Finite Group Databasebeta

← C7×D5×C17×D15 #49087969

Subgroups — C7×D5×C17×D15 #49087969

Order 35700.

192 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 64 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×C7×D5×C17C211yesmaximal, characteristic, complemented
2C5×C7×C17×D15C211yesmaximal, characteristic, complemented
3C7×C17×C3⋊(C5⋊D5)C211yesmaximal, characteristic, complemented
4C7×D52×C17—31nomaximal, Hall
5C3×C52×C7×C17C2211yescharacteristic, complemented, Hall
6C2×C7×C17×D15—51nomaximal
7D3×C7×D5×C17—51nomaximal
8C7×C17×C5⋊D5—31no—
9C5×C7×D5×C17—31no—
10C5×C7×D5×C17D311yescharacteristic, complemented
11D5×C17×D15C711yesmaximal, characteristic, direct product factor, Hall
12C7×C17×D15—51no—
13C7×C17×D15—51no—
14C7×C17×D15—102no—
15C7×C17×D15D511yescharacteristic, direct product factor
16C5×D3×C7×C17—51no—
17C3×C7×D5×C17D511yescharacteristic, complemented
18C2×C3×C5×C7×C17—51no—
19C52×C7×C17C2×D311yescharacteristic, complemented, Hall
20C17×C3⋊(C5⋊D5)C2×C711yescharacteristic, complemented
21C5×C17×D15C2×C711yescharacteristic, complemented
22C3×C5×D5×C17C2×C711yescharacteristic, complemented
23C2×C7×D5×C17—151no—
24C2×C7×D5×C17—151no—
25C7×D5×D15C1711yesmaximal, characteristic, direct product factor, Hall
26C3×C5×C7×C17—22no—
27C3×C5×C7×C17C2×D511yescharacteristic, complemented
28C3×C5×C7×C17C2×D511yescharacteristic, complemented
29D52×C17—31noHall
30C2×D3×C7×C17—251noHall
31C3×C52×C17C22×C711yescharacteristic, complemented, Hall
32C2×C5×C7×C17—51no—
33C2×C5×C7×C17—151no—
34C7×D5×C17—31no—
35C7×D5×C17—151no—
36C7×D5×C17—151no—
37C7×D5×C17—302no—
38C7×D5×C17D1511yescharacteristic, direct product factor
39C7×C3⋊(C5⋊D5)C2×C1711yescharacteristic, complemented
40C5×C7×D15C2×C1711yescharacteristic, complemented
41C3×C5×C7×D5C2×C1711yescharacteristic, complemented
42C2×C17×D15—51no—
43D3×D5×C17—51no—
44C17×C5⋊D5—31no—
45C5×D5×C17—31no—
46C5×D5×C17D3×C711yescharacteristic, complemented
47C2×C3×C7×C17—51no—
48D3×C7×C17—51no—
49D3×C7×C17—251no—
50C7×D52—31noHall
51C5×C7×C17—22no—
52C5×C7×C17D3×D511yescharacteristic, complemented
53C5×C7×C17C2×D1511yescharacteristic, complemented
54C3×C52×C7C22×C1711yescharacteristic, complemented, Hall
55C2×C3×C5×C17—51no—
56C17×D15—51no—
57C17×D15—51no—
58C17×D15—102no—
59C17×D15C7×D511yescharacteristic, direct product factor
60C5×D3×C17—51no—
61C3×D5×C17C7×D511yescharacteristic, complemented
62C22×C7×C17—751noHall
63C52×C17C2×D3×C711yescharacteristic, complemented, Hall
64C2×C7×D15—51no—
65D3×C7×D5—51no—
66C3×C7×C17D5211yescharacteristic, complemented, Hall
67C7×C5⋊D5—31no—
68C5×C7×D5—31no—
69C5×C7×D5D3×C1711yescharacteristic, complemented
70C2×D5×C17—151no—
71C2×D5×C17—151no—
72D5×D15C7×C1711yescharacteristic, direct product factor, Hall
73C3×C5×C17—22no—
74C3×C5×C17C2×C7×D511yescharacteristic, complemented
75C3×C5×C17C2×C7×D511yescharacteristic, complemented
76C2×C7×C17—51no—
77C2×C7×C17—151no—
78C2×C7×C17—751no—
79C2×C3×C5×C7—51no—
80C7×D15—51no—
81C7×D15—51no—
82C7×D15—102no—
83C7×D15D5×C1711yescharacteristic, direct product factor
84C5×D3×C7—51no—
85C3×C7×D5D5×C1711yescharacteristic, complemented
86C2×D3×C17—251noHall
87C52×C7C2×D3×C1711yescharacteristic, complemented, Hall
88C2×C5×C17—51no—
89C2×C5×C17—151no—
90D5×C17—31no—
91D5×C17—151no—
92D5×C17—151no—
93D5×C17—302no—
94D5×C17C7×D1511yescharacteristic, direct product factor
95C3⋊(C5⋊D5)C2×C7×C1711yescharacteristic, complemented
96C5×D15C2×C7×C1711yescharacteristic, complemented
97C3×C5×D5C2×C7×C1711yescharacteristic, complemented
98C2×C7×D5—151no—
99C2×C7×D5—151no—
100C7×C17D5×D1511yescharacteristic, direct product factor, Hall
101C3×C5×C7—22no—
102C3×C5×C7C2×D5×C1711yescharacteristic, complemented
103C3×C5×C7C2×D5×C1711yescharacteristic, complemented
104C2×C3×C17—51no—
105D3×C17—51no—
106D3×C17—251no—
107D52—31noHall
108C5×C17—22no—
109C5×C17D3×C7×D511yescharacteristic, complemented
110C5×C17C2×C7×D1511yescharacteristic, complemented
111C2×D3×C7—251noHall
112C3×C52C22×C7×C1711yescharacteristic, complemented, Hall
113C2×C5×C7—51no—
114C2×C5×C7—151no—
115C7×D5—31no—
116C7×D5—151no—
117C7×D5—151no—
118C7×D5—302no—
119C7×D5C17×D1511yescharacteristic, direct product factor
120C22×C17—751noHall
121C2×D15—51no—
122D3×D5—51no—
123C3×C17C7×D5211yescharacteristic, complemented, Hall
124C5⋊D5—31no—
125C5×D5—31no—
126C5×D5D3×C7×C1711yescharacteristic, complemented
127C2×C3×C7—51no—
128D3×C7—51no—
129D3×C7—251no—
130C5×C7—22no—
131C5×C7D3×D5×C1711yescharacteristic, complemented
132C5×C7C2×C17×D1511yescharacteristic, complemented
133C2×C17—51no—
134C2×C17—151no—
135C2×C17—751no—
136C2×C3×C5—51no—
137D15—51no—
138D15—51no—
139D15—102no—
140D15C7×D5×C1711yescharacteristic, direct product factor
141C3×D5C7×D5×C1711yescharacteristic, complemented
142C5×D3—51no—
143C22×C7—751noHall
144C52C2×D3×C7×C1711yescharacteristic, complemented, Sylow
145C3×C7D52×C1711yescharacteristic, complemented, Hall
146C2×D5—151no—
147C2×D5—151no—
148C17C7×D5×D1511yescharacteristic, direct product factor, Sylow
149C3×C5—22no—
150C3×C5C2×C7×D5×C1711yescharacteristic, complemented
151C3×C5C2×C7×D5×C1711yescharacteristic, complemented
152C2×C7—51no—
153C2×C7—151no—
154C2×C7—751no—
155C2×D3—251noHall
156C2×C5—51no—
157C2×C5—151no—
158D5—31no—
159D5—151no—
160D5—151no—
161D5—302no—
162D5C7×C17×D1511yescharacteristic, direct product factor
163C7D5×C17×D1511yescharacteristic, direct product factor, Sylow
164C2×C3—51no—
165D3—51no—
166D3—251no—
167C5—22no—
168C5D3×C7×D5×C1711yescharacteristic, complemented
169C5C2×C7×C17×D1511yescharacteristic, complemented
170C22—751noSylow
171C3C7×D52×C1711yescharacteristic, complemented, Sylow
172C2—51no—
173C2—151no—
174C2—751no—
subgroupG/H
center, hypercenterC7×C17D5×D15
commutator, cosocle, hypocenterC3×C52C22×C7×C17
FrattiniC1G
Fitting, socleC3×C52×C7×C17C22
LCSG ▷ C3×C52
UCSC1 ◁ C7×C17

Complements

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

NH ≅ G/Ntype
1. C3×C5×C7×D5×C17C2semidirect
2. C5×C7×C17×D15C2semidirect
3. C7×C17×C3⋊(C5⋊D5)C2semidirect
5. C3×C52×C7×C17C22semidirect
10. C5×C7×D5×C17D3semidirect
11. D5×C17×D15C7direct (N × H)
15. C7×C17×D15D5direct (N × H)
17. C3×C7×D5×C17D5semidirect
19. C52×C7×C17C2×D3semidirect
20. C17×C3⋊(C5⋊D5)C2×C7semidirect
21. C5×C17×D15C2×C7semidirect
22. C3×C5×D5×C17C2×C7semidirect
25. C7×D5×D15C17direct (N × H)
27. C3×C5×C7×C17C2×D5semidirect
28. C3×C5×C7×C17C2×D5semidirect
31. C3×C52×C17C22×C7semidirect
38. C7×D5×C17D15direct (N × H)
39. C7×C3⋊(C5⋊D5)C2×C17semidirect
40. C5×C7×D15C2×C17semidirect
41. C3×C5×C7×D5C2×C17semidirect
46. C5×D5×C17D3×C7semidirect
52. C5×C7×C17D3×D5semidirect
53. C5×C7×C17C2×D15semidirect
54. C3×C52×C7C22×C17semidirect
59. C17×D15C7×D5direct (N × H)
61. C3×D5×C17C7×D5semidirect
63. C52×C17C2×D3×C7semidirect
66. C3×C7×C17D52semidirect
69. C5×C7×D5D3×C17semidirect
72. D5×D15C7×C17direct (N × H)
74. C3×C5×C17C2×C7×D5semidirect
75. C3×C5×C17C2×C7×D5semidirect
83. C7×D15D5×C17direct (N × H)
85. C3×C7×D5D5×C17semidirect
87. C52×C7C2×D3×C17semidirect
94. D5×C17C7×D15direct (N × H)
95. C3⋊(C5⋊D5)C2×C7×C17semidirect
96. C5×D15C2×C7×C17semidirect
97. C3×C5×D5C2×C7×C17semidirect
100. C7×C17D5×D15direct (N × H)
102. C3×C5×C7C2×D5×C17semidirect
103. C3×C5×C7C2×D5×C17semidirect
109. C5×C17D3×C7×D5semidirect
110. C5×C17C2×C7×D15semidirect
112. C3×C52C22×C7×C17semidirect
119. C7×D5C17×D15direct (N × H)
123. C3×C17C7×D52semidirect
126. C5×D5D3×C7×C17semidirect
131. C5×C7D3×D5×C17semidirect
132. C5×C7C2×C17×D15semidirect
140. D15C7×D5×C17direct (N × H)
141. C3×D5C7×D5×C17semidirect
144. C52C2×D3×C7×C17semidirect
145. C3×C7D52×C17semidirect
148. C17C7×D5×D15direct (N × H)
150. C3×C5C2×C7×D5×C17semidirect
151. C3×C5C2×C7×D5×C17semidirect
162. D5C7×C17×D15direct (N × H)
163. C7D5×C17×D15direct (N × H)
168. C5D3×C7×D5×C17semidirect
169. C5C2×C7×C17×D15semidirect
171. C3C7×D52×C17semidirect

Maximal subgroups

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

subgroupindex
C3×C5×C7×D5×C172
C5×C7×C17×D152
C7×C17×C3⋊(C5⋊D5)2
C7×D52×C173
C2×C7×C17×D155
D3×C7×D5×C175
D5×C17×D157
C7×D5×D1517