Finite Group Databasebeta

← C2×C7×D1365 #50304530

Subgroups — C2×C7×D1365 #50304530

Order 38220.

208 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 70 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
1C7×D1365C212yesmaximal, direct product factor
2C2×C3×C5×C72×C13C211yesmaximal, characteristic, complemented
3C2×C7×D455—31nomaximal, Hall
4C3×C5×C72×C13C2211yescharacteristic, complemented, Hall
5C2×C7×D273—51nomaximal, Hall
6C7×D455—32no—
7C2×C5×C72×C13D311yescharacteristic, complemented
8C2×D1365C711yesmaximal, characteristic, direct product factor
9C2×C7×D195—71nomaximal
10C7×D273—52no—
11C2×C3×C72×C13D511yescharacteristic, complemented
12C5×C72×C13C2×D311yescharacteristic, complemented, Hall
13C2×C7×D105—131nomaximal, Hall
14D1365C2×C712yesdirect product factor
15C7×D195—72no—
16C2×C3×C5×C7×C13—23no—
17C2×C3×C5×C7×C13D711yescharacteristic, complemented
18C2×C3×C5×C7×C13C2×C711yescharacteristic, complemented
19C2×C7×D91—151noHall
20C3×C72×C13C2×D511yescharacteristic, complemented, Hall
21C2×D455—31no—
22C2×C7×D65—211no—
23C2×C3×C5×C72D1311yescharacteristic, complemented
24C7×D105—132no—
25C3×C5×C7×C13—23no—
26C3×C5×C7×C13C2×D711yescharacteristic, complemented
27C3×C5×C7×C13C22×C711yescharacteristic, complemented
28C2×C72×C13D1511yescharacteristic, complemented
29C7×D91—152no—
30C2×D273—51no—
31C2×C7×D39—351no—
32C2×C7×D35—391noHall
33C2×C5×C7×C13—23no—
34C2×C5×C7×C13D3×C711yescharacteristic, complemented
35C2×C5×C7×C13D2111yescharacteristic, complemented
36D455—32no—
37C7×D65—212no—
38C2×D195—71noHall
39C3×C5×C72C2×D1311yescharacteristic, complemented, Hall
40C72×C13C2×D1511yescharacteristic, complemented, Hall
41C2×C7×D21—651noHall
42C2×C3×C7×C13—23no—
43C2×C3×C7×C13C7×D511yescharacteristic, complemented
44C2×C3×C7×C13D3511yescharacteristic, complemented
45D273—52no—
46C7×D39—352no—
47C2×C5×C72D3911yescharacteristic, complemented
48C7×D35—392no—
49C5×C7×C13—23no—
50C5×C7×C13C2×D3×C711yescharacteristic, complemented
51C5×C7×C13C2×D2111yescharacteristic, complemented
52C2×D105—131no—
53C2×C7×D15—911no—
54C2×C3×C5×C13C7×D711yescharacteristic, complemented
55D195—72no—
56C2×D91—151no—
57C2×C7×D13—1051no—
58C2×C3×C72D6511yescharacteristic, complemented
59C7×D21—652no—
60C3×C7×C13—23no—
61C3×C7×C13C2×C7×D511yescharacteristic, complemented
62C3×C7×C13C2×D3511yescharacteristic, complemented
63C2×D65—211noHall
64C5×C72C2×D3911yescharacteristic, complemented, Hall
65C2×C3×C5×C7—23no—
66C2×C3×C5×C7C7×D1311yescharacteristic, complemented
67C2×C3×C5×C7D9111yescharacteristic, complemented
68D105—132no—
69C7×D15—912no—
70C2×C7×D7—1951noHall
71C3×C5×C13C2×C7×D711yescharacteristic, complemented, Hall
72C2×C7×C13—23no—
73C2×C7×C13C7×D1511yescharacteristic, complemented
74C2×C7×C13D10511yescharacteristic, complemented
75D91—152no—
76C7×D13—1052no—
77C2×D39—351noHall
78C3×C72C2×D6511yescharacteristic, complemented, Hall
79C2×D35—391no—
80C2×C7×D5—2731no—
81C2×C5×C13C7×D2111yescharacteristic, complemented
82D65—212no—
83C3×C5×C7—23no—
84C3×C5×C7C2×C7×D1311yescharacteristic, complemented
85C3×C5×C7C2×D9111yescharacteristic, complemented
86C2×C72D19511yescharacteristic, complemented
87C7×D7—1952no—
88C7×C13—23no—
89C7×C13C2×C7×D1511yescharacteristic, complemented
90C7×C13C2×D10511yescharacteristic, complemented
91C2×D21—651no—
92C2×D3×C7—4551no—
93C2×C3×C13C7×D3511yescharacteristic, complemented
94D39—352no—
95C2×C5×C7—23no—
96C2×C5×C7C7×D3911yescharacteristic, complemented
97C2×C5×C7D27311yescharacteristic, complemented
98D35—392no—
99C7×D5—2732no—
100C5×C13C2×C7×D2111yescharacteristic, complemented, Hall
101C2×D15—911noHall
102C2×D13—1051noHall
103C72C2×D19511yescharacteristic, complemented, Sylow
104C2×C3×C7—23no—
105C2×C3×C7C7×D6511yescharacteristic, complemented
106C2×C3×C7D45511yescharacteristic, complemented
107D21—652no—
108D3×C7—4552no—
109C3×C13C2×C7×D3511yescharacteristic, complemented, Hall
110C5×C7—23no—
111C5×C7C2×C7×D3911yescharacteristic, complemented
112C5×C7C2×D27311yescharacteristic, complemented
113C2×C3×C5C7×D9111yescharacteristic, complemented
114D15—912no—
115C22×C7—13651no—
116C2×D7—1951no—
117C2×C13C7×D10511yescharacteristic, complemented
118D13—1052no—
119C3×C7—23no—
120C3×C7C2×C7×D6511yescharacteristic, complemented
121C3×C7C2×D45511yescharacteristic, complemented
122C2×D5—2731noHall
123C3×C5C2×C7×D9111yescharacteristic, complemented, Hall
124C2×C7—23no—
125C2×C7—13652no—
126C2×C7C7×D19511yescharacteristic, complemented
127C2×C7D136511yescharacteristic, direct product factor
128D7—1952no—
129C13C2×C7×D10511yescharacteristic, complemented, Sylow
130C2×D3—4551noHall
131C2×C5C7×D27311yescharacteristic, complemented
132D5—2732no—
133C7—23no—
134C7C2×C7×D19511yescharacteristic, complemented
135C7C2×D136511yescharacteristic, direct product factor
136C2×C3C7×D45511yescharacteristic, complemented
137D3—4552no—
138C5C2×C7×D27311yescharacteristic, complemented, Sylow
139C22—13651noSylow
140C3C2×C7×D45511yescharacteristic, complemented, Sylow
141C2—13652no—
142C2C7×D136511yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C7D1365
commutator, cosocle, hypocenterC3×C5×C7×C13C22×C7
FrattiniC1G
Fitting, socleC2×C3×C5×C72×C13C2
LCSG ▷ C3×C5×C7×C13
UCSC1 ◁ C2×C7

Complements

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

NH ≅ G/Ntype
1. C7×D1365C2direct (N × H)
2. C2×C3×C5×C72×C13C2semidirect
4. C3×C5×C72×C13C22semidirect
7. C2×C5×C72×C13D3semidirect
8. C2×D1365C7direct (N × H)
11. C2×C3×C72×C13D5semidirect
12. C5×C72×C13C2×D3semidirect
14. D1365C2×C7direct (N × H)
17. C2×C3×C5×C7×C13D7semidirect
18. C2×C3×C5×C7×C13C2×C7semidirect
20. C3×C72×C13C2×D5semidirect
23. C2×C3×C5×C72D13semidirect
26. C3×C5×C7×C13C2×D7semidirect
27. C3×C5×C7×C13C22×C7semidirect
28. C2×C72×C13D15semidirect
34. C2×C5×C7×C13D3×C7semidirect
35. C2×C5×C7×C13D21semidirect
39. C3×C5×C72C2×D13semidirect
40. C72×C13C2×D15semidirect
43. C2×C3×C7×C13C7×D5semidirect
44. C2×C3×C7×C13D35semidirect
47. C2×C5×C72D39semidirect
50. C5×C7×C13C2×D3×C7semidirect
51. C5×C7×C13C2×D21semidirect
54. C2×C3×C5×C13C7×D7semidirect
58. C2×C3×C72D65semidirect
61. C3×C7×C13C2×C7×D5semidirect
62. C3×C7×C13C2×D35semidirect
64. C5×C72C2×D39semidirect
66. C2×C3×C5×C7C7×D13semidirect
67. C2×C3×C5×C7D91semidirect
71. C3×C5×C13C2×C7×D7semidirect
73. C2×C7×C13C7×D15semidirect
74. C2×C7×C13D105semidirect
78. C3×C72C2×D65semidirect
81. C2×C5×C13C7×D21semidirect
84. C3×C5×C7C2×C7×D13semidirect
85. C3×C5×C7C2×D91semidirect
86. C2×C72D195semidirect
89. C7×C13C2×C7×D15semidirect
90. C7×C13C2×D105semidirect
93. C2×C3×C13C7×D35semidirect
96. C2×C5×C7C7×D39semidirect
97. C2×C5×C7D273semidirect
100. C5×C13C2×C7×D21semidirect
103. C72C2×D195semidirect
105. C2×C3×C7C7×D65semidirect
106. C2×C3×C7D455semidirect
109. C3×C13C2×C7×D35semidirect
111. C5×C7C2×C7×D39semidirect
112. C5×C7C2×D273semidirect
113. C2×C3×C5C7×D91semidirect
117. C2×C13C7×D105semidirect
120. C3×C7C2×C7×D65semidirect
121. C3×C7C2×D455semidirect
123. C3×C5C2×C7×D91semidirect
126. C2×C7C7×D195semidirect
127. C2×C7D1365direct (N × H)
129. C13C2×C7×D105semidirect
131. C2×C5C7×D273semidirect
134. C7C2×C7×D195semidirect
135. C7C2×D1365direct (N × H)
136. C2×C3C7×D455semidirect
138. C5C2×C7×D273semidirect
140. C3C2×C7×D455semidirect
142. C2C7×D1365direct (N × H)

Maximal subgroups

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

subgroupindex
C7×D13652
C2×C3×C5×C72×C132
C2×C7×D4553
C2×C7×D2735
C2×D13657
C2×C7×D1957
C2×C7×D10513