Finite Group Databasebeta

← C13×D7×D105 #50304438

Subgroups — C13×D7×D105 #50304438

Order 38220.

208 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 56 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
2C7×C13×D105C211yesmaximal, characteristic, complemented
3C13×C3⋊(C5⋊(C7⋊D7))C211yesmaximal, characteristic, complemented
4C13×D7×D35—31nomaximal, Hall
5C3×C5×C72×C13C2211yescharacteristic, complemented, Hall
6C13×D7×D21—51nomaximal, Hall
7C13×C5⋊(C7⋊D7)—31no—
8C7×C13×D35—31no—
9C5×C7×C13×D7D311yescharacteristic, complemented
10C2×C13×D105—71nomaximal
11C13×D7×D15—71nomaximal
12C13×C3⋊(C7⋊D7)—51no—
13C7×C13×D21—51no—
14C3×C7×C13×D7D511yescharacteristic, complemented
15C5×C72×C13C2×D311yescharacteristic, complemented, Hall
16D7×D105C1311yesmaximal, characteristic, direct product factor, Hall
17C13×D105—71no—
18C13×D105—71no—
19C13×D105—143no—
20C13×D105D711yescharacteristic, direct product factor
21C7×C13×D15—71no—
22C3×C5×C13×D7D711yescharacteristic, complemented
23C2×C3×C5×C7×C13—71no—
24C13×D72—151noHall
25C3×C72×C13C2×D511yescharacteristic, complemented, Hall
26C2×C13×D35—211no—
27D5×C13×D7—211no—
28C3⋊(C5⋊(C7⋊D7))C2×C1311yescharacteristic, complemented
29C7×D105C2×C1311yescharacteristic, complemented
30C3×C5×C7×D7C2×C1311yescharacteristic, complemented
31C3×C5×C7×C13—23no—
32C3×C5×C7×C13C2×D711yescharacteristic, complemented
33C3×C5×C7×C13C2×D711yescharacteristic, complemented
34C13×C7⋊D7—151no—
35C7×C13×D7—151no—
36C7×C13×D7D1511yescharacteristic, complemented
37C2×C13×D21—351no—
38D3×C13×D7—351no—
39D7×D35—31noHall
40C2×C5×C7×C13—71no—
41C13×D35—31no—
42C13×D35—211no—
43C13×D35—211no—
44C13×D35—423no—
45C7×D5×C13—211no—
46C5×C13×D7D2111yescharacteristic, complemented
47C2×C13×D15—491noHall
48C3×C5×C72C22×C1311yescharacteristic, complemented, Hall
49C72×C13C2×D1511yescharacteristic, complemented, Hall
50D7×D21—51noHall
51C2×C3×C7×C13—71no—
52C13×D21—51no—
53C13×D21—351no—
54C13×D21—351no—
55C13×D21—703no—
56D3×C7×C13—351no—
57C3×C13×D7D3511yescharacteristic, complemented
58C5⋊(C7⋊D7)—31no—
59C7×D35—31no—
60C5×C7×D7D3×C1311yescharacteristic, complemented
61C5×C7×C13—23no—
62C5×C7×C13D3×D711yescharacteristic, complemented
63C5×C7×C13C2×D2111yescharacteristic, complemented
64C2×D105—71no—
65D7×D15—71no—
66C2×C3×C5×C13—71no—
67C13×D15—71no—
68C13×D15—491no—
69C2×C13×D7—1051no—
70C2×C13×D7—1051no—
71C3⋊(C7⋊D7)—51no—
72C7×D21—51no—
73C3×C7×D7D5×C1311yescharacteristic, complemented
74C3×C7×C13—23no—
75C3×C7×C13D5×D711yescharacteristic, complemented
76C3×C7×C13C2×D3511yescharacteristic, complemented
77C2×D5×C13—1471noHall
78C5×C72C2×D3×C1311yescharacteristic, complemented, Hall
79C2×C3×C5×C7—71no—
80D105—71no—
81D105—71no—
82D105—143no—
83D105C13×D711yescharacteristic, direct product factor
84C7×D15—71no—
85C3×C5×D7C13×D711yescharacteristic, complemented
86D72—151noHall
87C3×C5×C13D7211yescharacteristic, complemented, Hall
88C2×C7×C13—71no—
89C2×C7×C13—1051no—
90C13×D7—151no—
91C13×D7—1051no—
92C13×D7—1051no—
93C13×D7—2103no—
94C13×D7D10511yescharacteristic, direct product factor
95C2×D3×C13—2451noHall
96C3×C72C2×D5×C1311yescharacteristic, complemented, Hall
97C2×D35—211no—
98D5×D7—211no—
99C2×C5×C13—71no—
100D5×C13—211no—
101D5×C13—1471no—
102C3×C5×C7—23no—
103C3×C5×C7C2×C13×D711yescharacteristic, complemented
104C3×C5×C7C2×C13×D711yescharacteristic, complemented
105C7⋊D7—151no—
106C7×D7—151no—
107C7×D7C13×D1511yescharacteristic, complemented
108C7×C13—23no—
109C7×C13D7×D1511yescharacteristic, complemented
110C7×C13C2×D10511yescharacteristic, complemented
111C2×D21—351no—
112D3×D7—351no—
113C2×C3×C13—71no—
114D3×C13—351no—
115D3×C13—2451no—
116C2×C5×C7—71no—
117D35—31no—
118D35—211no—
119D35—211no—
120D35—423no—
121C5×D7C13×D2111yescharacteristic, complemented
122C7×D5—211no—
123C5×C13D7×D2111yescharacteristic, complemented, Hall
124C2×D15—491noHall
125C22×C13—7351noHall
126C72C2×C13×D1511yescharacteristic, complemented, Sylow
127C2×C3×C7—71no—
128D21—51no—
129D21—351no—
130D21—351no—
131D21—703no—
132C3×D7C13×D3511yescharacteristic, complemented
133D3×C7—351no—
134C3×C13D7×D3511yescharacteristic, complemented, Hall
135C5×C7—23no—
136C5×C7D3×C13×D711yescharacteristic, complemented
137C5×C7C2×C13×D2111yescharacteristic, complemented
138C2×C3×C5—71no—
139D15—71no—
140D15—491no—
141C2×D7—1051no—
142C2×D7—1051no—
143C2×C13—71no—
144C2×C13—1051no—
145C2×C13—7351no—
146C3×C7—23no—
147C3×C7D5×C13×D711yescharacteristic, complemented
148C3×C7C2×C13×D3511yescharacteristic, complemented
149C2×D5—1471noHall
150C3×C5C13×D7211yescharacteristic, complemented, Hall
151C2×C7—71no—
152C2×C7—1051no—
153D7—151no—
154D7—1051no—
155D7—1051no—
156D7—2103no—
157D7C13×D10511yescharacteristic, direct product factor
158C13D7×D10511yescharacteristic, direct product factor, Sylow
159C2×D3—2451noHall
160C2×C5—71no—
161D5—211no—
162D5—1471no—
163C7—23no—
164C7C13×D7×D1511yescharacteristic, complemented
165C7C2×C13×D10511yescharacteristic, complemented
166C2×C3—71no—
167D3—351no—
168D3—2451no—
169C5C13×D7×D2111yescharacteristic, complemented, Sylow
170C22—7351noSylow
171C3C13×D7×D3511yescharacteristic, complemented, Sylow
172C2—71no—
173C2—1051no—
174C2—7351no—
subgroupG/H
center, hypercenterC13D7×D105
commutator, cosocle, hypocenterC3×C5×C72C22×C13
FrattiniC1G
Fitting, socleC3×C5×C72×C13C22
LCSG ▷ C3×C5×C72
UCSC1 ◁ C13

Complements

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

NH ≅ G/Ntype
1. C3×C5×C7×C13×D7C2semidirect
2. C7×C13×D105C2semidirect
3. C13×C3⋊(C5⋊(C7⋊D7))C2semidirect
5. C3×C5×C72×C13C22semidirect
9. C5×C7×C13×D7D3semidirect
14. C3×C7×C13×D7D5semidirect
15. C5×C72×C13C2×D3semidirect
16. D7×D105C13direct (N × H)
20. C13×D105D7direct (N × H)
22. C3×C5×C13×D7D7semidirect
25. C3×C72×C13C2×D5semidirect
28. C3⋊(C5⋊(C7⋊D7))C2×C13semidirect
29. C7×D105C2×C13semidirect
30. C3×C5×C7×D7C2×C13semidirect
32. C3×C5×C7×C13C2×D7semidirect
33. C3×C5×C7×C13C2×D7semidirect
36. C7×C13×D7D15semidirect
46. C5×C13×D7D21semidirect
48. C3×C5×C72C22×C13semidirect
49. C72×C13C2×D15semidirect
57. C3×C13×D7D35semidirect
60. C5×C7×D7D3×C13semidirect
62. C5×C7×C13D3×D7semidirect
63. C5×C7×C13C2×D21semidirect
73. C3×C7×D7D5×C13semidirect
75. C3×C7×C13D5×D7semidirect
76. C3×C7×C13C2×D35semidirect
78. C5×C72C2×D3×C13semidirect
83. D105C13×D7direct (N × H)
85. C3×C5×D7C13×D7semidirect
87. C3×C5×C13D72semidirect
94. C13×D7D105direct (N × H)
96. C3×C72C2×D5×C13semidirect
103. C3×C5×C7C2×C13×D7semidirect
104. C3×C5×C7C2×C13×D7semidirect
107. C7×D7C13×D15semidirect
109. C7×C13D7×D15semidirect
110. C7×C13C2×D105semidirect
121. C5×D7C13×D21semidirect
123. C5×C13D7×D21semidirect
126. C72C2×C13×D15semidirect
132. C3×D7C13×D35semidirect
134. C3×C13D7×D35semidirect
136. C5×C7D3×C13×D7semidirect
137. C5×C7C2×C13×D21semidirect
147. C3×C7D5×C13×D7semidirect
148. C3×C7C2×C13×D35semidirect
150. C3×C5C13×D72semidirect
157. D7C13×D105direct (N × H)
158. C13D7×D105direct (N × H)
164. C7C13×D7×D15semidirect
165. C7C2×C13×D105semidirect
169. C5C13×D7×D21semidirect
171. C3C13×D7×D35semidirect

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
C7×C13×D1052
C13×C3⋊(C5⋊(C7⋊D7))2
C13×D7×D353
C13×D7×D215
C2×C13×D1057
C13×D7×D157
D7×D10513