Finite Group Databasebeta

← C3×C7×D5×C13×D7 #50304370

Subgroups — C3×C7×D5×C13×D7 #50304370

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×C7×C13×D7C211yesmaximal, characteristic, complemented
2C3×C72×D5×C13C211yesmaximal, characteristic, complemented
3C3×C7×C13×D35C211yesmaximal, characteristic, complemented
4C7×D5×C13×D7C311yesmaximal, characteristic, direct product factor, Hall
5C3×C5×C72×C13C2211yescharacteristic, complemented, Hall
6C2×C3×C7×C13×D7—51nomaximal, Hall
7C7×C13×D35C2×C311yescharacteristic, complemented
8C72×D5×C13C2×C311yescharacteristic, complemented
9C5×C7×C13×D7C2×C311yescharacteristic, complemented
10C2×C3×C7×D5×C13—71nomaximal
11C3×D5×C13×D7C711yesmaximal, characteristic, direct product factor
12C3×C7×C13×D7—51no—
13C3×C7×C13×D7D511yescharacteristic, direct product factor
14C2×C3×C72×C13—51no—
15C5×C72×C13C22×C311yescharacteristic, complemented, Hall
16C3×C7×D5×D7C1311yesmaximal, characteristic, direct product factor, Hall
17C3×C13×D35C2×C711yescharacteristic, complemented
18C3×C7×D5×C13—23no—
19C3×C7×D5×C13—71no—
20C3×C7×D5×C13D711yescharacteristic, direct product factor
21C3×C7×D5×C13C2×C711yescharacteristic, complemented
22C3×C5×C13×D7C2×C711yescharacteristic, complemented
23C2×C3×C5×C7×C13—71no—
24C2×C7×C13×D7—51noHall
25C3×C72×C13C2×D511yescharacteristic, complemented, Hall
26C2×C7×D5×C13—71no—
27D5×C13×D7C3×C711yescharacteristic, direct product factor
28C3×C7×D35C2×C1311yescharacteristic, complemented
29C3×C72×D5C2×C1311yescharacteristic, complemented
30C3×C5×C7×D7C2×C1311yescharacteristic, complemented
31C3×C5×C7×C13—23no—
32C3×C5×C7×C13C2×D711yescharacteristic, complemented
33C3×C5×C7×C13C22×C711yescharacteristic, complemented
34C2×C72×C13—51no—
35C7×C13×D7—51no—
36C7×C13×D7C3×D511yescharacteristic, direct product factor
37C22×C3×C7×C13—351no—
38C2×C3×C13×D7—51no—
39C7×D5×D7C3×C1311yescharacteristic, direct product factor, Hall
40C2×C5×C7×C13—71no—
41C13×D35C2×C3×C711yescharacteristic, complemented
42C7×D5×C13—23no—
43C7×D5×C13—71no—
44C7×D5×C13C3×D711yescharacteristic, direct product factor
45C7×D5×C13C2×C3×C711yescharacteristic, complemented
46C5×C13×D7C2×C3×C711yescharacteristic, complemented
47C2×C3×D5×C13—71noHall
48C3×C5×C72C22×C1311yescharacteristic, complemented, Hall
49C72×C13C2×C3×D511yescharacteristic, complemented, Hall
50C2×C3×C7×D7—51noHall
51C2×C3×C7×C13—51no—
52C2×C3×C7×C13—51no—
53C2×C3×C7×C13—71no—
54C2×C3×C7×C13—103no—
55C2×C3×C7×C13—351no—
56C3×C13×D7—51no—
57C3×C13×D7C7×D511yescharacteristic, direct product factor
58C7×D35C2×C3×C1311yescharacteristic, complemented
59C72×D5C2×C3×C1311yescharacteristic, complemented
60C5×C7×D7C2×C3×C1311yescharacteristic, complemented
61C5×C7×C13—23no—
62C5×C7×C13C2×C3×D711yescharacteristic, complemented
63C5×C7×C13C22×C3×C711yescharacteristic, complemented
64C2×C3×C7×D5—71no—
65C3×D5×D7C7×C1311yescharacteristic, direct product factor
66C2×C3×C5×C13—71no—
67C3×D5×C13—71no—
68C3×D5×C13C7×D711yescharacteristic, direct product factor
69C22×C7×C13—351no—
70C2×C13×D7—51no—
71C2×C3×C72—51no—
72C3×C7×D7—51no—
73C3×C7×D7D5×C1311yescharacteristic, direct product factor
74C3×C7×C13—23no—
75C3×C7×C13D5×D711yescharacteristic, direct product factor
76C3×C7×C13C2×C7×D511yescharacteristic, complemented
77C2×D5×C13—71noHall
78C5×C72C22×C3×C1311yescharacteristic, complemented, Hall
79C2×C3×C5×C7—71no—
80C3×D35C2×C7×C1311yescharacteristic, complemented
81C3×C7×D5—23no—
82C3×C7×D5—71no—
83C3×C7×D5C13×D711yescharacteristic, direct product factor
84C3×C7×D5C2×C7×C1311yescharacteristic, complemented
85C3×C5×D7C2×C7×C1311yescharacteristic, complemented
86C2×C7×D7—51noHall
87C3×C5×C13C2×C7×D711yescharacteristic, complemented, Hall
88C2×C7×C13—51no—
89C2×C7×C13—51no—
90C2×C7×C13—71no—
91C2×C7×C13—103no—
92C2×C7×C13—351no—
93C13×D7—51no—
94C13×D7C3×C7×D511yescharacteristic, direct product factor
95C22×C3×C13—351noHall
96C3×C72C2×D5×C1311yescharacteristic, complemented, Hall
97C2×C7×D5—71no—
98D5×D7C3×C7×C1311yescharacteristic, direct product factor
99C2×C5×C13—71no—
100D5×C13—71no—
101D5×C13C3×C7×D711yescharacteristic, direct product factor
102C3×C5×C7—23no—
103C3×C5×C7C2×C13×D711yescharacteristic, complemented
104C3×C5×C7C22×C7×C1311yescharacteristic, complemented
105C2×C72—51no—
106C7×D7—51no—
107C7×D7C3×D5×C1311yescharacteristic, direct product factor
108C7×C13—23no—
109C7×C13C3×D5×D711yescharacteristic, direct product factor
110C7×C13C2×C3×C7×D511yescharacteristic, complemented
111C22×C3×C7—351no—
112C2×C3×D7—51no—
113C2×C3×C13—51no—
114C2×C3×C13—71no—
115C2×C3×C13—351no—
116C2×C5×C7—71no—
117D35C2×C3×C7×C1311yescharacteristic, complemented
118C5×D7C2×C3×C7×C1311yescharacteristic, complemented
119C7×D5—23no—
120C7×D5—71no—
121C7×D5C3×C13×D711yescharacteristic, direct product factor
122C7×D5C2×C3×C7×C1311yescharacteristic, complemented
123C5×C13C2×C3×C7×D711yescharacteristic, complemented, Hall
124C2×C3×D5—71noHall
125C22×C13—351noHall
126C72C2×C3×D5×C1311yescharacteristic, complemented, Sylow
127C2×C3×C7—51no—
128C2×C3×C7—51no—
129C2×C3×C7—71no—
130C2×C3×C7—103no—
131C2×C3×C7—351no—
132C3×D7—51no—
133C3×D7C7×D5×C1311yescharacteristic, direct product factor
134C3×C13C7×D5×D711yescharacteristic, direct product factor, Hall
135C5×C7—23no—
136C5×C7C2×C3×C13×D711yescharacteristic, complemented
137C5×C7C22×C3×C7×C1311yescharacteristic, complemented
138C2×C3×C5—71no—
139C3×D5—71no—
140C3×D5C7×C13×D711yescharacteristic, direct product factor
141C22×C7—351no—
142C2×D7—51no—
143C2×C13—51no—
144C2×C13—71no—
145C2×C13—351no—
146C3×C7—23no—
147C3×C7D5×C13×D711yescharacteristic, direct product factor
148C3×C7C2×C7×D5×C1311yescharacteristic, complemented
149C2×D5—71noHall
150C3×C5C2×C7×C13×D711yescharacteristic, complemented, Hall
151C2×C7—51no—
152C2×C7—51no—
153C2×C7—71no—
154C2×C7—103no—
155C2×C7—351no—
156D7—51no—
157D7C3×C7×D5×C1311yescharacteristic, direct product factor
158C13C3×C7×D5×D711yescharacteristic, direct product factor, Sylow
159C22×C3—351noHall
160C2×C5—71no—
161D5—71no—
162D5C3×C7×C13×D711yescharacteristic, direct product factor
163C7—23no—
164C7C3×D5×C13×D711yescharacteristic, direct product factor
165C7C2×C3×C7×D5×C1311yescharacteristic, complemented
166C2×C3—51no—
167C2×C3—71no—
168C2×C3—351no—
169C5C2×C3×C7×C13×D711yescharacteristic, complemented, Sylow
170C22—351noSylow
171C3C7×D5×C13×D711yescharacteristic, direct product factor, Sylow
172C2—51no—
173C2—71no—
174C2—351no—
subgroupG/H
center, hypercenterC3×C7×C13D5×D7
commutator, cosocle, hypocenterC5×C7C22×C3×C7×C13
FrattiniC1G
Fitting, socleC3×C5×C72×C13C22
LCSG ▷ C5×C7
UCSC1 ◁ C3×C7×C13

Complements

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

NH ≅ G/Ntype
1. C3×C5×C7×C13×D7C2semidirect
2. C3×C72×D5×C13C2semidirect
3. C3×C7×C13×D35C2semidirect
4. C7×D5×C13×D7C3direct (N × H)
5. C3×C5×C72×C13C22semidirect
7. C7×C13×D35C2×C3semidirect
8. C72×D5×C13C2×C3semidirect
9. C5×C7×C13×D7C2×C3semidirect
11. C3×D5×C13×D7C7direct (N × H)
13. C3×C7×C13×D7D5direct (N × H)
15. C5×C72×C13C22×C3semidirect
16. C3×C7×D5×D7C13direct (N × H)
17. C3×C13×D35C2×C7semidirect
20. C3×C7×D5×C13D7direct (N × H)
21. C3×C7×D5×C13C2×C7semidirect
22. C3×C5×C13×D7C2×C7semidirect
25. C3×C72×C13C2×D5semidirect
27. D5×C13×D7C3×C7direct (N × H)
28. C3×C7×D35C2×C13semidirect
29. C3×C72×D5C2×C13semidirect
30. C3×C5×C7×D7C2×C13semidirect
32. C3×C5×C7×C13C2×D7semidirect
33. C3×C5×C7×C13C22×C7semidirect
36. C7×C13×D7C3×D5direct (N × H)
39. C7×D5×D7C3×C13direct (N × H)
41. C13×D35C2×C3×C7semidirect
44. C7×D5×C13C3×D7direct (N × H)
45. C7×D5×C13C2×C3×C7semidirect
46. C5×C13×D7C2×C3×C7semidirect
48. C3×C5×C72C22×C13semidirect
49. C72×C13C2×C3×D5semidirect
57. C3×C13×D7C7×D5direct (N × H)
58. C7×D35C2×C3×C13semidirect
59. C72×D5C2×C3×C13semidirect
60. C5×C7×D7C2×C3×C13semidirect
62. C5×C7×C13C2×C3×D7semidirect
63. C5×C7×C13C22×C3×C7semidirect
65. C3×D5×D7C7×C13direct (N × H)
68. C3×D5×C13C7×D7direct (N × H)
73. C3×C7×D7D5×C13direct (N × H)
75. C3×C7×C13D5×D7direct (N × H)
76. C3×C7×C13C2×C7×D5semidirect
78. C5×C72C22×C3×C13semidirect
80. C3×D35C2×C7×C13semidirect
83. C3×C7×D5C13×D7direct (N × H)
84. C3×C7×D5C2×C7×C13semidirect
85. C3×C5×D7C2×C7×C13semidirect
87. C3×C5×C13C2×C7×D7semidirect
94. C13×D7C3×C7×D5direct (N × H)
96. C3×C72C2×D5×C13semidirect
98. D5×D7C3×C7×C13direct (N × H)
101. D5×C13C3×C7×D7direct (N × H)
103. C3×C5×C7C2×C13×D7semidirect
104. C3×C5×C7C22×C7×C13semidirect
107. C7×D7C3×D5×C13direct (N × H)
109. C7×C13C3×D5×D7direct (N × H)
110. C7×C13C2×C3×C7×D5semidirect
117. D35C2×C3×C7×C13semidirect
118. C5×D7C2×C3×C7×C13semidirect
121. C7×D5C3×C13×D7direct (N × H)
122. C7×D5C2×C3×C7×C13semidirect
123. C5×C13C2×C3×C7×D7semidirect
126. C72C2×C3×D5×C13semidirect
133. C3×D7C7×D5×C13direct (N × H)
134. C3×C13C7×D5×D7direct (N × H)
136. C5×C7C2×C3×C13×D7semidirect
137. C5×C7C22×C3×C7×C13semidirect
140. C3×D5C7×C13×D7direct (N × H)
147. C3×C7D5×C13×D7direct (N × H)
148. C3×C7C2×C7×D5×C13semidirect
150. C3×C5C2×C7×C13×D7semidirect
157. D7C3×C7×D5×C13direct (N × H)
158. C13C3×C7×D5×D7direct (N × H)
162. D5C3×C7×C13×D7direct (N × H)
164. C7C3×D5×C13×D7direct (N × H)
165. C7C2×C3×C7×D5×C13semidirect
169. C5C2×C3×C7×C13×D7semidirect
171. C3C7×D5×C13×D7direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×C7×C13×D72
C3×C72×D5×C132
C3×C7×C13×D352
C7×D5×C13×D73
C2×C3×C7×C13×D75
C2×C3×C7×D5×C137
C3×D5×C13×D77
C3×C7×D5×D713