Finite Group Databasebeta

← C13×D21×D35 #50304467

Subgroups — C13×D21×D35 #50304467

Order 38220.

208 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 52 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×C7×C13×D21C211yesmaximal, 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×D35D311yescharacteristic, complemented
9C5×C7×C13×D7—31no—
10D3×C13×D35—71nomaximal
11D5×C13×D21—71nomaximal
12C13×C3⋊(C7⋊D7)—51no—
13C7×C13×D21D511yescharacteristic, complemented
14C3×C7×C13×D7—51no—
15C5×C72×C13C2×D311yescharacteristic, complemented, Hall
16D21×D35C1311yesmaximal, characteristic, direct product factor, Hall
17C13×D105—71no—
18C13×D105—71no—
19C13×D105—143no—
20C5×C13×D21D711yescharacteristic, complemented
21C5×D3×C7×C13—71no—
22C3×C13×D35D711yescharacteristic, complemented
23C3×C7×D5×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
29C5×C7×D21C2×C1311yescharacteristic, complemented
30C3×C7×D35C2×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—31no—
36C7×C13×D7—51no—
37C2×C13×D21—351no—
38D3×C13×D7—351no—
39D7×D35—31noHall
40C2×C5×C7×C13—211no—
41C13×D35—211no—
42C13×D35—211no—
43C13×D35—423no—
44C13×D35D2111yescharacteristic, direct product factor
45C7×D5×C13—71no—
46C5×C13×D7—31no—
47D3×D5×C13—491noHall
48C3×C5×C72C22×C1311yescharacteristic, complemented, Hall
49C72×C13D3×D511yescharacteristic, complemented, Hall
50D7×D21—51noHall
51C2×C3×C7×C13—351no—
52C13×D21—351no—
53C13×D21—351no—
54C13×D21—703no—
55C13×D21D3511yescharacteristic, direct product factor
56D3×C7×C13—71no—
57C3×C13×D7—51no—
58C5⋊(C7⋊D7)—31no—
59C7×D35D3×C1311yescharacteristic, complemented
60C5×C7×D7—31no—
61C5×C7×C13—23no—
62C5×C7×C13D3×D711yescharacteristic, complemented
63C5×C7×C13C2×D2111yescharacteristic, complemented
64D3×D35—71no—
65D5×D21—71no—
66C13×D15—491no—
67C5×D3×C13—71no—
68C3×D5×C13—71no—
69C2×C13×D7—1051no—
70C2×C13×D7—1051no—
71C3⋊(C7⋊D7)—51no—
72C7×D21D5×C1311yescharacteristic, complemented
73C3×C7×D7—51no—
74C3×C7×C13—23no—
75C3×C7×C13D5×D711yescharacteristic, complemented
76C3×C7×C13C2×D3511yescharacteristic, complemented
77C2×D5×C13—1471noHall
78C5×C72C2×D3×C1311yescharacteristic, complemented, Hall
79D105—71no—
80D105—71no—
81D105—143no—
82C5×D21C13×D711yescharacteristic, complemented
83C5×D3×C7—71no—
84C3×D35C13×D711yescharacteristic, complemented
85C3×C7×D5—71no—
86D72—151noHall
87C3×C5×C13D7211yescharacteristic, complemented, Hall
88C2×C7×C13—211no—
89C2×C7×C13—351no—
90C13×D7—31no—
91C13×D7—51no—
92C13×D7—1051no—
93C13×D7—1051no—
94C13×D7—2103no—
95C2×D3×C13—2451noHall
96C3×C72C2×D5×C1311yescharacteristic, complemented, Hall
97C2×D35—211no—
98D5×D7—211no—
99C2×C5×C13—211no—
100D5×C13—71no—
101D5×C13—1471no—
102C3×C5×C7—23no—
103C3×C5×C7C2×C13×D711yescharacteristic, complemented
104C3×C5×C7C2×C13×D711yescharacteristic, complemented
105C7⋊D7—151no—
106C7×D7—31no—
107C7×D7—51no—
108C7×C13—23no—
109C7×C13D5×D2111yescharacteristic, complemented
110C7×C13D3×D3511yescharacteristic, complemented
111C2×D21—351no—
112D3×D7—351no—
113C2×C3×C13—351no—
114D3×C13—71no—
115D3×C13—2451no—
116C2×C5×C7—211no—
117D35—211no—
118D35—211no—
119D35—423no—
120D35C13×D2111yescharacteristic, direct product factor
121C5×D7—31no—
122C7×D5—71no—
123C5×C13D7×D2111yescharacteristic, complemented, Hall
124D3×D5—491noHall
125C22×C13—7351noHall
126C72D3×D5×C1311yescharacteristic, complemented, Sylow
127C2×C3×C7—351no—
128D21—351no—
129D21—351no—
130D21—703no—
131D21C13×D3511yescharacteristic, direct product factor
132C3×D7—51no—
133D3×C7—71no—
134C3×C13D7×D3511yescharacteristic, complemented, Hall
135C5×C7—23no—
136C5×C7D3×C13×D711yescharacteristic, complemented
137C5×C7C2×C13×D2111yescharacteristic, complemented
138D15—491no—
139C3×D5—71no—
140C5×D3—71no—
141C2×D7—1051no—
142C2×D7—1051no—
143C2×C13—211no—
144C2×C13—351no—
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—211no—
152C2×C7—351no—
153D7—31no—
154D7—51no—
155D7—1051no—
156D7—1051no—
157D7—2103no—
158C13D21×D3511yescharacteristic, direct product factor, Sylow
159C2×D3—2451noHall
160C2×C5—211no—
161D5—71no—
162D5—1471no—
163C7—23no—
164C7D5×C13×D2111yescharacteristic, complemented
165C7D3×C13×D3511yescharacteristic, complemented
166C2×C3—351no—
167D3—71no—
168D3—2451no—
169C5C13×D7×D2111yescharacteristic, complemented, Sylow
170C22—7351noSylow
171C3C13×D7×D3511yescharacteristic, complemented, Sylow
172C2—211no—
173C2—351no—
174C2—7351no—
subgroupG/H
center, hypercenterC13D21×D35
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×C7×C13×D35C2semidirect
2. C5×C7×C13×D21C2semidirect
3. C13×C3⋊(C5⋊(C7⋊D7))C2semidirect
5. C3×C5×C72×C13C22semidirect
8. C7×C13×D35D3semidirect
13. C7×C13×D21D5semidirect
15. C5×C72×C13C2×D3semidirect
16. D21×D35C13direct (N × H)
20. C5×C13×D21D7semidirect
22. C3×C13×D35D7semidirect
25. C3×C72×C13C2×D5semidirect
28. C3⋊(C5⋊(C7⋊D7))C2×C13semidirect
29. C5×C7×D21C2×C13semidirect
30. C3×C7×D35C2×C13semidirect
32. C3×C5×C7×C13C2×D7semidirect
33. C3×C5×C7×C13C2×D7semidirect
44. C13×D35D21direct (N × H)
48. C3×C5×C72C22×C13semidirect
49. C72×C13D3×D5semidirect
55. C13×D21D35direct (N × H)
59. C7×D35D3×C13semidirect
62. C5×C7×C13D3×D7semidirect
63. C5×C7×C13C2×D21semidirect
72. C7×D21D5×C13semidirect
75. C3×C7×C13D5×D7semidirect
76. C3×C7×C13C2×D35semidirect
78. C5×C72C2×D3×C13semidirect
82. C5×D21C13×D7semidirect
84. C3×D35C13×D7semidirect
87. C3×C5×C13D72semidirect
96. C3×C72C2×D5×C13semidirect
103. C3×C5×C7C2×C13×D7semidirect
104. C3×C5×C7C2×C13×D7semidirect
109. C7×C13D5×D21semidirect
110. C7×C13D3×D35semidirect
120. D35C13×D21direct (N × H)
123. C5×C13D7×D21semidirect
126. C72D3×D5×C13semidirect
131. D21C13×D35direct (N × H)
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
158. C13D21×D35direct (N × H)
164. C7D5×C13×D21semidirect
165. C7D3×C13×D35semidirect
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×C7×C13×D352
C5×C7×C13×D212
C13×C3⋊(C5⋊(C7⋊D7))2
C13×D7×D353
C13×D7×D215
D3×C13×D357
D5×C13×D217
D21×D3513