Finite Group Databasebeta

← D7×D15×C13⋊C3 #30655481

Subgroups — D7×D15×C13⋊C3 #30655481

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
2C7×D15×C13⋊C3C211yesmaximal, characteristic, complemented
3C3×C5×D7×C13⋊C3C211yesmaximal, characteristic, complemented
4C13×D7×D15C311yesmaximal, characteristic, complemented
5D5×D7×C13⋊C3—31nomaximal
6C3×C5×C7×C13⋊C3C2211yescharacteristic, complemented, Hall
7D3×D7×C13⋊C3—51nomaximal, Hall
8C13⋊C3×D35—31no—
9C7×D5×C13⋊C3—31no—
10C5×D7×C13⋊C3—21no—
11C5×D7×C13⋊C3D311yescharacteristic, complemented
12C13×D105C2×C311yescharacteristic, complemented
13C7×C13×D15C2×C311yescharacteristic, complemented
14C3×C5×C13×D7C2×C311yescharacteristic, complemented
15C2×D15×C13⋊C3—71nomaximal, Hall
16D5×C13×D7—31noHall
17C13⋊C3×D21—51no—
18D3×C7×C13⋊C3—51no—
19C3×D7×C13⋊C3D511yescharacteristic, complemented
20C3×C5×C7×C13C22×C311yescharacteristic, complemented
21C5×C7×C13⋊C3—21no—
22C5×C7×C13⋊C3C2×D311yescharacteristic, complemented
23C3×D7×D15—131nomaximal, Hall
24C2×C3×C5×C13⋊C3—71no—
25D15×C13⋊C3—71no—
26D15×C13⋊C3D711yescharacteristic, direct product factor
27D3×C13×D7—51no—
28C2×D7×C13⋊C3—151no—
29C13×D35—31no—
30C7×D5×C13—31no—
31C5×C13×D7C3×D311yescharacteristic, complemented
32C3×C7×C13⋊C3C2×D511yescharacteristic, complemented, Hall
33C2×C13×D15—71no—
34C2×D5×C13⋊C3—211no—
35C3×D105—131no—
36C3×C7×D15—131no—
37C32×C5×D7—131no—
38C3×C5×C13⋊C3C2×D711yescharacteristic, complemented, Hall
39C13×D21—51no—
40D3×C7×C13—51no—
41C3×C13×D7C3×D511yescharacteristic, complemented
42C2×C7×C13⋊C3—151no—
43D7×C13⋊C3—21no—
44D7×C13⋊C3—151no—
45D7×C13⋊C3D1511yescharacteristic, direct product factor
46C2×D3×C13⋊C3—351noHall
47C5×C7×C13C2×C3×D311yescharacteristic, complemented, Hall
48D7×D15C13⋊C311yescharacteristic, direct product factor
49C3×D5×D7—391no—
50C2×C3×C5×C13—71no—
51C13×D15—71no—
52C13×D15C3×D711yescharacteristic, complemented
53C2×C5×C13⋊C3—71no—
54C2×C5×C13⋊C3—141no—
55D5×C13⋊C3—31no—
56D5×C13⋊C3—211no—
57C2×C13×D7—151noHall
58C32×C5×C7—131noHall
59C3×C7×C13C2×C3×D511yescharacteristic, complemented
60C7×C13⋊C3—21no—
61C7×C13⋊C3C2×D1511yescharacteristic, complemented
62C2×D5×C13—211noHall
63C3×D3×D7—651noHall
64C2×C3×C13⋊C3—71no—
65D3×C13⋊C3—51no—
66D3×C13⋊C3—351no—
67D105C2×C13⋊C311yescharacteristic, complemented
68C7×D15C2×C13⋊C311yescharacteristic, complemented
69C3×D35—391no—
70C3×C7×D5—391no—
71C3×C5×D7—131no—
72C3×C5×D7—261no—
73C3×C5×D7C2×C13⋊C311yescharacteristic, complemented
74C3×C5×C13C2×C3×D711yescharacteristic, complemented
75C5×C13⋊C3—21no—
76C5×C13⋊C3D3×D711yescharacteristic, complemented
77C2×C7×C13—151no—
78C13×D7—151no—
79C13×D7C3×D1511yescharacteristic, complemented
80C2×C3×D15—911noHall
81C2×D3×C13—351no—
82C22×C13⋊C3—1051no—
83D5×D7—31noHall
84C2×C5×C13—71no—
85D5×C13—31no—
86D5×C13—211no—
87C3×D21—651no—
88C3×D3×C7—651no—
89C32×D7—131no—
90C3×C13⋊C3D5×D711yescharacteristic, complemented, Hall
91C3×C5×C7—131no—
92C3×C5×C7—261no—
93C3×C5×C7C22×C13⋊C311yescharacteristic, complemented
94C7×C13C2×C3×D1511yescharacteristic, complemented, Hall
95C2×C32×C5—911no—
96C3×D15—131no—
97C3×D15—911no—
98C2×C3×D7—1951no—
99D3×D7—51no—
100C2×C3×C13—71no—
101D3×C13—51no—
102D3×C13—351no—
103C2×C13⋊C3—71no—
104C2×C13⋊C3—141no—
105C2×C13⋊C3—151no—
106C2×C13⋊C3—1051no—
107D35—31no—
108C5×D7D3×C13⋊C311yescharacteristic, complemented
109C7×D5—31no—
110C5×C13C3×D3×D711yescharacteristic, complemented, Hall
111C32×C7—131noHall
112C2×D15—71no—
113C2×C3×D5—2731no—
114C22×C13—1051noHall
115C32×C5—131noHall
116C2×C3×C7—1951no—
117D21—51no—
118C3×D7—131no—
119C3×D7—261no—
120C3×D7—1951no—
121C3×D7D5×C13⋊C311yescharacteristic, complemented
122D3×C7—51no—
123C3×C13C3×D5×D711yescharacteristic, complemented
124C13⋊C3—21no—
125C13⋊C3D7×D1511yescharacteristic, direct product factor
126C2×C3×D3—4551noHall
127C5×C7C2×D3×C13⋊C311yescharacteristic, complemented, Hall
128C2×C3×C5—71no—
129C2×C3×C5—911no—
130C2×C3×C5—1821no—
131D15—71no—
132D15D7×C13⋊C311yescharacteristic, direct product factor
133C3×D5—2731no—
134C3×D5—391no—
135C2×D7—151noHall
136C2×C13—71no—
137C2×C13—151no—
138C2×C13—1051no—
139C3×C7—131no—
140C3×C7—261no—
141C3×C7C2×D5×C13⋊C311yescharacteristic, complemented
142C2×D5—211noHall
143C2×C32—911no—
144C3×D3—651no—
145C3×D3—4551no—
146C3×C5—131no—
147C3×C5—261no—
148C3×C5C2×D7×C13⋊C311yescharacteristic, complemented
149C2×C7—151no—
150D7—151no—
151D7D15×C13⋊C311yescharacteristic, direct product factor
152C13C3×D7×D1511yescharacteristic, complemented, Sylow
153C22×C3—13651no—
154C2×D3—351no—
155C2×C5—71no—
156D5—31no—
157D5—211no—
158C32—131noSylow
159C7C2×D15×C13⋊C311yescharacteristic, complemented, Sylow
160C2×C3—71no—
161C2×C3—13651no—
162C2×C3—911no—
163C2×C3—1821no—
164C2×C3—1951no—
165D3—51no—
166D3—351no—
167C5D3×D7×C13⋊C311yescharacteristic, complemented, Sylow
168C22—1051noSylow
169C3—131no—
170C3—261no—
171C3D5×D7×C13⋊C311yescharacteristic, complemented
172C2—71no—
173C2—151no—
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. C7×D15×C13⋊C3C2semidirect
3. C3×C5×D7×C13⋊C3C2semidirect
4. C13×D7×D15C3semidirect
6. C3×C5×C7×C13⋊C3C22semidirect
11. C5×D7×C13⋊C3D3semidirect
12. C13×D105C2×C3semidirect
13. C7×C13×D15C2×C3semidirect
14. C3×C5×C13×D7C2×C3semidirect
19. C3×D7×C13⋊C3D5semidirect
20. C3×C5×C7×C13C22×C3semidirect
22. C5×C7×C13⋊C3C2×D3semidirect
26. D15×C13⋊C3D7direct (N × H)
31. C5×C13×D7C3×D3semidirect
32. C3×C7×C13⋊C3C2×D5semidirect
38. C3×C5×C13⋊C3C2×D7semidirect
41. C3×C13×D7C3×D5semidirect
45. D7×C13⋊C3D15direct (N × H)
47. C5×C7×C13C2×C3×D3semidirect
48. D7×D15C13⋊C3direct (N × H)
52. C13×D15C3×D7semidirect
59. C3×C7×C13C2×C3×D5semidirect
61. C7×C13⋊C3C2×D15semidirect
67. D105C2×C13⋊C3semidirect
68. C7×D15C2×C13⋊C3semidirect
73. C3×C5×D7C2×C13⋊C3semidirect
74. C3×C5×C13C2×C3×D7semidirect
76. C5×C13⋊C3D3×D7semidirect
79. C13×D7C3×D15semidirect
90. C3×C13⋊C3D5×D7semidirect
93. C3×C5×C7C22×C13⋊C3semidirect
94. C7×C13C2×C3×D15semidirect
108. C5×D7D3×C13⋊C3semidirect
110. C5×C13C3×D3×D7semidirect
121. C3×D7D5×C13⋊C3semidirect
123. C3×C13C3×D5×D7semidirect
125. C13⋊C3D7×D15direct (N × H)
127. C5×C7C2×D3×C13⋊C3semidirect
132. D15D7×C13⋊C3direct (N × H)
141. C3×C7C2×D5×C13⋊C3semidirect
148. C3×C5C2×D7×C13⋊C3semidirect
151. D7D15×C13⋊C3direct (N × H)
152. C13C3×D7×D15semidirect
159. C7C2×D15×C13⋊C3semidirect
167. C5D3×D7×C13⋊C3semidirect
171. C3D5×D7×C13⋊C3semidirect

Maximal subgroups

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

subgroupindex
C13⋊C3×D1052
C7×D15×C13⋊C32
C3×C5×D7×C13⋊C32
C13×D7×D153
D5×D7×C13⋊C33
D3×D7×C13⋊C35
C2×D15×C13⋊C37
C3×D7×D1513