Finite Group Databasebeta

← D51×C5⋊D35 #49088012

Subgroups — D51×C5⋊D35 #49088012

Order 35700.

320 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 86 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×C17×C5⋊D35C211yesmaximal, characteristic, complemented
2C52×C7×D51C211yesmaximal, characteristic, complemented
3C3⋊(C5⋊D595)C211yesmaximal, characteristic, complemented
4D17×C5⋊D35—31nomaximal, Hall
5C3×C52×C7×C17C2211yescharacteristic, complemented, Hall
6D35×D51—56nomaximal
7C5⋊D595—31no—
8C17×C5⋊D35D311yescharacteristic, complemented
9C52×C7×D17—31no—
10C5⋊D5×D51—71nomaximal, Hall
11D1785—56no—
12C5×C7×D51D516yescomplemented
13C3×C17×D35—56no—
14C52×C7×C17C2×D311yescharacteristic, complemented, Hall
15C3⋊(C5⋊D85)—71no—
16C52×D51D711yescharacteristic, complemented
17C3×C17×C5⋊D5—71no—
18D17×D35—156no—
19D3×C5⋊D35—171nomaximal, Hall
20C3×C5×C7×C17C2×D516yescomplemented
21D17×C5⋊D5—211noHall
22D7×D51—251noHall
23C3×C52×C17C2×D711yescharacteristic, complemented, Hall
24D595—156no—
25C17×D35—56no—
26C5×C7×D17—36no—
27C3⋊(C5⋊D35)—171no—
28C52×D3×C7—171no—
29C3×C5⋊D35D1711yescharacteristic, complemented
30D5×D51—356no—
31C5⋊D85—211no—
32C17×C5⋊D5—71no—
33C52×D17—31no—
34D357—251no—
35C7×D51C5⋊D511yescharacteristic, complemented
36C3×D7×C17—251no—
37C2×C5⋊D35—511noHall
38C5×C7×C17D3×D516yescomplemented
39C3×C52×C7C2×D1711yescharacteristic, complemented, Hall
40D255—356no—
41C5×D51D3516yescomplemented
42C3×D5×C17—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—511no—
49C5⋊D35D5111yescharacteristic, direct product factor
50D5×D17—1056no—
51D3×C5⋊D5—1191noHall
52C3×C5×C17C2×D3516yescomplemented
53D119—751no—
54C7×D17—31no—
55D7×C17—251no—
56D105—856no—
57C5×D3×C7—176no—
58C3×D35—56no—
59C2×D51—1751noHall
60C52×C7C2×D5111yescharacteristic, complemented, Hall
61D85—1056no—
62C5×D17—36no—
63D5×C17—356no—
64C3⋊(C5⋊D5)—1191no—
65C52×D3—171no—
66C3×C5⋊D5—71no—
67C2×D35—2556no—
68C7×C17D3×C5⋊D511yescharacteristic, complemented, Hall
69C3×C5×C7D5×D1716yescomplemented
70C2×C3×C17—1751no—
71D51—1751no—
72D51C5⋊D3511yescharacteristic, direct product factor
73C2×C5⋊D5—3571noHall
74C5×C17D3×D3516yescomplemented
75D3×D7—4251noHall
76C3×C52D7×D1711yescharacteristic, complemented, Hall
77C2×C5×C7—516no—
78D35—56no—
79D35—2556no—
80C2×D17—5251noHall
81D3×D5—5956no—
82C3×C17C2×C5⋊D3511yescharacteristic, complemented, Hall
83C2×C52—511no—
84C5⋊D5—71no—
85C5⋊D5—3571no—
86D21—4251no—
87C3×D7—251no—
88D3×C7—171no—
89C5×C7D5×D5116yescomplemented
90C2×C17—1751no—
91D17—31no—
92D17—5251no—
93D15—5956no—
94C3×D5—356no—
95C5×D3—176no—
96C2×D7—12751noHall
97C52D7×D5111yescharacteristic, complemented, Sylow
98C3×C7D17×C5⋊D511yescharacteristic, complemented, Hall
99C2×D5—17856no—
100C17D3×C5⋊D3511yescharacteristic, complemented, Sylow
101C3×C5D17×D3516yescomplemented
102C2×C7—511no—
103D7—251no—
104D7—12751no—
105C2×D3—29751noHall
106C2×C5—516no—
107D5—356no—
108D5—17856no—
109C7C5⋊D5×D5111yescharacteristic, complemented, Sylow
110C2×C3—1751no—
111D3—171no—
112D3—29751no—
113C5D35×D5116yescomplemented
114C22—89251noSylow
115C3D17×C5⋊D3511yescharacteristic, complemented, Sylow
116C2—511no—
117C2—1751no—
118C2—89251no—
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×C17×C5⋊D35C2semidirect
2. C52×C7×D51C2semidirect
3. C3⋊(C5⋊D595)C2semidirect
5. C3×C52×C7×C17C22semidirect
8. C17×C5⋊D35D3semidirect
12. C5×C7×D51D5semidirect
14. C52×C7×C17C2×D3semidirect
16. C52×D51D7semidirect
20. C3×C5×C7×C17C2×D5semidirect
23. C3×C52×C17C2×D7semidirect
29. C3×C5⋊D35D17semidirect
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
49. C5⋊D35D51direct (N × H)
52. C3×C5×C17C2×D35semidirect
60. C52×C7C2×D51semidirect
68. C7×C17D3×C5⋊D5semidirect
69. C3×C5×C7D5×D17semidirect
72. D51C5⋊D35direct (N × H)
74. C5×C17D3×D35semidirect
76. C3×C52D7×D17semidirect
82. C3×C17C2×C5⋊D35semidirect
89. C5×C7D5×D51semidirect
97. C52D7×D51semidirect
98. C3×C7D17×C5⋊D5semidirect
100. C17D3×C5⋊D35semidirect
101. C3×C5D17×D35semidirect
109. C7C5⋊D5×D51semidirect
113. C5D35×D51semidirect
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×C17×C5⋊D352
C52×C7×D512
C3⋊(C5⋊D595)2
D17×C5⋊D353
D35×D515
C5⋊D5×D517
D3×C5⋊D3517