Finite Group Databasebeta

← C5×D3×C7×D85 #49087939

Subgroups — C5×D3×C7×D85 #49087939

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×D85C211yesmaximal, characteristic, complemented
2C52×D3×C7×C17C211yesmaximal, characteristic, complemented
3C5×C7×D255C211yesmaximal, characteristic, complemented
4C2×C5×C7×D85—31nomaximal, Hall
5C3×C52×C7×C17C2211yescharacteristic, complemented, Hall
6D3×C7×D85C511yesmaximal, characteristic, direct product factor
7C5×D3×C7×D17—51nomaximal
8C5×C7×D85—31no—
9C5×C7×D85D311yescharacteristic, direct product factor
10C2×C52×C7×C17—31no—
11C5×D3×D85C711yesmaximal, characteristic, direct product factor, Hall
12C7×D255C2×C511yescharacteristic, complemented
13C5×C7×D51—51no—
14C5×D3×C7×C17—22no—
15C5×D3×C7×C17D511yescharacteristic, complemented
16C5×D3×C7×C17C2×C511yescharacteristic, complemented
17C3×C7×D85C2×C511yescharacteristic, complemented
18C3×C5×C7×D17—51no—
19C52×C7×C17C2×D311yescharacteristic, complemented, Hall
20C5×D255C2×C711yescharacteristic, complemented
21C52×D3×C17C2×C711yescharacteristic, complemented
22C3×C5×D85C2×C711yescharacteristic, complemented
23C2×C5×C7×D17—151no—
24C2×C7×D85—31no—
25C5×D3×C7×D5—171nomaximal, Hall
26C3×C5×C7×C17—22no—
27C3×C5×C7×C17C2×D511yescharacteristic, complemented
28C3×C5×C7×C17C22×C511yescharacteristic, complemented
29C2×C5×D85—31noHall
30D3×C7×D17—51noHall
31C3×C52×C17C22×C711yescharacteristic, complemented, Hall
32C2×C5×C7×C17—31no—
33C2×C5×C7×C17—31no—
34C2×C5×C7×C17—62no—
35C7×D85—31no—
36C7×D85C5×D311yescharacteristic, direct product factor
37C5×C7×D17—51no—
38C5×C7×D17—151no—
39C5×C7×D15—171no—
40C52×D3×C7D1711yescharacteristic, complemented
41C3×C5×C7×D5—171no—
42D3×D85C5×C711yescharacteristic, direct product factor
43C5×D3×D17—51no—
44C2×C52×C17—31no—
45C5×D85—31no—
46C5×D85D3×C711yescharacteristic, direct product factor
47C7×D51—51no—
48D3×C7×C17C5×D511yescharacteristic, complemented
49C3×C7×D17—51no—
50C2×C5×C7×D5—511noHall
51C5×C7×C17—22no—
52C5×C7×C17D3×D511yescharacteristic, complemented
53C5×C7×C17C2×C5×D311yescharacteristic, complemented
54C3×C52×C7C2×D1711yescharacteristic, complemented, Hall
55D255C2×C5×C711yescharacteristic, complemented
56C5×D51—51no—
57C5×D3×C17—22no—
58C5×D3×C17C7×D511yescharacteristic, complemented
59C5×D3×C17C2×C5×C711yescharacteristic, complemented
60C3×D85C2×C5×C711yescharacteristic, complemented
61C3×C5×D17—51no—
62C2×C7×D17—151noHall
63C52×C17C2×D3×C711yescharacteristic, complemented, Hall
64C2×C5×D3×C7—851no—
65D3×C7×D5—171no—
66C3×C7×C17C2×C5×D511yescharacteristic, complemented, Hall
67C2×C52×C7—31no—
68C5×C7×D5—171no—
69C5×C7×D5—511no—
70C2×D85—31no—
71C2×C5×D17—151no—
72C5×D3×D5—171noHall
73C3×C5×C17—22no—
74C3×C5×C17C2×C7×D511yescharacteristic, complemented
75C3×C5×C17C22×C5×C711yescharacteristic, complemented
76C2×C7×C17—31no—
77C7×D17—51no—
78C7×D17—151no—
79C2×C3×C5×C7—851no—
80C7×D15—171no—
81C5×D3×C7—22no—
82C5×D3×C7—851no—
83C5×D3×C7C5×D1711yescharacteristic, complemented
84C5×D3×C7D8511yescharacteristic, direct product factor
85C3×C7×D5—171no—
86D3×D17—51noHall
87C52×C7D3×D1711yescharacteristic, complemented, Hall
88C2×C5×C17—31no—
89C2×C5×C17—31no—
90C2×C5×C17—62no—
91D85—31no—
92D85C5×D3×C711yescharacteristic, direct product factor
93C5×D17—51no—
94C5×D17—151no—
95C5×D15—171no—
96C52×D3C7×D1711yescharacteristic, complemented
97C3×C5×D5—171no—
98C22×C5×C7—2551no—
99C2×C7×D5—511no—
100C7×C17C5×D3×D511yescharacteristic, complemented, Hall
101C3×C5×C7—22no—
102C3×C5×C7C2×C5×D1711yescharacteristic, complemented
103C3×C5×C7C2×D8511yescharacteristic, complemented
104D51—51no—
105C3×D17—51no—
106D3×C17C5×C7×D511yescharacteristic, complemented
107C2×C5×D5—511noHall
108C5×C17—22no—
109C5×C17D3×C7×D511yescharacteristic, complemented
110C5×C17C2×C5×D3×C711yescharacteristic, complemented
111C2×D3×C7—851noHall
112C3×C52C2×C7×D1711yescharacteristic, complemented, Hall
113C2×C5×C7—31no—
114C2×C5×C7—31no—
115C2×C5×C7—62no—
116C2×C5×C7—851no—
117C2×C5×C7—2551no—
118C7×D5—171no—
119C7×D5—511no—
120C2×D17—151noHall
121C2×C5×D3—851no—
122D3×D5—171no—
123C3×C17C2×C5×C7×D511yescharacteristic, complemented, Hall
124C2×C52—31no—
125C5×D5—171no—
126C5×D5—511no—
127C2×C3×C7—851no—
128D3×C7—851no—
129D3×C7C5×D8511yescharacteristic, direct product factor
130C5×C7—22no—
131C5×C7C5×D3×D1711yescharacteristic, complemented
132C5×C7D3×D8511yescharacteristic, direct product factor
133C2×C17—31no—
134D17—51no—
135D17—151no—
136C2×C3×C5—851no—
137D15—171no—
138C3×D5—171no—
139C5×D3—22no—
140C5×D3—851no—
141C5×D3C5×C7×D1711yescharacteristic, complemented
142C5×D3C7×D8511yescharacteristic, direct product factor
143C22×C7—2551noHall
144C52D3×C7×D1711yescharacteristic, complemented, Sylow
145C3×C7C2×C5×D8511yescharacteristic, complemented, Hall
146C22×C5—2551no—
147C2×D5—511no—
148C17C5×D3×C7×D511yescharacteristic, complemented, Sylow
149C3×C5—22no—
150C3×C5C2×C7×D8511yescharacteristic, complemented
151C3×C5C2×C5×C7×D1711yescharacteristic, complemented
152C2×C7—31no—
153C2×C7—851no—
154C2×C7—2551no—
155C2×D3—851noHall
156C2×C5—31no—
157C2×C5—31no—
158C2×C5—62no—
159C2×C5—851no—
160C2×C5—2551no—
161D5—171no—
162D5—511no—
163C7C5×D3×D8511yescharacteristic, direct product factor, Sylow
164C2×C3—851no—
165D3—851no—
166D3C5×C7×D8511yescharacteristic, direct product factor
167C5—22no—
168C5C5×D3×C7×D1711yescharacteristic, complemented
169C5D3×C7×D8511yescharacteristic, direct product factor
170C22—2551noSylow
171C3C2×C5×C7×D8511yescharacteristic, complemented, Sylow
172C2—31no—
173C2—851no—
174C2—2551no—
subgroupG/H
center, hypercenterC5×C7D3×D85
commutator, cosocle, hypocenterC3×C5×C17C22×C5×C7
FrattiniC1G
Fitting, socleC3×C52×C7×C17C22
LCSG ▷ C3×C5×C17
UCSC1 ◁ C5×C7

Complements

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

NH ≅ G/Ntype
1. C3×C5×C7×D85C2semidirect
2. C52×D3×C7×C17C2semidirect
3. C5×C7×D255C2semidirect
5. C3×C52×C7×C17C22semidirect
6. D3×C7×D85C5direct (N × H)
9. C5×C7×D85D3direct (N × H)
11. C5×D3×D85C7direct (N × H)
12. C7×D255C2×C5semidirect
15. C5×D3×C7×C17D5semidirect
16. C5×D3×C7×C17C2×C5semidirect
17. C3×C7×D85C2×C5semidirect
19. C52×C7×C17C2×D3semidirect
20. C5×D255C2×C7semidirect
21. C52×D3×C17C2×C7semidirect
22. C3×C5×D85C2×C7semidirect
27. C3×C5×C7×C17C2×D5semidirect
28. C3×C5×C7×C17C22×C5semidirect
31. C3×C52×C17C22×C7semidirect
36. C7×D85C5×D3direct (N × H)
40. C52×D3×C7D17semidirect
42. D3×D85C5×C7direct (N × H)
46. C5×D85D3×C7direct (N × H)
48. D3×C7×C17C5×D5semidirect
52. C5×C7×C17D3×D5semidirect
53. C5×C7×C17C2×C5×D3semidirect
54. C3×C52×C7C2×D17semidirect
55. D255C2×C5×C7semidirect
58. C5×D3×C17C7×D5semidirect
59. C5×D3×C17C2×C5×C7semidirect
60. C3×D85C2×C5×C7semidirect
63. C52×C17C2×D3×C7semidirect
66. C3×C7×C17C2×C5×D5semidirect
74. C3×C5×C17C2×C7×D5semidirect
75. C3×C5×C17C22×C5×C7semidirect
83. C5×D3×C7C5×D17semidirect
84. C5×D3×C7D85direct (N × H)
87. C52×C7D3×D17semidirect
92. D85C5×D3×C7direct (N × H)
96. C52×D3C7×D17semidirect
100. C7×C17C5×D3×D5semidirect
102. C3×C5×C7C2×C5×D17semidirect
103. C3×C5×C7C2×D85semidirect
106. D3×C17C5×C7×D5semidirect
109. C5×C17D3×C7×D5semidirect
110. C5×C17C2×C5×D3×C7semidirect
112. C3×C52C2×C7×D17semidirect
123. C3×C17C2×C5×C7×D5semidirect
129. D3×C7C5×D85direct (N × H)
131. C5×C7C5×D3×D17semidirect
132. C5×C7D3×D85direct (N × H)
141. C5×D3C5×C7×D17semidirect
142. C5×D3C7×D85direct (N × H)
144. C52D3×C7×D17semidirect
145. C3×C7C2×C5×D85semidirect
148. C17C5×D3×C7×D5semidirect
150. C3×C5C2×C7×D85semidirect
151. C3×C5C2×C5×C7×D17semidirect
163. C7C5×D3×D85direct (N × H)
166. D3C5×C7×D85direct (N × H)
168. C5C5×D3×C7×D17semidirect
169. C5D3×C7×D85direct (N × H)
171. C3C2×C5×C7×D85semidirect

Maximal subgroups

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

subgroupindex
C3×C5×C7×D852
C52×D3×C7×C172
C5×C7×D2552
C2×C5×C7×D853
D3×C7×D855
C5×D3×C7×D175
C5×D3×D857
C5×D3×C7×D517