Finite Group Databasebeta

← C3×C5×C7×D105 #36348072

Subgroups — C3×C5×C7×D105 #36348072

Order 22050.

336 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 72 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
1C32×C52×C72C211yesmaximal, characteristic, complemented, Hall
2C5×C7×D105C311yesmaximal, characteristic, direct product factor
3C3×C5×C7×D35—31nomaximal
4C3×C7×D105C511yesmaximal, characteristic, direct product factor
5C3×C5×C7×D21—51nomaximal
6C3×C52×C72—21no—
7C3×C52×C72D311yescharacteristic, complemented
8C3×C52×C72C2×C311yescharacteristic, complemented
9C3×C5×D105C711yesmaximal, characteristic, direct product factor
10C3×C5×C7×D15—71nomaximal
11C5×C7×D35—31noHall
12C32×C5×C72—22no—
13C32×C5×C72D511yescharacteristic, complemented
14C32×C5×C72C2×C511yescharacteristic, complemented
15C32×C52×C7—23no—
16C32×C52×C7D711yescharacteristic, complemented
17C32×C52×C7C2×C711yescharacteristic, complemented
18C7×D105C3×C511yescharacteristic, direct product factor
19C5×C7×D21—51no—
20C3×C7×D35—31no—
21C3×C5×C7×D7—151no—
22C52×C72C3×D311yescharacteristic, complemented, Hall
23C5×D105C3×C711yescharacteristic, direct product factor
24C5×C7×D15—71no—
25C3×C5×D35—31no—
26C3×C5×C7×D5—211no—
27C3×C7×D21—51noHall
28C3×C5×C72—24no—
29C3×C5×C72—22no—
30C3×C5×C72—22no—
31C3×C5×C72—21no—
32C3×C5×C72—21no—
33C3×C5×C72C5×D311yescharacteristic, complemented
34C3×C5×C72C3×D511yescharacteristic, complemented
35C3×C5×C72D1511yescharacteristic, complemented
36C3×C5×C72C2×C3×C511yescharacteristic, complemented
37C3×D105C5×C711yescharacteristic, direct product factor
38C3×C7×D15—71no—
39C3×C5×D21—51no—
40C3×C5×D3×C7—351no—
41C3×C52×C7—26no—
42C3×C52×C7—21no—
43C3×C52×C7—21no—
44C3×C52×C7—23no—
45C3×C52×C7—23no—
46C3×C52×C7D3×C711yescharacteristic, complemented
47C3×C52×C7C3×D711yescharacteristic, complemented
48C3×C52×C7D2111yescharacteristic, complemented
49C3×C52×C7C2×C3×C711yescharacteristic, complemented
50C7×D35—31no—
51C5×C7×D7—151no—
52C3×C5×D15—71noHall
53C32×C72C5×D511yescharacteristic, complemented, Hall
54C5×D35—31no—
55C5×C7×D5—211no—
56C32×C5×C7—212no—
57C32×C5×C7—23no—
58C32×C5×C7—23no—
59C32×C5×C7—22no—
60C32×C5×C7—22no—
61C32×C5×C7C7×D511yescharacteristic, complemented
62C32×C5×C7C5×D711yescharacteristic, complemented
63C32×C5×C7D3511yescharacteristic, complemented
64C32×C5×C7C2×C5×C711yescharacteristic, complemented
65C7×D21—51no—
66C3×C7×D7—151no—
67C5×C72—22no—
68C5×C72C3×C5×D311yescharacteristic, complemented
69C5×C72C3×D1511yescharacteristic, complemented
70C32×C52C7×D711yescharacteristic, complemented, Hall
71C2×C3×C5×C7—1051no—
72D105C3×C5×C711yescharacteristic, direct product factor
73C7×D15—71no—
74C5×D21—51no—
75C5×D3×C7—351no—
76C3×D35—31no—
77C3×C7×D5—211no—
78C3×C5×D7—151no—
79C52×C7—23no—
80C52×C7C3×D3×C711yescharacteristic, complemented
81C52×C7C3×D2111yescharacteristic, complemented
82C5×D15—71no—
83C3×C5×D5—211no—
84C3×C72—21no—
85C3×C72C3×C5×D511yescharacteristic, complemented
86C3×C72C5×D1511yescharacteristic, complemented
87C3×D21—51no—
88C3×D3×C7—351no—
89C3×C5×C7—224no—
90C3×C5×C7—24no—
91C3×C5×C7—24no—
92C3×C5×C7—26no—
93C3×C5×C7—26no—
94C3×C5×C7—212no—
95C3×C5×C7—212no—
96C3×C5×C7—21no—
97C3×C5×C7—21no—
98C3×C5×C7—21no—
99C3×C5×C7—21no—
100C3×C5×C7—22no—
101C3×C5×C7—22no—
102C3×C5×C7—22no—
103C3×C5×C7—22no—
104C3×C5×C7—23no—
105C3×C5×C7—23no—
106C3×C5×C7—23no—
107C3×C5×C7—23no—
108C3×C5×C7C3×C5×D711yescharacteristic, complemented
109C3×C5×C7C3×C7×D511yescharacteristic, complemented
110C3×C5×C7C3×D3511yescharacteristic, complemented
111C3×C5×C7C5×D3×C711yescharacteristic, complemented
112C3×C5×C7C5×D2111yescharacteristic, complemented
113C3×C5×C7C7×D1511yescharacteristic, complemented
114C3×C5×C7D10511yescharacteristic, direct product factor
115C3×C5×C7C2×C3×C5×C711yescharacteristic, complemented
116C7×D7—151noHall
117C3×D15—71no—
118C3×C5×D3—351no—
119C3×C52—21no—
120C3×C52C3×C7×D711yescharacteristic, complemented
121C3×C52C7×D2111yescharacteristic, complemented
122C2×C5×C7—1051no—
123D35—31no—
124C5×D7—151no—
125C7×D5—211no—
126C32×C7—23no—
127C32×C7C5×C7×D511yescharacteristic, complemented
128C32×C7C5×D3511yescharacteristic, complemented
129C5×D5—211noHall
130C72C3×C5×D1511yescharacteristic, complemented, Sylow
131C32×C5—22no—
132C32×C5C5×C7×D711yescharacteristic, complemented
133C32×C5C7×D3511yescharacteristic, complemented
134C2×C3×C7—1051no—
135D21—51no—
136C3×D7—151no—
137D3×C7—351no—
138C5×C7—212no—
139C5×C7—22no—
140C5×C7—22no—
141C5×C7—23no—
142C5×C7—23no—
143C5×C7C3×C5×D3×C711yescharacteristic, complemented
144C5×C7C3×C5×D2111yescharacteristic, complemented
145C5×C7C3×C7×D1511yescharacteristic, complemented
146C5×C7C3×D10511yescharacteristic, direct product factor
147C2×C3×C5—1051no—
148D15—71no—
149C3×D5—211no—
150C5×D3—351no—
151C52C3×C7×D2111yescharacteristic, complemented, Sylow
152C3×C7—26no—
153C3×C7—21no—
154C3×C7—21no—
155C3×C7—23no—
156C3×C7—23no—
157C3×C7C3×C5×C7×D511yescharacteristic, complemented
158C3×C7C3×C5×D3511yescharacteristic, complemented
159C3×C7C5×C7×D1511yescharacteristic, complemented
160C3×C7C5×D10511yescharacteristic, direct product factor
161C3×D3—351noHall
162C3×C5—24no—
163C3×C5—21no—
164C3×C5—21no—
165C3×C5—22no—
166C3×C5—22no—
167C3×C5C3×C5×C7×D711yescharacteristic, complemented
168C3×C5C3×C7×D3511yescharacteristic, complemented
169C3×C5C5×C7×D2111yescharacteristic, complemented
170C3×C5C7×D10511yescharacteristic, direct product factor
171C2×C7—1051no—
172D7—151no—
173C2×C5—1051no—
174D5—211no—
175C32C5×C7×D3511yescharacteristic, complemented, Sylow
176C7—23no—
177C7C3×C5×C7×D1511yescharacteristic, complemented
178C7C3×C5×D10511yescharacteristic, direct product factor
179C2×C3—1051no—
180D3—351no—
181C5—22no—
182C5C3×C5×C7×D2111yescharacteristic, complemented
183C5C3×C7×D10511yescharacteristic, direct product factor
184C3—21no—
185C3C3×C5×C7×D3511yescharacteristic, complemented
186C3C5×C7×D10511yescharacteristic, direct product factor
187C2—1051noSylow
subgroupG/H
center, hypercenterC3×C5×C7D105
commutator, cosocle, hypocenterC3×C5×C7C2×C3×C5×C7
FrattiniC1G
Fitting, socleC32×C52×C72C2
LCSG ▷ C3×C5×C7
UCSC1 ◁ C3×C5×C7

Complements

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

NH ≅ G/Ntype
1. C32×C52×C72C2semidirect
2. C5×C7×D105C3direct (N × H)
4. C3×C7×D105C5direct (N × H)
7. C3×C52×C72D3semidirect
8. C3×C52×C72C2×C3semidirect
9. C3×C5×D105C7direct (N × H)
13. C32×C5×C72D5semidirect
14. C32×C5×C72C2×C5semidirect
16. C32×C52×C7D7semidirect
17. C32×C52×C7C2×C7semidirect
18. C7×D105C3×C5direct (N × H)
22. C52×C72C3×D3semidirect
23. C5×D105C3×C7direct (N × H)
33. C3×C5×C72C5×D3semidirect
34. C3×C5×C72C3×D5semidirect
35. C3×C5×C72D15semidirect
36. C3×C5×C72C2×C3×C5semidirect
37. C3×D105C5×C7direct (N × H)
46. C3×C52×C7D3×C7semidirect
47. C3×C52×C7C3×D7semidirect
48. C3×C52×C7D21semidirect
49. C3×C52×C7C2×C3×C7semidirect
53. C32×C72C5×D5semidirect
61. C32×C5×C7C7×D5semidirect
62. C32×C5×C7C5×D7semidirect
63. C32×C5×C7D35semidirect
64. C32×C5×C7C2×C5×C7semidirect
68. C5×C72C3×C5×D3semidirect
69. C5×C72C3×D15semidirect
70. C32×C52C7×D7semidirect
72. D105C3×C5×C7direct (N × H)
80. C52×C7C3×D3×C7semidirect
81. C52×C7C3×D21semidirect
85. C3×C72C3×C5×D5semidirect
86. C3×C72C5×D15semidirect
108. C3×C5×C7C3×C5×D7semidirect
109. C3×C5×C7C3×C7×D5semidirect
110. C3×C5×C7C3×D35semidirect
111. C3×C5×C7C5×D3×C7semidirect
112. C3×C5×C7C5×D21semidirect
113. C3×C5×C7C7×D15semidirect
114. C3×C5×C7D105direct (N × H)
115. C3×C5×C7C2×C3×C5×C7semidirect
120. C3×C52C3×C7×D7semidirect
121. C3×C52C7×D21semidirect
127. C32×C7C5×C7×D5semidirect
128. C32×C7C5×D35semidirect
130. C72C3×C5×D15semidirect
132. C32×C5C5×C7×D7semidirect
133. C32×C5C7×D35semidirect
143. C5×C7C3×C5×D3×C7semidirect
144. C5×C7C3×C5×D21semidirect
145. C5×C7C3×C7×D15semidirect
146. C5×C7C3×D105direct (N × H)
151. C52C3×C7×D21semidirect
157. C3×C7C3×C5×C7×D5semidirect
158. C3×C7C3×C5×D35semidirect
159. C3×C7C5×C7×D15semidirect
160. C3×C7C5×D105direct (N × H)
167. C3×C5C3×C5×C7×D7semidirect
168. C3×C5C3×C7×D35semidirect
169. C3×C5C5×C7×D21semidirect
170. C3×C5C7×D105direct (N × H)
175. C32C5×C7×D35semidirect
177. C7C3×C5×C7×D15semidirect
178. C7C3×C5×D105direct (N × H)
182. C5C3×C5×C7×D21semidirect
183. C5C3×C7×D105direct (N × H)
185. C3C3×C5×C7×D35semidirect
186. C3C5×C7×D105direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C52×C722
C5×C7×D1053
C3×C5×C7×D353
C3×C7×D1055
C3×C5×C7×D215
C3×C5×D1057
C3×C5×C7×D157