Finite Group Databasebeta

← C2×C3×C7×C13×D35 #50304517

Subgroups — C2×C3×C7×C13×D35 #50304517

Order 38220.

208 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 88 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×D35C212yesmaximal, direct product factor
2C2×C3×C5×C72×C13C211yesmaximal, characteristic, complemented
3C2×C7×C13×D35C311yesmaximal, characteristic, direct product factor, Hall
4C3×C5×C72×C13C2211yescharacteristic, complemented, Hall
5C2×C3×C7×C13×D7—51nomaximal, Hall
6C7×C13×D35C2×C312yesdirect product factor
7C2×C5×C72×C13C2×C311yescharacteristic, complemented
8C2×C3×C13×D35C711yesmaximal, characteristic, direct product factor
9C2×C3×C7×D5×C13—71nomaximal
10C3×C7×C13×D7—52no—
11C2×C3×C72×C13D511yescharacteristic, complemented
12C5×C72×C13C22×C311yescharacteristic, complemented, Hall
13C2×C3×C7×D35C1311yesmaximal, characteristic, direct product factor, Hall
14C3×C13×D35C2×C712yesdirect product factor
15C3×C7×D5×C13—72no—
16C2×C3×C5×C7×C13—23no—
17C2×C3×C5×C7×C13D711yescharacteristic, complemented
18C2×C3×C5×C7×C13C2×C711yescharacteristic, complemented
19C2×C7×C13×D7—51noHall
20C3×C72×C13C2×D511yescharacteristic, complemented, Hall
21C2×C13×D35C3×C711yescharacteristic, direct product factor
22C2×C7×D5×C13—71no—
23C2×C3×C5×C72C2×C1311yescharacteristic, complemented
24C3×C7×D35C2×C1312yesdirect product factor
25C3×C5×C7×C13—23no—
26C3×C5×C7×C13C2×D711yescharacteristic, complemented
27C3×C5×C7×C13C22×C711yescharacteristic, complemented
28C2×C72×C13C3×D511yescharacteristic, complemented
29C7×C13×D7—52no—
30C22×C3×C7×C13—351no—
31C2×C3×C13×D7—51no—
32C2×C7×D35C3×C1311yescharacteristic, direct product factor, Hall
33C2×C5×C7×C13—23no—
34C2×C5×C7×C13C3×D711yescharacteristic, complemented
35C2×C5×C7×C13C2×C3×C711yescharacteristic, complemented
36C13×D35C2×C3×C712yesdirect product factor
37C7×D5×C13—72no—
38C2×C3×D5×C13—71noHall
39C3×C5×C72C22×C1311yescharacteristic, complemented, Hall
40C72×C13C2×C3×D511yescharacteristic, complemented, Hall
41C2×C3×C7×D7—51noHall
42C2×C3×C7×C13—23no—
43C2×C3×C7×C13—352no—
44C2×C3×C7×C13C7×D511yescharacteristic, complemented
45C2×C3×C7×C13D3511yescharacteristic, direct product factor
46C3×C13×D7—52no—
47C2×C5×C72C2×C3×C1311yescharacteristic, complemented
48C7×D35C2×C3×C1312yesdirect product factor
49C5×C7×C13—23no—
50C5×C7×C13C2×C3×D711yescharacteristic, complemented
51C5×C7×C13C22×C3×C711yescharacteristic, complemented
52C2×C3×D35C7×C1311yescharacteristic, direct product factor
53C2×C3×C7×D5—71no—
54C2×C3×C5×C13C7×D711yescharacteristic, complemented
55C3×D5×C13—72no—
56C22×C7×C13—351no—
57C2×C13×D7—51no—
58C2×C3×C72D5×C1311yescharacteristic, complemented
59C3×C7×D7—52no—
60C3×C7×C13—23no—
61C3×C7×C13C2×C7×D511yescharacteristic, complemented
62C3×C7×C13C2×D3511yescharacteristic, direct product factor
63C2×D5×C13—71noHall
64C5×C72C22×C3×C1311yescharacteristic, complemented, Hall
65C2×C3×C5×C7—23no—
66C2×C3×C5×C7C13×D711yescharacteristic, complemented
67C2×C3×C5×C7C2×C7×C1311yescharacteristic, complemented
68C3×D35C2×C7×C1312yesdirect product factor
69C3×C7×D5—72no—
70C2×C7×D7—51noHall
71C3×C5×C13C2×C7×D711yescharacteristic, complemented, Hall
72C2×C7×C13—23no—
73C2×C7×C13—352no—
74C2×C7×C13C3×C7×D511yescharacteristic, complemented
75C2×C7×C13C3×D3511yescharacteristic, direct product factor
76C13×D7—52no—
77C22×C3×C13—351noHall
78C3×C72C2×D5×C1311yescharacteristic, complemented, Hall
79C2×D35C3×C7×C1311yescharacteristic, direct product factor
80C2×C7×D5—71no—
81C2×C5×C13C3×C7×D711yescharacteristic, complemented
82D5×C13—72no—
83C3×C5×C7—23no—
84C3×C5×C7C2×C13×D711yescharacteristic, complemented
85C3×C5×C7C22×C7×C1311yescharacteristic, complemented
86C2×C72C3×D5×C1311yescharacteristic, complemented
87C7×D7—52no—
88C7×C13—23no—
89C7×C13C2×C3×C7×D511yescharacteristic, complemented
90C7×C13C2×C3×D3511yescharacteristic, direct product factor
91C22×C3×C7—351no—
92C2×C3×D7—51no—
93C2×C3×C13—352no—
94C2×C3×C13C7×D3511yescharacteristic, direct product factor
95C2×C5×C7—23no—
96C2×C5×C7C3×C13×D711yescharacteristic, complemented
97C2×C5×C7C2×C3×C7×C1311yescharacteristic, complemented
98D35C2×C3×C7×C1312yesdirect product factor
99C7×D5—72no—
100C5×C13C2×C3×C7×D711yescharacteristic, complemented, Hall
101C2×C3×D5—71noHall
102C22×C13—351noHall
103C72C2×C3×D5×C1311yescharacteristic, complemented, Sylow
104C2×C3×C7—23no—
105C2×C3×C7—352no—
106C2×C3×C7C7×D5×C1311yescharacteristic, complemented
107C2×C3×C7C13×D3511yescharacteristic, direct product factor
108C3×D7—52no—
109C3×C13C2×C7×D3511yescharacteristic, direct product factor, Hall
110C5×C7—23no—
111C5×C7C2×C3×C13×D711yescharacteristic, complemented
112C5×C7C22×C3×C7×C1311yescharacteristic, complemented
113C2×C3×C5C7×C13×D711yescharacteristic, complemented
114C3×D5—72no—
115C22×C7—351no—
116C2×D7—51no—
117C2×C13—352no—
118C2×C13C3×C7×D3511yescharacteristic, direct product factor
119C3×C7—23no—
120C3×C7C2×C7×D5×C1311yescharacteristic, complemented
121C3×C7C2×C13×D3511yescharacteristic, direct product factor
122C2×D5—71noHall
123C3×C5C2×C7×C13×D711yescharacteristic, complemented, Hall
124C2×C7—23no—
125C2×C7—352no—
126C2×C7C3×C7×D5×C1311yescharacteristic, complemented
127C2×C7C3×C13×D3511yescharacteristic, direct product factor
128D7—52no—
129C13C2×C3×C7×D3511yescharacteristic, direct product factor, Sylow
130C22×C3—351noHall
131C2×C5C3×C7×C13×D711yescharacteristic, complemented
132D5—72no—
133C7—23no—
134C7C2×C3×C7×D5×C1311yescharacteristic, complemented
135C7C2×C3×C13×D3511yescharacteristic, direct product factor
136C2×C3—352no—
137C2×C3C7×C13×D3511yescharacteristic, direct product factor
138C5C2×C3×C7×C13×D711yescharacteristic, complemented, Sylow
139C22—351noSylow
140C3C2×C7×C13×D3511yescharacteristic, direct product factor, Sylow
141C2—352no—
142C2C3×C7×C13×D3511yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3×C7×C13D35
commutator, cosocle, hypocenterC5×C7C22×C3×C7×C13
FrattiniC1G
Fitting, socleC2×C3×C5×C72×C13C2
LCSG ▷ C5×C7
UCSC1 ◁ C2×C3×C7×C13

Complements

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

NH ≅ G/Ntype
1. C3×C7×C13×D35C2direct (N × H)
2. C2×C3×C5×C72×C13C2semidirect
3. C2×C7×C13×D35C3direct (N × H)
4. C3×C5×C72×C13C22semidirect
6. C7×C13×D35C2×C3direct (N × H)
7. C2×C5×C72×C13C2×C3semidirect
8. C2×C3×C13×D35C7direct (N × H)
11. C2×C3×C72×C13D5semidirect
12. C5×C72×C13C22×C3semidirect
13. C2×C3×C7×D35C13direct (N × H)
14. C3×C13×D35C2×C7direct (N × H)
17. C2×C3×C5×C7×C13D7semidirect
18. C2×C3×C5×C7×C13C2×C7semidirect
20. C3×C72×C13C2×D5semidirect
21. C2×C13×D35C3×C7direct (N × H)
23. C2×C3×C5×C72C2×C13semidirect
24. C3×C7×D35C2×C13direct (N × H)
26. C3×C5×C7×C13C2×D7semidirect
27. C3×C5×C7×C13C22×C7semidirect
28. C2×C72×C13C3×D5semidirect
32. C2×C7×D35C3×C13direct (N × H)
34. C2×C5×C7×C13C3×D7semidirect
35. C2×C5×C7×C13C2×C3×C7semidirect
36. C13×D35C2×C3×C7direct (N × H)
39. C3×C5×C72C22×C13semidirect
40. C72×C13C2×C3×D5semidirect
44. C2×C3×C7×C13C7×D5semidirect
45. C2×C3×C7×C13D35direct (N × H)
47. C2×C5×C72C2×C3×C13semidirect
48. C7×D35C2×C3×C13direct (N × H)
50. C5×C7×C13C2×C3×D7semidirect
51. C5×C7×C13C22×C3×C7semidirect
52. C2×C3×D35C7×C13direct (N × H)
54. C2×C3×C5×C13C7×D7semidirect
58. C2×C3×C72D5×C13semidirect
61. C3×C7×C13C2×C7×D5semidirect
62. C3×C7×C13C2×D35direct (N × H)
64. C5×C72C22×C3×C13semidirect
66. C2×C3×C5×C7C13×D7semidirect
67. C2×C3×C5×C7C2×C7×C13semidirect
68. C3×D35C2×C7×C13direct (N × H)
71. C3×C5×C13C2×C7×D7semidirect
74. C2×C7×C13C3×C7×D5semidirect
75. C2×C7×C13C3×D35direct (N × H)
78. C3×C72C2×D5×C13semidirect
79. C2×D35C3×C7×C13direct (N × H)
81. C2×C5×C13C3×C7×D7semidirect
84. C3×C5×C7C2×C13×D7semidirect
85. C3×C5×C7C22×C7×C13semidirect
86. C2×C72C3×D5×C13semidirect
89. C7×C13C2×C3×C7×D5semidirect
90. C7×C13C2×C3×D35direct (N × H)
94. C2×C3×C13C7×D35direct (N × H)
96. C2×C5×C7C3×C13×D7semidirect
97. C2×C5×C7C2×C3×C7×C13semidirect
98. D35C2×C3×C7×C13direct (N × H)
100. C5×C13C2×C3×C7×D7semidirect
103. C72C2×C3×D5×C13semidirect
106. C2×C3×C7C7×D5×C13semidirect
107. C2×C3×C7C13×D35direct (N × H)
109. C3×C13C2×C7×D35direct (N × H)
111. C5×C7C2×C3×C13×D7semidirect
112. C5×C7C22×C3×C7×C13semidirect
113. C2×C3×C5C7×C13×D7semidirect
118. C2×C13C3×C7×D35direct (N × H)
120. C3×C7C2×C7×D5×C13semidirect
121. C3×C7C2×C13×D35direct (N × H)
123. C3×C5C2×C7×C13×D7semidirect
126. C2×C7C3×C7×D5×C13semidirect
127. C2×C7C3×C13×D35direct (N × H)
129. C13C2×C3×C7×D35direct (N × H)
131. C2×C5C3×C7×C13×D7semidirect
134. C7C2×C3×C7×D5×C13semidirect
135. C7C2×C3×C13×D35direct (N × H)
137. C2×C3C7×C13×D35direct (N × H)
138. C5C2×C3×C7×C13×D7semidirect
140. C3C2×C7×C13×D35direct (N × H)
142. C2C3×C7×C13×D35direct (N × H)

Maximal subgroups

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

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