Finite Group Databasebeta

← D3×C7×C13×D35 #50304459

Subgroups — D3×C7×C13×D35 #50304459

Order 38220.

208 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 208 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×C7×C13×D35C211yesmaximal, characteristic, complemented
2C5×D3×C72×C13C211yesmaximal, characteristic, complemented
3C7×C13×D105C211yesmaximal, characteristic, complemented
4C2×C7×C13×D35—31nomaximal, Hall
5C3×C5×C72×C13C2211yescharacteristic, complemented, Hall
6D3×C7×C13×D7—51nomaximal, Hall
7C7×C13×D35—31no—
8C7×C13×D35D311yescharacteristic, direct product factor
9C2×C5×C72×C13—31no—
10D3×C13×D35C711yesmaximal, characteristic, direct product factor
11D3×C7×D5×C13—71nomaximal
12C7×C13×D21—51no—
13D3×C72×C13D511yescharacteristic, complemented
14C3×C7×C13×D7—51no—
15C5×C72×C13C2×D311yescharacteristic, complemented, Hall
16D3×C7×D35C1311yesmaximal, characteristic, direct product factor, Hall
17C13×D105C2×C711yescharacteristic, complemented
18C7×C13×D15—71no—
19C5×D3×C7×C13—23no—
20C5×D3×C7×C13D711yescharacteristic, complemented
21C5×D3×C7×C13C2×C711yescharacteristic, complemented
22C3×C13×D35C2×C711yescharacteristic, complemented
23C3×C7×D5×C13—71no—
24C2×C7×C13×D7—151noHall
25C3×C72×C13C2×D511yescharacteristic, complemented, Hall
26C2×C13×D35—31no—
27C2×C7×D5×C13—211no—
28C7×D105C2×C1311yescharacteristic, complemented
29C5×D3×C72C2×C1311yescharacteristic, complemented
30C3×C7×D35C2×C1311yescharacteristic, complemented
31C3×C5×C7×C13—23no—
32C3×C5×C7×C13C2×D711yescharacteristic, complemented
33C3×C5×C7×C13C22×C711yescharacteristic, complemented
34C2×C72×C13—31no—
35C7×C13×D7—51no—
36C7×C13×D7—151no—
37C2×D3×C7×C13—351no—
38D3×C13×D7—51no—
39C2×C7×D35—31noHall
40C2×C5×C7×C13—31no—
41C2×C5×C7×C13—31no—
42C2×C5×C7×C13—63no—
43C13×D35—31no—
44C13×D35D3×C711yescharacteristic, direct product factor
45C7×D5×C13—71no—
46C7×D5×C13—211no—
47D3×D5×C13—71noHall
48C3×C5×C72C22×C1311yescharacteristic, complemented, Hall
49C72×C13D3×D511yescharacteristic, complemented, Hall
50D3×C7×D7—51noHall
51C2×C3×C7×C13—351no—
52C13×D21—51no—
53D3×C7×C13—23no—
54D3×C7×C13—351no—
55D3×C7×C13C7×D511yescharacteristic, complemented
56D3×C7×C13D3511yescharacteristic, direct product factor
57C3×C13×D7—51no—
58C2×C5×C72—31no—
59C7×D35—31no—
60C7×D35D3×C1311yescharacteristic, direct product factor
61C5×C7×C13—23no—
62C5×C7×C13D3×D711yescharacteristic, complemented
63C5×C7×C13C2×D3×C711yescharacteristic, complemented
64D3×D35C7×C1311yescharacteristic, direct product factor
65D3×C7×D5—71no—
66C13×D15—71no—
67C5×D3×C13C7×D711yescharacteristic, complemented
68C3×D5×C13—71no—
69C22×C7×C13—1051no—
70C2×C13×D7—151no—
71C7×D21—51no—
72D3×C72D5×C1311yescharacteristic, complemented
73C3×C7×D7—51no—
74C3×C7×C13—23no—
75C3×C7×C13C2×C7×D511yescharacteristic, complemented
76C3×C7×C13C2×D3511yescharacteristic, complemented
77C2×D5×C13—211noHall
78C5×C72C2×D3×C1311yescharacteristic, complemented, Hall
79D105C2×C7×C1311yescharacteristic, complemented
80C7×D15—71no—
81C5×D3×C7—23no—
82C5×D3×C7C13×D711yescharacteristic, complemented
83C5×D3×C7C2×C7×C1311yescharacteristic, complemented
84C3×D35C2×C7×C1311yescharacteristic, complemented
85C3×C7×D5—71no—
86C2×C7×D7—151noHall
87C3×C5×C13C2×C7×D711yescharacteristic, complemented, Hall
88C2×C7×C13—31no—
89C2×C7×C13—31no—
90C2×C7×C13—63no—
91C2×C7×C13—351no—
92C2×C7×C13—1051no—
93C13×D7—51no—
94C13×D7—151no—
95C2×D3×C13—351noHall
96C3×C72C2×D5×C1311yescharacteristic, complemented, Hall
97C2×D35—31no—
98C2×C7×D5—211no—
99C2×C5×C13—31no—
100D5×C13—71no—
101D5×C13—211no—
102C3×C5×C7—23no—
103C3×C5×C7C2×C13×D711yescharacteristic, complemented
104C3×C5×C7C22×C7×C1311yescharacteristic, complemented
105C2×C72—31no—
106C7×D7—51no—
107C7×D7—151no—
108C7×C13—23no—
109C7×C13D3×C7×D511yescharacteristic, complemented
110C7×C13D3×D3511yescharacteristic, direct product factor
111C2×D3×C7—351no—
112D3×D7—51no—
113C2×C3×C13—351no—
114D3×C13—351no—
115D3×C13C7×D3511yescharacteristic, direct product factor
116C2×C5×C7—31no—
117C2×C5×C7—31no—
118C2×C5×C7—63no—
119D35—31no—
120D35D3×C7×C1311yescharacteristic, direct product factor
121C7×D5—71no—
122C7×D5—211no—
123C5×C13D3×C7×D711yescharacteristic, complemented, Hall
124D3×D5—71noHall
125C22×C13—1051noHall
126C72D3×D5×C1311yescharacteristic, complemented, Sylow
127C2×C3×C7—351no—
128D21—51no—
129C3×D7—51no—
130D3×C7—23no—
131D3×C7—351no—
132D3×C7C7×D5×C1311yescharacteristic, complemented
133D3×C7C13×D3511yescharacteristic, direct product factor
134C3×C13C2×C7×D3511yescharacteristic, complemented, Hall
135C5×C7—23no—
136C5×C7D3×C13×D711yescharacteristic, complemented
137C5×C7C2×D3×C7×C1311yescharacteristic, complemented
138D15—71no—
139C3×D5—71no—
140C5×D3C7×C13×D711yescharacteristic, complemented
141C22×C7—1051no—
142C2×D7—151no—
143C2×C13—31no—
144C2×C13—351no—
145C2×C13—1051no—
146C3×C7—23no—
147C3×C7C2×C7×D5×C1311yescharacteristic, complemented
148C3×C7C2×C13×D3511yescharacteristic, complemented
149C2×D5—211noHall
150C3×C5C2×C7×C13×D711yescharacteristic, complemented, Hall
151C2×C7—31no—
152C2×C7—31no—
153C2×C7—63no—
154C2×C7—351no—
155C2×C7—1051no—
156D7—51no—
157D7—151no—
158C13D3×C7×D3511yescharacteristic, direct product factor, Sylow
159C2×D3—351noHall
160C2×C5—31no—
161D5—71no—
162D5—211no—
163C7—23no—
164C7D3×C7×D5×C1311yescharacteristic, complemented
165C7D3×C13×D3511yescharacteristic, direct product factor
166C2×C3—351no—
167D3—351no—
168D3C7×C13×D3511yescharacteristic, direct product factor
169C5D3×C7×C13×D711yescharacteristic, complemented, Sylow
170C22—1051noSylow
171C3C2×C7×C13×D3511yescharacteristic, complemented, Sylow
172C2—31no—
173C2—351no—
174C2—1051no—
subgroupG/H
center, hypercenterC7×C13D3×D35
commutator, cosocle, hypocenterC3×C5×C7C22×C7×C13
FrattiniC1G
Fitting, socleC3×C5×C72×C13C22
LCSG ▷ C3×C5×C7
UCSC1 ◁ C7×C13

Complements

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

NH ≅ G/Ntype
1. C3×C7×C13×D35C2semidirect
2. C5×D3×C72×C13C2semidirect
3. C7×C13×D105C2semidirect
5. C3×C5×C72×C13C22semidirect
8. C7×C13×D35D3direct (N × H)
10. D3×C13×D35C7direct (N × H)
13. D3×C72×C13D5semidirect
15. C5×C72×C13C2×D3semidirect
16. D3×C7×D35C13direct (N × H)
17. C13×D105C2×C7semidirect
20. C5×D3×C7×C13D7semidirect
21. C5×D3×C7×C13C2×C7semidirect
22. C3×C13×D35C2×C7semidirect
25. C3×C72×C13C2×D5semidirect
28. C7×D105C2×C13semidirect
29. C5×D3×C72C2×C13semidirect
30. C3×C7×D35C2×C13semidirect
32. C3×C5×C7×C13C2×D7semidirect
33. C3×C5×C7×C13C22×C7semidirect
44. C13×D35D3×C7direct (N × H)
48. C3×C5×C72C22×C13semidirect
49. C72×C13D3×D5semidirect
55. D3×C7×C13C7×D5semidirect
56. D3×C7×C13D35direct (N × H)
60. C7×D35D3×C13direct (N × H)
62. C5×C7×C13D3×D7semidirect
63. C5×C7×C13C2×D3×C7semidirect
64. D3×D35C7×C13direct (N × H)
67. C5×D3×C13C7×D7semidirect
72. D3×C72D5×C13semidirect
75. C3×C7×C13C2×C7×D5semidirect
76. C3×C7×C13C2×D35semidirect
78. C5×C72C2×D3×C13semidirect
79. D105C2×C7×C13semidirect
82. C5×D3×C7C13×D7semidirect
83. C5×D3×C7C2×C7×C13semidirect
84. C3×D35C2×C7×C13semidirect
87. C3×C5×C13C2×C7×D7semidirect
96. C3×C72C2×D5×C13semidirect
103. C3×C5×C7C2×C13×D7semidirect
104. C3×C5×C7C22×C7×C13semidirect
109. C7×C13D3×C7×D5semidirect
110. C7×C13D3×D35direct (N × H)
115. D3×C13C7×D35direct (N × H)
120. D35D3×C7×C13direct (N × H)
123. C5×C13D3×C7×D7semidirect
126. C72D3×D5×C13semidirect
132. D3×C7C7×D5×C13semidirect
133. D3×C7C13×D35direct (N × H)
134. C3×C13C2×C7×D35semidirect
136. C5×C7D3×C13×D7semidirect
137. C5×C7C2×D3×C7×C13semidirect
140. C5×D3C7×C13×D7semidirect
147. C3×C7C2×C7×D5×C13semidirect
148. C3×C7C2×C13×D35semidirect
150. C3×C5C2×C7×C13×D7semidirect
158. C13D3×C7×D35direct (N × H)
164. C7D3×C7×D5×C13semidirect
165. C7D3×C13×D35direct (N × H)
168. D3C7×C13×D35direct (N × H)
169. C5D3×C7×C13×D7semidirect
171. C3C2×C7×C13×D35semidirect

Maximal subgroups

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

subgroupindex
C3×C7×C13×D352
C5×D3×C72×C132
C7×C13×D1052
C2×C7×C13×D353
D3×C7×C13×D75
D3×C13×D357
D3×C7×D5×C137
D3×C7×D3513