Finite Group Databasebeta

← D13⋊C3×D105 #30655477

Subgroups — D13⋊C3×D105 #30655477

Order 16380.

176 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 47 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
2C3⋊(C5⋊((C13⋊C3)⋊D7))C211yesmaximal, characteristic, complemented
3C3×C5×C7×D13⋊C3C211yesmaximal, characteristic, complemented
4D13×D105C311yesmaximal, characteristic, complemented
5D35×D13⋊C3—31nomaximal
6C3×C5×C7×C13⋊C3C2211yescharacteristic, complemented, Hall
7D21×D13⋊C3—51nomaximal, Hall
8C5⋊((C13⋊C3)⋊D7)—31no—
9C13⋊C3×D35—31no—
10C5×C7×D13⋊C3—21no—
11C5×C7×D13⋊C3D311yescharacteristic, complemented
12D1365C2×C311yescharacteristic, complemented
13C13×D105C2×C311yescharacteristic, complemented
14C3×C5×C7×D13C2×C311yescharacteristic, complemented
15D15×D13⋊C3—71nomaximal, Hall
16D13×D35—31noHall
17C3⋊((C13⋊C3)⋊D7)—51no—
18C13⋊C3×D21—51no—
19C3×C7×D13⋊C3D511yescharacteristic, complemented
20C3×C5×C7×C13C22×C311yescharacteristic, complemented
21C5×C7×C13⋊C3—21no—
22C5×C7×C13⋊C3C2×D311yescharacteristic, complemented
23C2×C3×D105—131nomaximal, Hall
24C3⋊(C5⋊(D13⋊C3))—71no—
25D15×C13⋊C3—71no—
26C3×C5×D13⋊C3D711yescharacteristic, complemented
27D13×D21—51no—
28D7×D13⋊C3—151no—
29D455—31no—
30C13×D35—31no—
31C5×C7×D13C3×D311yescharacteristic, complemented
32C3×C7×C13⋊C3C2×D511yescharacteristic, complemented, Hall
33D13×D15—71no—
34D5×D13⋊C3—211no—
35C2×C32×C5×C7—131no—
36C3×D105—131no—
37C3×D105—131no—
38C3×C5×C13⋊C3C2×D711yescharacteristic, complemented, Hall
39D273—51no—
40C13×D21—51no—
41C3×C7×D13C3×D511yescharacteristic, complemented
42(C13⋊C3)⋊D7—151no—
43D7×C13⋊C3—151no—
44C7×D13⋊C3—21no—
45C7×D13⋊C3D1511yescharacteristic, complemented
46D3×D13⋊C3—351noHall
47C5×C7×C13C2×C3×D311yescharacteristic, complemented, Hall
48C2×D105—131no—
49C2×C3×D35—391no—
50D195—71no—
51C13×D15—71no—
52C3×C5×D13C3×D711yescharacteristic, complemented
53C5⋊(D13⋊C3)—211no—
54D5×C13⋊C3—211no—
55C5×D13⋊C3—21no—
56C5×D13⋊C3D2111yescharacteristic, complemented
57D7×D13—151noHall
58C32×C5×C7—131noHall
59C3×C7×C13C2×C3×D511yescharacteristic, complemented
60C7×C13⋊C3—21no—
61C7×C13⋊C3C2×D1511yescharacteristic, complemented
62D5×D13—211noHall
63C2×C3×D21—651noHall
64C3⋊(D13⋊C3)—351no—
65D3×C13⋊C3—351no—
66C3×D13⋊C3D3511yescharacteristic, complemented
67C2×C3×C5×C7—131no—
68C2×C3×C5×C7—131no—
69C2×C3×C5×C7—261no—
70D105—131no—
71D105D13⋊C311yescharacteristic, direct product factor
72C3×D35—391no—
73C3×D35—781no—
74C3×C5×C13C2×C3×D711yescharacteristic, complemented
75C5×C13⋊C3—21no—
76C5×C13⋊C3C2×D2111yescharacteristic, complemented
77D91—151no—
78C7×D13C3×D1511yescharacteristic, complemented
79C13×D7—151no—
80C2×C3×D15—911noHall
81D3×D13—351no—
82C2×D13⋊C3—1051no—
83C2×D35—391noHall
84D65—211no—
85C5×D13C3×D2111yescharacteristic, complemented
86D5×C13—211no—
87C2×C32×C7—131no—
88C3×D21—651no—
89C3×D21—1301no—
90C3×C13⋊C3C2×D3511yescharacteristic, complemented, Hall
91C3×C5×C7—261no—
92C3×C5×C7—521no—
93C3×C5×C7C2×D13⋊C311yescharacteristic, complemented
94C7×C13C2×C3×D1511yescharacteristic, complemented, Hall
95C2×C32×C5—131no—
96C3×D15—911no—
97C3×D15—1821no—
98C2×D21—651no—
99C2×C3×D7—1951no—
100D39—351no—
101C3×D13C3×D3511yescharacteristic, complemented
102D3×C13—351no—
103C2×C13⋊C3—1051no—
104D13⋊C3—21no—
105D13⋊C3—1051no—
106D13⋊C3D10511yescharacteristic, direct product factor
107C2×C5×C7—131no—
108D35—31no—
109D35—391no—
110C5×C13C2×C3×D2111yescharacteristic, complemented, Hall
111C32×C7—261noHall
112C2×D15—911no—
113C2×C3×D5—2731no—
114C2×D13—1051noHall
115C32×C5—261noHall
116C2×C3×C7—131no—
117C2×C3×C7—131no—
118C2×C3×C7—261no—
119D21—51no—
120D21—651no—
121C3×D7—3901no—
122C3×D7—1951no—
123C3×C13C2×C3×D3511yescharacteristic, complemented
124C13⋊C3—21no—
125C13⋊C3C2×D10511yescharacteristic, complemented
126C2×C3×D3—4551noHall
127C5×C7D3×D13⋊C311yescharacteristic, complemented, Hall
128C2×C3×C5—131no—
129C2×C3×C5—131no—
130C2×C3×C5—261no—
131D15—71no—
132D15—911no—
133C3×D5—2731no—
134C3×D5—5461no—
135C2×D7—1951noHall
136C2×C13—1051no—
137D13—1051no—
138D13C3×D10511yescharacteristic, complemented
139C3×C7—261no—
140C3×C7—521no—
141C3×C7D5×D13⋊C311yescharacteristic, complemented
142C2×D5—2731noHall
143C2×C32—131no—
144C3×D3—9101no—
145C3×D3—4551no—
146C3×C5—261no—
147C3×C5—521no—
148C3×C5D7×D13⋊C311yescharacteristic, complemented
149C2×C7—131no—
150D7—151no—
151D7—1951no—
152C13C2×C3×D10511yescharacteristic, complemented, Sylow
153C22×C3—13651no—
154C2×D3—4551no—
155C2×C5—131no—
156D5—2731no—
157D5—211no—
158C32—261noSylow
159C7D15×D13⋊C311yescharacteristic, complemented, Sylow
160C2×C3—131no—
161C2×C3—131no—
162C2×C3—261no—
163C2×C3—13651no—
164C2×C3—27301no—
165D3—351no—
166D3—4551no—
167C5D21×D13⋊C311yescharacteristic, complemented, Sylow
168C22—13651noSylow
169C3—261no—
170C3—521no—
171C3D35×D13⋊C311yescharacteristic, complemented
172C2—131no—
173C2—13651no—
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. C3⋊(C5⋊((C13⋊C3)⋊D7))C2semidirect
3. C3×C5×C7×D13⋊C3C2semidirect
4. D13×D105C3semidirect
6. C3×C5×C7×C13⋊C3C22semidirect
11. C5×C7×D13⋊C3D3semidirect
12. D1365C2×C3semidirect
13. C13×D105C2×C3semidirect
14. C3×C5×C7×D13C2×C3semidirect
19. C3×C7×D13⋊C3D5semidirect
20. C3×C5×C7×C13C22×C3semidirect
22. C5×C7×C13⋊C3C2×D3semidirect
26. C3×C5×D13⋊C3D7semidirect
31. C5×C7×D13C3×D3semidirect
32. C3×C7×C13⋊C3C2×D5semidirect
38. C3×C5×C13⋊C3C2×D7semidirect
41. C3×C7×D13C3×D5semidirect
45. C7×D13⋊C3D15semidirect
47. C5×C7×C13C2×C3×D3semidirect
52. C3×C5×D13C3×D7semidirect
56. C5×D13⋊C3D21semidirect
59. C3×C7×C13C2×C3×D5semidirect
61. C7×C13⋊C3C2×D15semidirect
66. C3×D13⋊C3D35semidirect
71. D105D13⋊C3direct (N × H)
74. C3×C5×C13C2×C3×D7semidirect
76. C5×C13⋊C3C2×D21semidirect
78. C7×D13C3×D15semidirect
85. C5×D13C3×D21semidirect
90. C3×C13⋊C3C2×D35semidirect
93. C3×C5×C7C2×D13⋊C3semidirect
94. C7×C13C2×C3×D15semidirect
101. C3×D13C3×D35semidirect
106. D13⋊C3D105direct (N × H)
110. C5×C13C2×C3×D21semidirect
123. C3×C13C2×C3×D35semidirect
125. C13⋊C3C2×D105semidirect
127. C5×C7D3×D13⋊C3semidirect
138. D13C3×D105semidirect
141. C3×C7D5×D13⋊C3semidirect
148. C3×C5D7×D13⋊C3semidirect
152. C13C2×C3×D105semidirect
159. C7D15×D13⋊C3semidirect
167. C5D21×D13⋊C3semidirect
171. C3D35×D13⋊C3semidirect

Maximal subgroups

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

subgroupindex
C13⋊C3×D1052
C3⋊(C5⋊((C13⋊C3)⋊D7))2
C3×C5×C7×D13⋊C32
D13×D1053
D35×D13⋊C33
D21×D13⋊C35
D15×D13⋊C37
C2×C3×D10513