5×C7×D51D516yescomplemented
13C3×D595—56no—
14C52×C7×C17C2×D311yescharacteristic, complemented, Hall
15C17×C3⋊(C5⋊D5)—71no—
16C52×D51D711yescharacteristic, complemented
17C3×C5⋊D85—71no—
18D17×D35—156no—
19D3×C5⋊D35—171nomaximal, Hall
20C3×C5×C7×C17C2×D516yescomplemented
21D17×C5⋊D5—211noHall
22D21⋊D17—251noHall
23C3×C52×C17C2×D711yescharacteristic, complemented, Hall
24D595—56no—
25C17×D35—156no—
26C5×C7×D17—36no—
27C3⋊(C5⋊D35)D1711yescharacteristic, complemented
28C52×D3×C7—171no—
29C3×C5⋊D35—171no—
30D15⋊D17—356no—
31C5⋊D85—71no—
32C17×C5⋊D5—211no—
33C52×D17—31no—
34C17×D21—251no—
35C7×D51C5⋊D511yescharacteristic, complemented
36C3×D119—251no—
37C2×C5⋊D35—511noHall
38C5×C7×C17D3×D516yescomplemented
39C3×C52×C7C2×D1711yescharacteristic, complemented, Hall
40C17×D15—356no—
41C5×D51D3516yescomplemented
42C3×D85—356no—
43D7×D17—751noHall
44C52×C17D3×D711yescharacteristic, complemented, Hall
45D3×D35—856no—
46C3×C7×C17C2×C5⋊D511yescharacteristic, complemented, Hall
47C2×C52×C7—511no—
48C5⋊D35—31no—
49C5⋊D35—171no—
50D5×D17—1056no—
51D3×C5⋊D5—1191noHall
52C3×C5×C17C2×D3516yescomplemented
53D119—251no—
54C7×D17—31no—
55D7×C17—751no—
56D105—56no—
57C5×D3×C7—176no—
58C3×D35—856no—
59D3×D17—1751noHall
60C52×C7D3×D1711yescharacteristic, complemented, Hall
61D85—356no—
62C5×D17—36no—
63D5×C17—1056no—
64C3⋊(C5⋊D5)—71no—
65C52×D3—171no—
66C3×C5⋊D5—1191no—
67C2×D35—2556no—
68C7×C17D3×C5⋊D511yescharacteristic, complemented, Hall
69C3×C5×C7D5×D1716yescomplemented
70D51C5⋊D3511yescharacteristic, complemented
71C3×D17—1751no—
72D3×C17—1751no—
73C2×C5⋊D5—3571noHall
74C5×C17D3×D3516yescomplemented
75D3×D7—4251noHall
76C3×C52D7×D1711yescharacteristic, complemented, Hall
77C2×C5×C7—516no—
78D35—156no—
79D35—856no—
80C2×D17—5251noHall
81D3×D5—5956no—
82C3×C17C2×C5⋊D3511yescharacteristic, complemented, Hall
83C2×C52—511no—
84C5⋊D5—211no—
85C5⋊D5—1191no—
86D21—251no—
87C3×D7—4251no—
88D3×C7—171no—
89C5×C7D15⋊D1716yescomplemented
90C2×C17—5251no—
91D17—31no—
92D17—1751no—
93D15—356no—
94C3×D5—5956no—
95C5×D3—176no—
96C2×D7—12751noHall
97C52D21⋊D1711yescharacteristic, complemented, Sylow
98C3×C7D17×C5⋊D511yescharacteristic, complemented, Hall
99C2×D5—17856no—
100C17D3×C5⋊D3511yescharacteristic, complemented, Sylow
101C3×C5D17×D3516yescomplemented
102C2×C7—511no—
103D7—751no—
104D7—4251no—
105C2×D3—29751noHall
106C2×C5—516no—
107D5—5956no—
108D5—1056no—
109C7D51⋊(C5⋊D5)11yescharacteristic, complemented, Sylow
110C2×C3—29751no—
111D3—171no—
112D3—1751no—
113C5D51⋊D3516yescomplemented
114C22—89251noSylow
115C3D17×C5⋊D3511yescharacteristic, complemented, Sylow
116C2—5251no—
117C2—511no—
118C2—29751no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C52×C7×C17C22
LCSG ▷ C3×C52×C7×C17
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C5⋊D595C2semidirect
2. C52×C7×D51C2semidirect
3. C17×C3⋊(C5⋊D35)C2semidirect
5. C3×C52×C7×C17C22semidirect
7. C5⋊D595D3semidirect
12. C5×C7×D51D5semidirect
14. C52×C7×C17C2×D3semidirect
16. C52×D51D7semidirect
20. C3×C5×C7×C17C2×D5semidirect
23. C3×C52×C17C2×D7semidirect
27. C3⋊(C5⋊D35)D17semidirect
35. C7×D51C5⋊D5semidirect
38. C5×C7×C17D3×D5semidirect
39. C3×C52×C7C2×D17semidirect
41. C5×D51D35semidirect
44. C52×C17D3×D7semidirect
46. C3×C7×C17C2×C5⋊D5semidirect
52. C3×C5×C17C2×D35semidirect
60. C52×C7D3×D17semidirect
68. C7×C17D3×C5⋊D5semidirect
69. C3×C5×C7D5×D17semidirect
70. D51C5⋊D35semidirect
74. C5×C17D3×D35semidirect
76. C3×C52D7×D17semidirect
82. C3×C17C2×C5⋊D35semidirect
89. C5×C7D15⋊D17semidirect
97. C52D21⋊D17semidirect
98. C3×C7D17×C5⋊D5semidirect
100. C17D3×C5⋊D35semidirect
101. C3×C5D17×D35semidirect
109. C7D51⋊(C5⋊D5)semidirect
113. C5D51⋊D35semidirect
115. C3D17×C5⋊D35semidirect

Maximal subgroups

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

subgroupindex
C3×C5⋊D5952
C52×C7×D512
C17×C3⋊(C5⋊D35)2
D17×C5⋊D353
D51⋊D355
D51⋊(C5⋊D5)7
D3×C5⋊D3517