Finite Group Databasebeta

← D3×C13⋊C3×D35 #30655541

Subgroups — D3×C13⋊C3×D35 #30655541

Order 16380.

176 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 48 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
1C13⋊C3×D105C211yesmaximal, characteristic, complemented
2C5×D3×C7×C13⋊C3C211yesmaximal, characteristic, complemented
3C3×C13⋊C3×D35C211yesmaximal, characteristic, complemented
4D3×C13×D35C311yesmaximal, characteristic, complemented
5C2×C13⋊C3×D35—31nomaximal
6C3×C5×C7×C13⋊C3C2211yescharacteristic, complemented, Hall
7D3×D7×C13⋊C3—51nomaximal, Hall
8C13⋊C3×D35—21no—
9C13⋊C3×D35—31no—
10C13⋊C3×D35D311yescharacteristic, direct product factor
11C13×D105C2×C311yescharacteristic, complemented
12C5×D3×C7×C13C2×C311yescharacteristic, complemented
13C3×C13×D35C2×C311yescharacteristic, complemented
14C2×C5×C7×C13⋊C3—31no—
15D3×D5×C13⋊C3—71nomaximal, Hall
16C2×C13×D35—31noHall
17C13⋊C3×D21—51no—
18D3×C7×C13⋊C3D511yescharacteristic, complemented
19C3×D7×C13⋊C3—51no—
20C3×C5×C7×C13C22×C311yescharacteristic, complemented
21C5×C7×C13⋊C3—21no—
22C5×C7×C13⋊C3C2×D311yescharacteristic, complemented
23C3×D3×D35—131nomaximal, Hall
24D15×C13⋊C3—71no—
25C5×D3×C13⋊C3D711yescharacteristic, complemented
26C3×D5×C13⋊C3—71no—
27D3×C13×D7—51no—
28C2×D7×C13⋊C3—151no—
29C2×C5×C7×C13—31no—
30C13×D35—31no—
31C13×D35C3×D311yescharacteristic, complemented
32C3×C7×C13⋊C3C2×D511yescharacteristic, complemented, Hall
33D3×D5×C13—71no—
34C2×D5×C13⋊C3—211no—
35C3×D105—131no—
36C3×C5×D3×C7—131no—
37C32×D35—131no—
38C3×C5×C13⋊C3C2×D711yescharacteristic, complemented, Hall
39C13×D21—51no—
40D3×C7×C13C3×D511yescharacteristic, complemented
41C3×C13×D7—51no—
42C2×C7×C13⋊C3—31no—
43D7×C13⋊C3—51no—
44D7×C13⋊C3—101no—
45D7×C13⋊C3—151no—
46C2×D3×C13⋊C3—351noHall
47C5×C7×C13C2×C3×D311yescharacteristic, complemented, Hall
48C2×C3×D35—391no—
49D3×D35C13⋊C311yescharacteristic, direct product factor
50C13×D15—71no—
51C5×D3×C13C3×D711yescharacteristic, complemented
52C3×D5×C13—71no—
53C2×C5×C13⋊C3—31no—
54D5×C13⋊C3—71no—
55D5×C13⋊C3—141no—
56D5×C13⋊C3—211no—
57C2×C13×D7—151noHall
58C32×C5×C7—131noHall
59C3×C7×C13C2×C3×D511yescharacteristic, complemented
60C7×C13⋊C3—21no—
61C7×C13⋊C3D3×D511yescharacteristic, complemented
62C2×D5×C13—211noHall
63C3×D3×D7—651noHall
64C2×C3×C13⋊C3—351no—
65D3×C13⋊C3—351no—
66D3×C13⋊C3D3511yescharacteristic, direct product factor
67C2×C3×C5×C7—391no—
68D105C2×C13⋊C311yescharacteristic, complemented
69C5×D3×C7C2×C13⋊C311yescharacteristic, complemented
70C3×D35—131no—
71C3×D35—261no—
72C3×D35—391no—
73C3×D35C2×C13⋊C311yescharacteristic, complemented
74C3×C5×C13C2×C3×D711yescharacteristic, complemented
75C5×C13⋊C3—21no—
76C5×C13⋊C3D3×D711yescharacteristic, complemented
77C2×C7×C13—31no—
78C13×D7—51no—
79C13×D7—151no—
80C3×D3×D5—911noHall
81C2×D3×C13—351no—
82C22×C13⋊C3—1051no—
83C2×D35—31noHall
84C2×C5×C13—31no—
85D5×C13—71no—
86D5×C13—211no—
87C3×D21—651no—
88C3×D3×C7—131no—
89C32×D7—651no—
90C3×C13⋊C3C2×D3511yescharacteristic, complemented, Hall
91C3×C5×C7—131no—
92C3×C5×C7—261no—
93C3×C5×C7C22×C13⋊C311yescharacteristic, complemented
94C7×C13C3×D3×D511yescharacteristic, complemented, Hall
95C3×D15—911no—
96C3×C5×D3—131no—
97C32×D5—911no—
98C2×C3×D7—1951no—
99D3×D7—51no—
100C2×C3×C13—351no—
101D3×C13—351no—
102D3×C13C3×D3511yescharacteristic, complemented
103C2×C13⋊C3—31no—
104C2×C13⋊C3—351no—
105C2×C13⋊C3—701no—
106C2×C13⋊C3—1051no—
107C2×C5×C7—31no—
108D35—31no—
109D35D3×C13⋊C311yescharacteristic, direct product factor
110C5×C13C3×D3×D711yescharacteristic, complemented, Hall
111C32×C7—131noHall
112C2×C3×D5—2731no—
113D3×D5—71no—
114C22×C13—1051noHall
115C32×C5—131noHall
116C2×C3×C7—391no—
117D21—51no—
118C3×D7—51no—
119C3×D7—651no—
120C3×D7—1301no—
121C3×D7—1951no—
122D3×C7D5×C13⋊C311yescharacteristic, complemented
123C3×C13C2×C3×D3511yescharacteristic, complemented
124C13⋊C3—21no—
125C13⋊C3D3×D3511yescharacteristic, direct product factor
126C2×C3×D3—4551noHall
127C5×C7C2×D3×C13⋊C311yescharacteristic, complemented, Hall
128C2×C3×C5—391no—
129D15—71no—
130C3×D5—71no—
131C3×D5—2731no—
132C3×D5—911no—
133C3×D5—1821no—
134C5×D3D7×C13⋊C311yescharacteristic, complemented
135C2×D7—151noHall
136C2×C13—31no—
137C2×C13—351no—
138C2×C13—1051no—
139C3×C7—131no—
140C3×C7—261no—
141C3×C7C2×D5×C13⋊C311yescharacteristic, complemented
142C2×D5—211noHall
143C2×C32—4551no—
144C3×D3—131no—
145C3×D3—4551no—
146C3×C5—131no—
147C3×C5—261no—
148C3×C5C2×D7×C13⋊C311yescharacteristic, complemented
149C2×C7—31no—
150D7—51no—
151D7—151no—
152C13C3×D3×D3511yescharacteristic, complemented, Sylow
153C22×C3—13651no—
154C2×D3—351no—
155C2×C5—31no—
156D5—71no—
157D5—211no—
158C32—131noSylow
159C7D3×D5×C13⋊C311yescharacteristic, complemented, Sylow
160C2×C3—351no—
161C2×C3—391no—
162C2×C3—13651no—
163C2×C3—9101no—
164C2×C3—4551no—
165D3—351no—
166D3C13⋊C3×D3511yescharacteristic, direct product factor
167C5D3×D7×C13⋊C311yescharacteristic, complemented, Sylow
168C22—1051noSylow
169C3—131no—
170C3—261no—
171C3C2×C13⋊C3×D3511yescharacteristic, complemented
172C2—31no—
173C2—351no—
174C2—1051no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C7×C13C22×C3
LCSG ▷ C3×C5×C7×C13
UCSC1

Complements

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

NH ≅ G/Ntype
1. C13⋊C3×D105C2semidirect
2. C5×D3×C7×C13⋊C3C2semidirect
3. C3×C13⋊C3×D35C2semidirect
4. D3×C13×D35C3semidirect
6. C3×C5×C7×C13⋊C3C22semidirect
10. C13⋊C3×D35D3direct (N × H)
11. C13×D105C2×C3semidirect
12. C5×D3×C7×C13C2×C3semidirect
13. C3×C13×D35C2×C3semidirect
18. D3×C7×C13⋊C3D5semidirect
20. C3×C5×C7×C13C22×C3semidirect
22. C5×C7×C13⋊C3C2×D3semidirect
25. C5×D3×C13⋊C3D7semidirect
31. C13×D35C3×D3semidirect
32. C3×C7×C13⋊C3C2×D5semidirect
38. C3×C5×C13⋊C3C2×D7semidirect
40. D3×C7×C13C3×D5semidirect
47. C5×C7×C13C2×C3×D3semidirect
49. D3×D35C13⋊C3direct (N × H)
51. C5×D3×C13C3×D7semidirect
59. C3×C7×C13C2×C3×D5semidirect
61. C7×C13⋊C3D3×D5semidirect
66. D3×C13⋊C3D35direct (N × H)
68. D105C2×C13⋊C3semidirect
69. C5×D3×C7C2×C13⋊C3semidirect
73. C3×D35C2×C13⋊C3semidirect
74. C3×C5×C13C2×C3×D7semidirect
76. C5×C13⋊C3D3×D7semidirect
90. C3×C13⋊C3C2×D35semidirect
93. C3×C5×C7C22×C13⋊C3semidirect
94. C7×C13C3×D3×D5semidirect
102. D3×C13C3×D35semidirect
109. D35D3×C13⋊C3direct (N × H)
110. C5×C13C3×D3×D7semidirect
122. D3×C7D5×C13⋊C3semidirect
123. C3×C13C2×C3×D35semidirect
125. C13⋊C3D3×D35direct (N × H)
127. C5×C7C2×D3×C13⋊C3semidirect
134. C5×D3D7×C13⋊C3semidirect
141. C3×C7C2×D5×C13⋊C3semidirect
148. C3×C5C2×D7×C13⋊C3semidirect
152. C13C3×D3×D35semidirect
159. C7D3×D5×C13⋊C3semidirect
166. D3C13⋊C3×D35direct (N × H)
167. C5D3×D7×C13⋊C3semidirect
171. C3C2×C13⋊C3×D35semidirect

Maximal subgroups

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

subgroupindex
C13⋊C3×D1052
C5×D3×C7×C13⋊C32
C3×C13⋊C3×D352
D3×C13×D353
C2×C13⋊C3×D353
D3×D7×C13⋊C35
D3×D5×C13⋊C37
C3×D3×D3513