Finite Group Databasebeta

← C3×C5×C7×D7×D13 #50304341

Subgroups — C3×C5×C7×D7×D13 #50304341

Order 38220.

208 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 80 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
2C3×C5×C7×C13×D7C211yesmaximal, characteristic, complemented
3C3×C5×C7×D91C211yesmaximal, characteristic, complemented
4C5×C7×D7×D13C311yesmaximal, characteristic, direct product factor, Hall
5C3×C5×C72×C13C2211yescharacteristic, complemented, Hall
6C3×C7×D7×D13C511yesmaximal, characteristic, direct product factor, Hall
7C5×C7×D91C2×C311yescharacteristic, complemented
8C5×C7×C13×D7C2×C311yescharacteristic, complemented
9C5×C72×D13C2×C311yescharacteristic, complemented
10C2×C3×C5×C7×D13—71nomaximal
11C3×C5×D7×D13C711yesmaximal, characteristic, direct product factor
12C3×C7×D91C2×C511yescharacteristic, complemented
13C3×C7×C13×D7C2×C511yescharacteristic, complemented
14C3×C72×D13C2×C511yescharacteristic, complemented
15C5×C72×C13C22×C311yescharacteristic, complemented, Hall
16C2×C3×C5×C7×D7—131nomaximal, Hall
17C3×C5×D91C2×C711yescharacteristic, complemented
18C3×C5×C13×D7C2×C711yescharacteristic, complemented
19C3×C5×C7×D13—23no—
20C3×C5×C7×D13—71no—
21C3×C5×C7×D13D711yescharacteristic, direct product factor
22C3×C5×C7×D13C2×C711yescharacteristic, complemented
23C2×C3×C5×C7×C13—71no—
24C7×D7×D13C3×C511yescharacteristic, direct product factor, Hall
25C3×C72×C13C22×C511yescharacteristic, complemented, Hall
26C2×C5×C7×D13—71no—
27C5×D7×D13C3×C711yescharacteristic, direct product factor
28C2×C3×C5×C72—131no—
29C3×C5×C7×D7—131no—
30C3×C5×C7×D7D1311yescharacteristic, direct product factor
31C3×C5×C7×C13—23no—
32C3×C5×C7×C13C2×D711yescharacteristic, complemented
33C3×C5×C7×C13C22×C711yescharacteristic, complemented
34C7×D91C2×C3×C511yescharacteristic, complemented
35C7×C13×D7C2×C3×C511yescharacteristic, complemented
36C72×D13C2×C3×C511yescharacteristic, complemented
37C2×C3×C7×D13—71no—
38C3×D7×D13C5×C711yescharacteristic, direct product factor
39C2×C5×C7×D7—131noHall
40C2×C5×C7×C13—71no—
41C5×D91C2×C3×C711yescharacteristic, complemented
42C5×C13×D7C2×C3×C711yescharacteristic, complemented
43C5×C7×D13—23no—
44C5×C7×D13—71no—
45C5×C7×D13C3×D711yescharacteristic, direct product factor
46C5×C7×D13C2×C3×C711yescharacteristic, complemented
47C2×C3×C5×D13—71noHall
48C3×C5×C72C2×D1311yescharacteristic, complemented, Hall
49C72×C13C22×C3×C511yescharacteristic, complemented, Hall
50C2×C3×C7×D7—131noHall
51C2×C3×C7×C13—71no—
52C3×D91C2×C5×C711yescharacteristic, complemented
53C3×C13×D7C2×C5×C711yescharacteristic, complemented
54C3×C7×D13—23no—
55C3×C7×D13—71no—
56C3×C7×D13C5×D711yescharacteristic, direct product factor
57C3×C7×D13C2×C5×C711yescharacteristic, complemented
58C2×C5×C72—131no—
59C5×C7×D7—131no—
60C5×C7×D7C3×D1311yescharacteristic, direct product factor
61C5×C7×C13—23no—
62C5×C7×C13C2×C3×D711yescharacteristic, complemented
63C5×C7×C13C22×C3×C711yescharacteristic, complemented
64C22×C3×C5×C7—911no—
65C2×C3×C5×D7—131no—
66C2×C3×C5×C13—71no—
67C3×C5×D13—71no—
68C3×C5×D13C7×D711yescharacteristic, direct product factor
69C2×C7×D13—71no—
70D7×D13C3×C5×C711yescharacteristic, direct product factor
71C2×C3×C72—131no—
72C3×C7×D7—131no—
73C3×C7×D7C5×D1311yescharacteristic, direct product factor
74C3×C7×C13—23no—
75C3×C7×C13C2×C5×D711yescharacteristic, complemented
76C3×C7×C13C22×C5×C711yescharacteristic, complemented
77C2×C5×D13—71noHall
78C5×C72C2×C3×D1311yescharacteristic, complemented, Hall
79C2×C3×C5×C7—71no—
80C2×C3×C5×C7—131no—
81C2×C3×C5×C7—131no—
82C2×C3×C5×C7—263no—
83C2×C3×C5×C7—911no—
84C3×C5×D7—131no—
85C3×C5×D7C7×D1311yescharacteristic, direct product factor
86C2×C7×D7—131noHall
87C3×C5×C13C2×C7×D711yescharacteristic, complemented, Hall
88C2×C7×C13—71no—
89D91C2×C3×C5×C711yescharacteristic, complemented
90C7×D13—23no—
91C7×D13—71no—
92C7×D13C3×C5×D711yescharacteristic, direct product factor
93C7×D13C2×C3×C5×C711yescharacteristic, complemented
94C13×D7C2×C3×C5×C711yescharacteristic, complemented
95C2×C3×D13—71noHall
96C3×C72C2×C5×D1311yescharacteristic, complemented, Hall
97C22×C5×C7—911no—
98C2×C5×D7—131no—
99C2×C5×C13—71no—
100C5×D13—71no—
101C5×D13C3×C7×D711yescharacteristic, direct product factor
102C3×C5×C7—23no—
103C3×C5×C7D7×D1311yescharacteristic, direct product factor
104C3×C5×C7C2×C7×D1311yescharacteristic, complemented
105C2×C72—131no—
106C7×D7—131no—
107C7×D7C3×C5×D1311yescharacteristic, direct product factor
108C7×C13—23no—
109C7×C13C2×C3×C5×D711yescharacteristic, complemented
110C7×C13C22×C3×C5×C711yescharacteristic, complemented
111C22×C3×C7—911no—
112C2×C3×D7—131no—
113C2×C3×C13—71no—
114C3×D13—71no—
115C3×D13C5×C7×D711yescharacteristic, direct product factor
116C2×C5×C7—71no—
117C2×C5×C7—131no—
118C2×C5×C7—131no—
119C2×C5×C7—263no—
120C2×C5×C7—911no—
121C5×D7—131no—
122C5×D7C3×C7×D1311yescharacteristic, direct product factor
123C5×C13C2×C3×C7×D711yescharacteristic, complemented, Hall
124C22×C3×C5—911noHall
125C2×D13—71noHall
126C72C2×C3×C5×D1311yescharacteristic, complemented, Sylow
127C2×C3×C7—71no—
128C2×C3×C7—131no—
129C2×C3×C7—131no—
130C2×C3×C7—263no—
131C2×C3×C7—911no—
132C3×D7—131no—
133C3×D7C5×C7×D1311yescharacteristic, direct product factor
134C3×C13C2×C5×C7×D711yescharacteristic, complemented, Hall
135C5×C7—23no—
136C5×C7C3×D7×D1311yescharacteristic, direct product factor
137C5×C7C2×C3×C7×D1311yescharacteristic, complemented
138C2×C3×C5—71no—
139C2×C3×C5—131no—
140C2×C3×C5—911no—
141C22×C7—911no—
142C2×D7—131no—
143C2×C13—71no—
144D13—71no—
145D13C3×C5×C7×D711yescharacteristic, direct product factor
146C3×C7—23no—
147C3×C7C5×D7×D1311yescharacteristic, direct product factor
148C3×C7C2×C5×C7×D1311yescharacteristic, complemented
149C22×C5—911noHall
150C3×C5C7×D7×D1311yescharacteristic, direct product factor, Hall
151C2×C7—71no—
152C2×C7—131no—
153C2×C7—131no—
154C2×C7—263no—
155C2×C7—911no—
156D7—131no—
157D7C3×C5×C7×D1311yescharacteristic, direct product factor
158C13C2×C3×C5×C7×D711yescharacteristic, complemented, Sylow
159C22×C3—911noHall
160C2×C5—71no—
161C2×C5—131no—
162C2×C5—911no—
163C7—23no—
164C7C3×C5×D7×D1311yescharacteristic, direct product factor
165C7C2×C3×C5×C7×D1311yescharacteristic, complemented
166C2×C3—71no—
167C2×C3—131no—
168C2×C3—911no—
169C5C3×C7×D7×D1311yescharacteristic, direct product factor, Sylow
170C22—911noSylow
171C3C5×C7×D7×D1311yescharacteristic, direct product factor, Sylow
172C2—71no—
173C2—131no—
174C2—911no—
subgroupG/H
center, hypercenterC3×C5×C7D7×D13
commutator, cosocle, hypocenterC7×C13C22×C3×C5×C7
FrattiniC1G
Fitting, socleC3×C5×C72×C13C22
LCSG ▷ C7×C13
UCSC1 ◁ C3×C5×C7

Complements

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

NH ≅ G/Ntype
1. C3×C5×C72×D13C2semidirect
2. C3×C5×C7×C13×D7C2semidirect
3. C3×C5×C7×D91C2semidirect
4. C5×C7×D7×D13C3direct (N × H)
5. C3×C5×C72×C13C22semidirect
6. C3×C7×D7×D13C5direct (N × H)
7. C5×C7×D91C2×C3semidirect
8. C5×C7×C13×D7C2×C3semidirect
9. C5×C72×D13C2×C3semidirect
11. C3×C5×D7×D13C7direct (N × H)
12. C3×C7×D91C2×C5semidirect
13. C3×C7×C13×D7C2×C5semidirect
14. C3×C72×D13C2×C5semidirect
15. C5×C72×C13C22×C3semidirect
17. C3×C5×D91C2×C7semidirect
18. C3×C5×C13×D7C2×C7semidirect
21. C3×C5×C7×D13D7direct (N × H)
22. C3×C5×C7×D13C2×C7semidirect
24. C7×D7×D13C3×C5direct (N × H)
25. C3×C72×C13C22×C5semidirect
27. C5×D7×D13C3×C7direct (N × H)
30. C3×C5×C7×D7D13direct (N × H)
32. C3×C5×C7×C13C2×D7semidirect
33. C3×C5×C7×C13C22×C7semidirect
34. C7×D91C2×C3×C5semidirect
35. C7×C13×D7C2×C3×C5semidirect
36. C72×D13C2×C3×C5semidirect
38. C3×D7×D13C5×C7direct (N × H)
41. C5×D91C2×C3×C7semidirect
42. C5×C13×D7C2×C3×C7semidirect
45. C5×C7×D13C3×D7direct (N × H)
46. C5×C7×D13C2×C3×C7semidirect
48. C3×C5×C72C2×D13semidirect
49. C72×C13C22×C3×C5semidirect
52. C3×D91C2×C5×C7semidirect
53. C3×C13×D7C2×C5×C7semidirect
56. C3×C7×D13C5×D7direct (N × H)
57. C3×C7×D13C2×C5×C7semidirect
60. C5×C7×D7C3×D13direct (N × H)
62. C5×C7×C13C2×C3×D7semidirect
63. C5×C7×C13C22×C3×C7semidirect
68. C3×C5×D13C7×D7direct (N × H)
70. D7×D13C3×C5×C7direct (N × H)
73. C3×C7×D7C5×D13direct (N × H)
75. C3×C7×C13C2×C5×D7semidirect
76. C3×C7×C13C22×C5×C7semidirect
78. C5×C72C2×C3×D13semidirect
85. C3×C5×D7C7×D13direct (N × H)
87. C3×C5×C13C2×C7×D7semidirect
89. D91C2×C3×C5×C7semidirect
92. C7×D13C3×C5×D7direct (N × H)
93. C7×D13C2×C3×C5×C7semidirect
94. C13×D7C2×C3×C5×C7semidirect
96. C3×C72C2×C5×D13semidirect
101. C5×D13C3×C7×D7direct (N × H)
103. C3×C5×C7D7×D13direct (N × H)
104. C3×C5×C7C2×C7×D13semidirect
107. C7×D7C3×C5×D13direct (N × H)
109. C7×C13C2×C3×C5×D7semidirect
110. C7×C13C22×C3×C5×C7semidirect
115. C3×D13C5×C7×D7direct (N × H)
122. C5×D7C3×C7×D13direct (N × H)
123. C5×C13C2×C3×C7×D7semidirect
126. C72C2×C3×C5×D13semidirect
133. C3×D7C5×C7×D13direct (N × H)
134. C3×C13C2×C5×C7×D7semidirect
136. C5×C7C3×D7×D13direct (N × H)
137. C5×C7C2×C3×C7×D13semidirect
145. D13C3×C5×C7×D7direct (N × H)
147. C3×C7C5×D7×D13direct (N × H)
148. C3×C7C2×C5×C7×D13semidirect
150. C3×C5C7×D7×D13direct (N × H)
157. D7C3×C5×C7×D13direct (N × H)
158. C13C2×C3×C5×C7×D7semidirect
164. C7C3×C5×D7×D13direct (N × H)
165. C7C2×C3×C5×C7×D13semidirect
169. C5C3×C7×D7×D13direct (N × H)
171. C3C5×C7×D7×D13direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×C72×D132
C3×C5×C7×C13×D72
C3×C5×C7×D912
C5×C7×D7×D133
C3×C7×D7×D135
C2×C3×C5×C7×D137
C3×C5×D7×D137
C2×C3×C5×C7×D713