Finite Group Databasebeta

← C17×#14523665 #49087988

Subgroups — C17×#14523665 #49087988

Order 35700.

192 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 50 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×C7×C17×C5⋊D5C211yesmaximal, characteristic, complemented
2C5×C17×D105C212yesmaximal, complemented
3C17×(C5⋊D5)⋊D7—31nomaximal, Hall
4C3×C52×C7×C17C2211yescharacteristic, complemented, Hall
5D5×C17×D21—52nomaximal
6C7×C17×C5⋊D5D311yescharacteristic, complemented
7C5×C17×D35—32no—
8C17×D15⋊D5—71nomaximal, Hall
9C17×D105D512yescomplemented
10C5×C17×D21—52no—
11C3×C7×D5×C17—52no—
12C3×C7×D5×C17—102no—
13C52×C7×C17C2×D311yescharacteristic, complemented, Hall
14C5×C17×D15—72no—
15C3×C17×C5⋊D5D711yescharacteristic, complemented
16D5×D7×C17—152no—
17#14523665C1711yesmaximal, characteristic, direct product factor, Hall
18C3×C5×C7×C17—22no—
19C3×C5×C7×C17C2×D512yescomplemented
20D52×C17—211noHall
21C2×C17×D21—251noHall
22C3×C52×C17C2×D711yescharacteristic, complemented, Hall
23C17×D35—32no—
24C7×D5×C17—52no—
25C7×D5×C17—102no—
26C5×D7×C17—152no—
27C5×D105C2×C1712yescomplemented
28C3×C7×C5⋊D5C2×C1711yescharacteristic, complemented
29D3×D5×C17—352no—
30C17×C5⋊D5D2111yescharacteristic, complemented
31C5×D5×C17—212no—
32C2×C3×C7×C17—251no—
33C17×D21—52no—
34(C5⋊D5)⋊D7—31noHall
35C5×C7×C17—22no—
36C5×C7×C17D3×D512yescomplemented
37C3×C52×C7C22×C1711yescharacteristic, complemented, Hall
38C17×D15—72no—
39C5×D3×C17—352no—
40C3×D5×C17—52no—
41C3×D5×C17—102no—
42C2×D7×C17—751noHall
43C52×C17C2×D2111yescharacteristic, complemented, Hall
44D5×D21—52no—
45C3×C7×C17D5211yescharacteristic, complemented, Hall
46C7×C5⋊D5D3×C1711yescharacteristic, complemented
47C5×D35—32no—
48C2×D5×C17—1052no—
49D15⋊D5—71noHall
50C3×C5×C17—22no—
51C3×C5×C17D5×D712yescomplemented
52C2×C7×C17—251no—
53D7×C17—152no—
54D105D5×C1712yescomplemented
55C5×D21—52no—
56C3×C7×D5—52no—
57C3×C7×D5—102no—
58C2×D3×C17—1751noHall
59C52×C7C2×D3×C1711yescharacteristic, complemented, Hall
60C2×C5×C17—1052no—
61D5×C17—52no—
62D5×C17—102no—
63D5×C17—212no—
64C5×D15—72no—
65C3×C5⋊D5D7×C1711yescharacteristic, complemented
66D5×D7—152no—
67C7×C17D15⋊D511yescharacteristic, complemented, Hall
68C3×C5×C7—22no—
69C3×C5×C7C2×D5×C1712yescomplemented
70C2×C3×C17—251no—
71D3×C17—352no—
72D52—211noHall
73C5×C17—22no—
74C5×C17D5×D2112yescomplemented
75C2×D21—251noHall
76C3×C52C2×D7×C1711yescharacteristic, complemented, Hall
77D35—32no—
78C5×D7—152no—
79C7×D5—52no—
80C7×D5—102no—
81C22×C17—5251noHall
82D3×D5—352no—
83C3×C17(C5⋊D5)⋊D711yescharacteristic, complemented, Hall
84C5⋊D5C17×D2111yescharacteristic, complemented
85C5×D5—212no—
86C2×C3×C7—251no—
87D21—52no—
88C5×C7—22no—
89C5×C7D3×D5×C1712yescomplemented
90C2×C17—251no—
91C2×C17—1052no—
92D15—72no—
93C3×D5—52no—
94C3×D5—102no—
95C5×D3—352no—
96C2×D7—751noHall
97C52C2×C17×D2111yescharacteristic, complemented, Sylow
98C3×C7D52×C1711yescharacteristic, complemented, Hall
99C2×D5—1052no—
100C17#1452366511yescharacteristic, direct product factor, Sylow
101C3×C5—22no—
102C3×C5D5×D7×C1712yescomplemented
103C2×C7—251no—
104D7—152no—
105C2×D3—1751noHall
106C2×C5—1052no—
107D5—52no—
108D5—102no—
109D5—212no—
110C7C17×D15⋊D511yescharacteristic, complemented, Sylow
111C2×C3—251no—
112D3—352no—
113C5—22no—
114C5D5×C17×D2112yescomplemented
115C22—5251noSylow
116C3C17×(C5⋊D5)⋊D711yescharacteristic, complemented, Sylow
117C2—251no—
118C2—1052no—
subgroupG/H
center, hypercenterC17#14523665
commutator, cosocle, hypocenterC3×C52×C7C22×C17
FrattiniC1G
Fitting, socleC3×C52×C7×C17C22
LCSG ▷ C3×C52×C7
UCSC1 ◁ C17

Complements

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

NH ≅ G/Ntype
1. C3×C7×C17×C5⋊D5C2semidirect
2. C5×C17×D105C2semidirect
4. C3×C52×C7×C17C22semidirect
6. C7×C17×C5⋊D5D3semidirect
9. C17×D105D5semidirect
13. C52×C7×C17C2×D3semidirect
15. C3×C17×C5⋊D5D7semidirect
17. #14523665C17direct (N × H)
19. C3×C5×C7×C17C2×D5semidirect
22. C3×C52×C17C2×D7semidirect
27. C5×D105C2×C17semidirect
28. C3×C7×C5⋊D5C2×C17semidirect
30. C17×C5⋊D5D21semidirect
36. C5×C7×C17D3×D5semidirect
37. C3×C52×C7C22×C17semidirect
43. C52×C17C2×D21semidirect
45. C3×C7×C17D52semidirect
46. C7×C5⋊D5D3×C17semidirect
51. C3×C5×C17D5×D7semidirect
54. D105D5×C17semidirect
59. C52×C7C2×D3×C17semidirect
65. C3×C5⋊D5D7×C17semidirect
67. C7×C17D15⋊D5semidirect
69. C3×C5×C7C2×D5×C17semidirect
74. C5×C17D5×D21semidirect
76. C3×C52C2×D7×C17semidirect
83. C3×C17(C5⋊D5)⋊D7semidirect
84. C5⋊D5C17×D21semidirect
89. C5×C7D3×D5×C17semidirect
97. C52C2×C17×D21semidirect
98. C3×C7D52×C17semidirect
100. C17#14523665direct (N × H)
102. C3×C5D5×D7×C17semidirect
110. C7C17×D15⋊D5semidirect
114. C5D5×C17×D21semidirect
116. C3C17×(C5⋊D5)⋊D7semidirect

Maximal subgroups

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

subgroupindex
C3×C7×C17×C5⋊D52
C5×C17×D1052
C17×(C5⋊D5)⋊D73
D5×C17×D215
C17×D15⋊D57
#1452366517