Finite Group Databasebeta

← C7×D13×D105 #50304433

Subgroups — C7×D13×D105 #50304433

Order 38220.

208 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 56 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×C72×D13C211yesmaximal, characteristic, complemented
2C7×C13×D105C211yesmaximal, characteristic, complemented
3C7×D1365C211yesmaximal, characteristic, complemented
4C7×D13×D35—31nomaximal, Hall
5C3×C5×C72×C13C2211yescharacteristic, complemented, Hall
6C7×D13×D21—51nomaximal, Hall
7C7×D455—31no—
8C7×C13×D35—31no—
9C5×C72×D13D311yescharacteristic, complemented
10D13×D105C711yesmaximal, characteristic, direct product factor
11C7×D13×D15—71nomaximal
12C7×D273—51no—
13C7×C13×D21—51no—
14C3×C72×D13D511yescharacteristic, complemented
15C5×C72×C13C2×D311yescharacteristic, complemented, Hall
16C2×C7×D105—131nomaximal, Hall
17D1365C2×C711yescharacteristic, complemented
18C13×D105C2×C711yescharacteristic, complemented
19C7×D195—71no—
20C7×C13×D15—71no—
21C3×C5×C7×D13—23no—
22C3×C5×C7×D13D711yescharacteristic, complemented
23C3×C5×C7×D13C2×C711yescharacteristic, complemented
24C7×D7×D13—151noHall
25C3×C72×C13C2×D511yescharacteristic, complemented, Hall
26D13×D35—31no—
27C7×D5×D13—211no—
28C2×C3×C5×C72—131no—
29C7×D105—131no—
30C7×D105D1311yescharacteristic, direct product factor
31C3×C5×C7×C13—23no—
32C3×C5×C7×C13C2×D711yescharacteristic, complemented
33C3×C5×C7×C13C22×C711yescharacteristic, complemented
34C7×D91—151no—
35C7×C13×D7—151no—
36C72×D13D1511yescharacteristic, complemented
37D13×D21—51no—
38D3×C7×D13—351no—
39C2×C7×D35—391noHall
40D455—31no—
41C13×D35—31no—
42C7×D65—211no—
43C7×D5×C13—211no—
44C5×C7×D13—23no—
45C5×C7×D13D3×C711yescharacteristic, complemented
46C5×C7×D13D2111yescharacteristic, complemented
47D13×D15—71noHall
48C3×C5×C72C2×D1311yescharacteristic, complemented, Hall
49C72×C13C2×D1511yescharacteristic, complemented, Hall
50C2×C7×D21—651noHall
51D273—51no—
52C13×D21—51no—
53C7×D39—351no—
54D3×C7×C13—351no—
55C3×C7×D13—23no—
56C3×C7×D13C7×D511yescharacteristic, complemented
57C3×C7×D13D3511yescharacteristic, complemented
58C2×C5×C72—131no—
59C7×D35—31no—
60C7×D35—391no—
61C5×C7×C13—23no—
62C5×C7×C13C2×D3×C711yescharacteristic, complemented
63C5×C7×C13C2×D2111yescharacteristic, complemented
64C2×D105—131no—
65C2×C7×D15—911no—
66D195—71no—
67C13×D15—71no—
68C3×C5×D13C7×D711yescharacteristic, complemented
69C2×C7×D13—1051no—
70D7×D13—151no—
71C2×C3×C72—131no—
72C7×D21—51no—
73C7×D21—651no—
74C3×C7×C13—23no—
75C3×C7×C13C2×C7×D511yescharacteristic, complemented
76C3×C7×C13C2×D3511yescharacteristic, complemented
77D5×D13—211noHall
78C5×C72D3×D1311yescharacteristic, complemented, Hall
79C2×C3×C5×C7—131no—
80C2×C3×C5×C7—131no—
81C2×C3×C5×C7—263no—
82D105—131no—
83D105C7×D1311yescharacteristic, direct product factor
84C7×D15—71no—
85C7×D15—911no—
86C2×C7×D7—1951noHall
87C3×C5×C13C2×C7×D711yescharacteristic, complemented, Hall
88C2×C7×C13—1051no—
89D91—151no—
90C7×D13—23no—
91C7×D13—1051no—
92C7×D13C7×D1511yescharacteristic, complemented
93C7×D13D10511yescharacteristic, direct product factor
94C13×D7—151no—
95D3×D13—351noHall
96C3×C72D5×D1311yescharacteristic, complemented, Hall
97C2×D35—391no—
98C2×C7×D5—2731no—
99D65—211no—
100C5×D13C7×D2111yescharacteristic, complemented
101D5×C13—211no—
102C3×C5×C7—23no—
103C3×C5×C7D7×D1311yescharacteristic, complemented
104C3×C5×C7C2×C7×D1311yescharacteristic, complemented
105C2×C72—131no—
106C7×D7—151no—
107C7×D7—1951no—
108C7×C13—23no—
109C7×C13C2×C7×D1511yescharacteristic, complemented
110C7×C13C2×D10511yescharacteristic, complemented
111C2×D21—651no—
112C2×D3×C7—4551no—
113D39—351no—
114C3×D13C7×D3511yescharacteristic, complemented
115D3×C13—351no—
116C2×C5×C7—131no—
117C2×C5×C7—131no—
118C2×C5×C7—263no—
119D35—31no—
120D35—391no—
121C7×D5—2731no—
122C7×D5—211no—
123C5×C13C2×C7×D2111yescharacteristic, complemented, Hall
124C2×D15—911noHall
125C2×D13—1051noHall
126C72D13×D1511yescharacteristic, complemented, Sylow
127C2×C3×C7—131no—
128C2×C3×C7—131no—
129C2×C3×C7—263no—
130D21—51no—
131D21—651no—
132D3×C7—351no—
133D3×C7—4551no—
134C3×C13C2×C7×D3511yescharacteristic, complemented, Hall
135C5×C7—23no—
136C5×C7D3×C7×D1311yescharacteristic, complemented
137C5×C7D13×D2111yescharacteristic, complemented
138C2×C3×C5—131no—
139D15—71no—
140D15—911no—
141C22×C7—13651no—
142C2×D7—1951no—
143C2×C13—1051no—
144D13—1051no—
145D13C7×D10511yescharacteristic, direct product factor
146C3×C7—23no—
147C3×C7C7×D5×D1311yescharacteristic, complemented
148C3×C7D13×D3511yescharacteristic, complemented
149C2×D5—2731noHall
150C3×C5C7×D7×D1311yescharacteristic, complemented, Hall
151C2×C7—131no—
152C2×C7—131no—
153C2×C7—263no—
154C2×C7—13651no—
155C2×C7—1051no—
156D7—151no—
157D7—1951no—
158C13C2×C7×D10511yescharacteristic, complemented, Sylow
159C2×D3—4551noHall
160C2×C5—131no—
161D5—2731no—
162D5—211no—
163C7—23no—
164C7C7×D13×D1511yescharacteristic, complemented
165C7D13×D10511yescharacteristic, direct product factor
166C2×C3—131no—
167D3—351no—
168D3—4551no—
169C5C7×D13×D2111yescharacteristic, complemented, Sylow
170C22—13651noSylow
171C3C7×D13×D3511yescharacteristic, complemented, Sylow
172C2—131no—
173C2—13651no—
174C2—1051no—
subgroupG/H
center, hypercenterC7D13×D105
commutator, cosocle, hypocenterC3×C5×C7×C13C22×C7
FrattiniC1G
Fitting, socleC3×C5×C72×C13C22
LCSG ▷ C3×C5×C7×C13
UCSC1 ◁ C7

Complements

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

NH ≅ G/Ntype
1. C3×C5×C72×D13C2semidirect
2. C7×C13×D105C2semidirect
3. C7×D1365C2semidirect
5. C3×C5×C72×C13C22semidirect
9. C5×C72×D13D3semidirect
10. D13×D105C7direct (N × H)
14. C3×C72×D13D5semidirect
15. C5×C72×C13C2×D3semidirect
17. D1365C2×C7semidirect
18. C13×D105C2×C7semidirect
22. C3×C5×C7×D13D7semidirect
23. C3×C5×C7×D13C2×C7semidirect
25. C3×C72×C13C2×D5semidirect
30. C7×D105D13direct (N × H)
32. C3×C5×C7×C13C2×D7semidirect
33. C3×C5×C7×C13C22×C7semidirect
36. C72×D13D15semidirect
45. C5×C7×D13D3×C7semidirect
46. C5×C7×D13D21semidirect
48. C3×C5×C72C2×D13semidirect
49. C72×C13C2×D15semidirect
56. C3×C7×D13C7×D5semidirect
57. C3×C7×D13D35semidirect
62. C5×C7×C13C2×D3×C7semidirect
63. C5×C7×C13C2×D21semidirect
68. C3×C5×D13C7×D7semidirect
75. C3×C7×C13C2×C7×D5semidirect
76. C3×C7×C13C2×D35semidirect
78. C5×C72D3×D13semidirect
83. D105C7×D13direct (N × H)
87. C3×C5×C13C2×C7×D7semidirect
92. C7×D13C7×D15semidirect
93. C7×D13D105direct (N × H)
96. C3×C72D5×D13semidirect
100. C5×D13C7×D21semidirect
103. C3×C5×C7D7×D13semidirect
104. C3×C5×C7C2×C7×D13semidirect
109. C7×C13C2×C7×D15semidirect
110. C7×C13C2×D105semidirect
114. C3×D13C7×D35semidirect
123. C5×C13C2×C7×D21semidirect
126. C72D13×D15semidirect
134. C3×C13C2×C7×D35semidirect
136. C5×C7D3×C7×D13semidirect
137. C5×C7D13×D21semidirect
145. D13C7×D105direct (N × H)
147. C3×C7C7×D5×D13semidirect
148. C3×C7D13×D35semidirect
150. C3×C5C7×D7×D13semidirect
158. C13C2×C7×D105semidirect
164. C7C7×D13×D15semidirect
165. C7D13×D105direct (N × H)
169. C5C7×D13×D21semidirect
171. C3C7×D13×D35semidirect

Maximal subgroups

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

subgroupindex
C3×C5×C72×D132
C7×C13×D1052
C7×D13652
C7×D13×D353
C7×D13×D215
D13×D1057
C7×D13×D157
C2×C7×D10513