Finite Group Databasebeta

← C5×D5×C17×D21 #49087941

Subgroups — C5×D5×C17×D21 #49087941

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
2C52×C17×D21C211yesmaximal, characteristic, complemented
3C5×C17×D105C211yesmaximal, characteristic, complemented
4C5×D5×D7×C17—31nomaximal, Hall
5C3×C52×C7×C17C2211yescharacteristic, complemented, Hall
6C2×C5×C17×D21—51nomaximal
7D5×C17×D21C511yesmaximal, characteristic, direct product factor
8C5×C17×D35—31no—
9C5×C7×D5×C17D311yescharacteristic, complemented
10C52×D7×C17—31no—
11C5×D3×D5×C17—71nomaximal, Hall
12C17×D105C2×C511yescharacteristic, complemented
13C5×C17×D21—22no—
14C5×C17×D21—51no—
15C5×C17×D21D511yescharacteristic, direct product factor
16C5×C17×D21C2×C511yescharacteristic, complemented
17C3×C7×D5×C17C2×C511yescharacteristic, complemented
18C2×C3×C5×C7×C17—51no—
19C52×C7×C17C2×D311yescharacteristic, complemented, Hall
20C5×C17×D15—71no—
21C52×D3×C17—71no—
22C3×C5×D5×C17D711yescharacteristic, complemented
23C2×C5×D7×C17—151no—
24D5×D7×C17—31no—
25C5×D5×D21C1711yesmaximal, characteristic, direct product factor, Hall
26C3×C5×C7×C17—22no—
27C3×C5×C7×C17C2×D511yescharacteristic, complemented
28C3×C5×C7×C17C22×C511yescharacteristic, complemented
29C2×C5×D5×C17—211noHall
30C2×C17×D21—51noHall
31C3×C52×C17C2×D711yescharacteristic, complemented, Hall
32C2×C5×C7×C17—51no—
33C17×D35—31no—
34C7×D5×C17C5×D311yescharacteristic, complemented
35C5×D7×C17—31no—
36C5×D7×C17—31no—
37C5×D7×C17—62no—
38C5×D7×C17—151no—
39C5×D105C2×C1711yescharacteristic, complemented
40C52×D21C2×C1711yescharacteristic, complemented
41C3×C5×C7×D5C2×C1711yescharacteristic, complemented
42C2×C5×D3×C17—351no—
43D3×D5×C17—71no—
44C2×C52×C17—211no—
45C5×D5×C17—211no—
46C5×D5×C17D2111yescharacteristic, direct product factor
47C2×C3×C7×C17—51no—
48C17×D21—51no—
49C17×D21C5×D511yescharacteristic, direct product factor
50C5×D5×D7—31noHall
51C5×C7×C17—22no—
52C5×C7×C17D3×D511yescharacteristic, complemented
53C5×C7×C17C2×C5×D311yescharacteristic, complemented
54C3×C52×C7C22×C1711yescharacteristic, complemented, Hall
55C2×C3×C5×C17—51no—
56C17×D15—71no—
57C5×D3×C17—71no—
58C5×D3×C17—71no—
59C5×D3×C17—142no—
60C5×D3×C17—351no—
61C3×D5×C17C5×D711yescharacteristic, complemented
62C2×D7×C17—151noHall
63C52×C17C2×D2111yescharacteristic, complemented, Hall
64C2×C5×D21—51no—
65D5×D21C5×C1711yescharacteristic, direct product factor
66C3×C7×C17C2×C5×D511yescharacteristic, complemented, Hall
67C5×D35—31no—
68C5×C7×D5D3×C1711yescharacteristic, complemented
69C52×D7—31no—
70C22×C5×C17—1051no—
71C2×D5×C17—211no—
72C5×D3×D5—71noHall
73C3×C5×C17—22no—
74C3×C5×C17D5×D711yescharacteristic, complemented
75C3×C5×C17C2×C5×D711yescharacteristic, complemented
76C2×C7×C17—51no—
77D7×C17—31no—
78D7×C17—151no—
79C2×C3×C5×C7—51no—
80D105C2×C5×C1711yescharacteristic, complemented
81C5×D21—22no—
82C5×D21—51no—
83C5×D21D5×C1711yescharacteristic, direct product factor
84C5×D21C2×C5×C1711yescharacteristic, complemented
85C3×C7×D5C2×C5×C1711yescharacteristic, complemented
86C2×D3×C17—351noHall
87C52×C7C2×D3×C1711yescharacteristic, complemented, Hall
88C2×C5×C17—51no—
89C2×C5×C17—211no—
90C2×C5×C17—211no—
91C2×C5×C17—422no—
92C2×C5×C17—1051no—
93D5×C17—211no—
94D5×C17C5×D2111yescharacteristic, direct product factor
95C5×D15—71no—
96C52×D3—71no—
97C3×C5×D5D7×C1711yescharacteristic, complemented
98C2×C5×D7—151no—
99D5×D7—31no—
100C7×C17C5×D3×D511yescharacteristic, complemented, Hall
101C3×C5×C7—22no—
102C3×C5×C7C2×D5×C1711yescharacteristic, complemented
103C3×C5×C7C22×C5×C1711yescharacteristic, complemented
104C2×C3×C17—51no—
105D3×C17—71no—
106D3×C17—351no—
107C2×C5×D5—211noHall
108C5×C17—22no—
109C5×C17D5×D2111yescharacteristic, direct product factor
110C5×C17C2×C5×D2111yescharacteristic, complemented
111C2×D21—51noHall
112C3×C52C2×D7×C1711yescharacteristic, complemented, Hall
113C2×C5×C7—51no—
114D35—31no—
115C5×D7—31no—
116C5×D7—31no—
117C5×D7—62no—
118C5×D7—151no—
119C7×D5C5×D3×C1711yescharacteristic, complemented
120C22×C17—1051noHall
121C2×C5×D3—351no—
122D3×D5—71no—
123C3×C17C5×D5×D711yescharacteristic, complemented, Hall
124C2×C52—211no—
125C5×D5—211no—
126C5×D5C17×D2111yescharacteristic, direct product factor
127C2×C3×C7—51no—
128D21—51no—
129D21C5×D5×C1711yescharacteristic, direct product factor
130C5×C7—22no—
131C5×C7D3×D5×C1711yescharacteristic, complemented
132C5×C7C2×C5×D3×C1711yescharacteristic, complemented
133C2×C17—51no—
134C2×C17—211no—
135C2×C17—1051no—
136C2×C3×C5—51no—
137D15—71no—
138C3×D5C5×D7×C1711yescharacteristic, complemented
139C5×D3—71no—
140C5×D3—71no—
141C5×D3—142no—
142C5×D3—351no—
143C2×D7—151noHall
144C52C2×C17×D2111yescharacteristic, complemented, Sylow
145C3×C7C2×C5×D5×C1711yescharacteristic, complemented, Hall
146C22×C5—1051no—
147C2×D5—211no—
148C17C5×D5×D2111yescharacteristic, direct product factor, Sylow
149C3×C5—22no—
150C3×C5D5×D7×C1711yescharacteristic, complemented
151C3×C5C2×C5×D7×C1711yescharacteristic, complemented
152C2×C7—51no—
153D7—31no—
154D7—151no—
155C2×D3—351noHall
156C2×C5—51no—
157C2×C5—211no—
158C2×C5—211no—
159C2×C5—422no—
160C2×C5—1051no—
161D5—211no—
162D5C5×C17×D2111yescharacteristic, direct product factor
163C7C5×D3×D5×C1711yescharacteristic, complemented, Sylow
164C2×C3—51no—
165D3—71no—
166D3—351no—
167C5—22no—
168C5D5×C17×D2111yescharacteristic, direct product factor
169C5C2×C5×C17×D2111yescharacteristic, complemented
170C22—1051noSylow
171C3C5×D5×D7×C1711yescharacteristic, complemented, Sylow
172C2—51no—
173C2—211no—
174C2—1051no—
subgroupG/H
center, hypercenterC5×C17D5×D21
commutator, cosocle, hypocenterC3×C5×C7C22×C5×C17
FrattiniC1G
Fitting, socleC3×C52×C7×C17C22
LCSG ▷ C3×C5×C7
UCSC1 ◁ C5×C17

Complements

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

NH ≅ G/Ntype
1. C3×C5×C7×D5×C17C2semidirect
2. C52×C17×D21C2semidirect
3. C5×C17×D105C2semidirect
5. C3×C52×C7×C17C22semidirect
7. D5×C17×D21C5direct (N × H)
9. C5×C7×D5×C17D3semidirect
12. C17×D105C2×C5semidirect
15. C5×C17×D21D5direct (N × H)
16. C5×C17×D21C2×C5semidirect
17. C3×C7×D5×C17C2×C5semidirect
19. C52×C7×C17C2×D3semidirect
22. C3×C5×D5×C17D7semidirect
25. C5×D5×D21C17direct (N × H)
27. C3×C5×C7×C17C2×D5semidirect
28. C3×C5×C7×C17C22×C5semidirect
31. C3×C52×C17C2×D7semidirect
34. C7×D5×C17C5×D3semidirect
39. C5×D105C2×C17semidirect
40. C52×D21C2×C17semidirect
41. C3×C5×C7×D5C2×C17semidirect
46. C5×D5×C17D21direct (N × H)
49. C17×D21C5×D5direct (N × H)
52. C5×C7×C17D3×D5semidirect
53. C5×C7×C17C2×C5×D3semidirect
54. C3×C52×C7C22×C17semidirect
61. C3×D5×C17C5×D7semidirect
63. C52×C17C2×D21semidirect
65. D5×D21C5×C17direct (N × H)
66. C3×C7×C17C2×C5×D5semidirect
68. C5×C7×D5D3×C17semidirect
74. C3×C5×C17D5×D7semidirect
75. C3×C5×C17C2×C5×D7semidirect
80. D105C2×C5×C17semidirect
83. C5×D21D5×C17direct (N × H)
84. C5×D21C2×C5×C17semidirect
85. C3×C7×D5C2×C5×C17semidirect
87. C52×C7C2×D3×C17semidirect
94. D5×C17C5×D21direct (N × H)
97. C3×C5×D5D7×C17semidirect
100. C7×C17C5×D3×D5semidirect
102. C3×C5×C7C2×D5×C17semidirect
103. C3×C5×C7C22×C5×C17semidirect
109. C5×C17D5×D21direct (N × H)
110. C5×C17C2×C5×D21semidirect
112. C3×C52C2×D7×C17semidirect
119. C7×D5C5×D3×C17semidirect
123. C3×C17C5×D5×D7semidirect
126. C5×D5C17×D21direct (N × H)
129. D21C5×D5×C17direct (N × H)
131. C5×C7D3×D5×C17semidirect
132. C5×C7C2×C5×D3×C17semidirect
138. C3×D5C5×D7×C17semidirect
144. C52C2×C17×D21semidirect
145. C3×C7C2×C5×D5×C17semidirect
148. C17C5×D5×D21direct (N × H)
150. C3×C5D5×D7×C17semidirect
151. C3×C5C2×C5×D7×C17semidirect
162. D5C5×C17×D21direct (N × H)
163. C7C5×D3×D5×C17semidirect
168. C5D5×C17×D21direct (N × H)
169. C5C2×C5×C17×D21semidirect
171. C3C5×D5×D7×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
C52×C17×D212
C5×C17×D1052
C5×D5×D7×C173
C2×C5×C17×D215
D5×C17×D215
C5×D3×D5×C177
C5×D5×D2117