Finite Group Databasebeta

← D39⋊D105 #30655730

Subgroups — D39⋊D105 #30655730

Order 16380.

176 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 45 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×D1365C211yesmaximal, characteristic, complemented
3C3×C5×C7×D39C211yesmaximal, characteristic, complemented
4D39⋊D35—31nomaximal
5D13×D105—31nomaximal
6C32×C5×C7×C13C2211yescharacteristic, complemented, Hall
7D39⋊D21—51nomaximal, Hall
8D1365D311yescharacteristic, complemented
9C13×D105—31no—
10C13×D105—31no—
11C13×D105—61no—
12C5×C7×D39D311yescharacteristic, complemented
13C3×D455—31no—
14C3×C5×C7×D13—31no—
15D39⋊D15—71nomaximal, Hall
16D13×D35—91noHall
17C13×C3⋊D21—51no—
18C3×D273—51no—
19C3×C7×D39D511yescharacteristic, complemented
20C3×C5×C7×C13—21no—
21C3×C5×C7×C13C2×D311yescharacteristic, complemented
22C3×C5×C7×C13C2×D311yescharacteristic, complemented
23D3×D105—131nomaximal, Hall
24C13×C3⋊D15—71no—
25C3×D195—71no—
26C3×C5×D39D711yescharacteristic, complemented
27D21⋊D13—151no—
28D13×D21—151no—
29D455—31no—
30C13×D35—91no—
31C5×C7×D13—31no—
32C32×C7×C13C2×D511yescharacteristic, complemented, Hall
33D15⋊D13—211no—
34D13×D15—211no—
35C3⋊D105D1311yescharacteristic, complemented
36C3×D105—131no—
37C3×C5×D3×C7—131no—
38C32×C5×C13C2×D711yescharacteristic, complemented, Hall
39D273—51no—
40C13×D21—151no—
41C13×D21—151no—
42C13×D21—301no—
43C7×D39D1511yescharacteristic, complemented
44C3×D91—151no—
45C3×C7×D13—31no—
46(C3⋊D3)⋊D13—351noHall
47C5×C7×C13D3211yescharacteristic, complemented, Hall
48C2×D105—391no—
49D3×D35—391no—
50D195—71no—
51C13×D15—211no—
52C13×D15—211no—
53C13×D15—421no—
54C5×D39D2111yescharacteristic, complemented
55C3×D65—211no—
56C3×C5×D13—31no—
57D7×D13—451noHall
58C32×C5×C7C2×D1311yescharacteristic, complemented, Hall
59C3×C7×C13—21no—
60C3×C7×C13D3×D511yescharacteristic, complemented
61C3×C7×C13C2×D1511yescharacteristic, complemented
62D5×D13—631noHall
63D3×D21—651noHall
64C13×C3⋊D3—351no—
65C3×D39—351no—
66C3×D39D3511yescharacteristic, complemented
67C2×C3×C5×C7—391no—
68D105—31no—
69D105—31no—
70D105—61no—
71D105—131no—
72C5×D3×C7—131no—
73C3×D35—391no—
74C3×C5×C13—21no—
75C3×C5×C13D3×D711yescharacteristic, complemented
76C3×C5×C13C2×D2111yescharacteristic, complemented
77D91—151no—
78C7×D13—31no—
79C13×D7—451no—
80D3×D15—911noHall
81D3×D13—1051no—
82D3×D13—1051no—
83C2×D35—1171noHall
84D65—211no—
85C5×D13—31no—
86D5×C13—631no—
87C3⋊D21—51no—
88C3×D21—651no—
89C3×D3×C7—131no—
90C32×C13C2×D3511yescharacteristic, complemented, Hall
91C3×C5×C7—21no—
92C3×C5×C7D3×D1311yescharacteristic, complemented
93C3×C5×C7D3×D1311yescharacteristic, complemented
94C7×C13D3×D1511yescharacteristic, complemented, Hall
95C3⋊D15—71no—
96C3×D15—911no—
97C3×C5×D3—131no—
98C2×D21—1951no—
99D3×D7—1951no—
100D39—351no—
101D39D10511yescharacteristic, complemented
102C3×D13—31no—
103C3×D13—1051no—
104D3×C13—1051no—
105D3×C13—1051no—
106D3×C13—2101no—
107C2×C5×C7—391no—
108D35—91no—
109D35—391no—
110C5×C13D3×D2111yescharacteristic, complemented, Hall
111C32×C7D5×D1311yescharacteristic, complemented, Hall
112C2×D15—2731no—
113D3×D5—2731no—
114C2×D13—3151noHall
115C32×C5D7×D1311yescharacteristic, complemented, Hall
116C2×C3×C7—391no—
117D21—151no—
118D21—151no—
119D21—301no—
120D21—651no—
121C3×D7—1951no—
122D3×C7—131no—
123C3×C13—21no—
124C3×C13D3×D3511yescharacteristic, complemented
125C3×C13C2×D10511yescharacteristic, complemented
126D32—4551noHall
127C5×C7(C3⋊D3)⋊D1311yescharacteristic, complemented, Hall
128C2×C3×C5—391no—
129D15—211no—
130D15—211no—
131D15—421no—
132D15—911no—
133C3×D5—2731no—
134C5×D3—131no—
135C2×D7—5851noHall
136C2×C13—3151no—
137D13—31no—
138D13—1051no—
139C3×C7—21no—
140C3×C7D13×D1511yescharacteristic, complemented
141C3×C7D15⋊D1311yescharacteristic, complemented
142C2×D5—8191noHall
143C3⋊D3—351no—
144C3×D3—131no—
145C3×D3—4551no—
146C3×C5—21no—
147C3×C5D13×D2111yescharacteristic, complemented
148C3×C5D21⋊D1311yescharacteristic, complemented
149C2×C7—391no—
150D7—451no—
151D7—1951no—
152C13D3×D10511yescharacteristic, complemented, Sylow
153C2×D3—13651no—
154C2×D3—13651no—
155C2×C5—391no—
156D5—2731no—
157D5—631no—
158C32D13×D3511yescharacteristic, complemented, Sylow
159C7D39⋊D1511yescharacteristic, complemented, Sylow
160C2×C3—391no—
161C2×C3—13651no—
162D3—131no—
163D3—1051no—
164D3—1051no—
165D3—4551no—
166D3—2101no—
167C5D39⋊D2111yescharacteristic, complemented, Sylow
168C22—40951noSylow
169C3—21no—
170C3D13×D10511yescharacteristic, complemented
171C3D39⋊D3511yescharacteristic, complemented
172C2—391no—
173C2—3151no—
174C2—13651no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C5×C7×C13C22
LCSG ▷ C32×C5×C7×C13
UCSC1

Complements

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

NH ≅ G/Ntype
1. C13×C3⋊D105C2semidirect
2. C3×D1365C2semidirect
3. C3×C5×C7×D39C2semidirect
6. C32×C5×C7×C13C22semidirect
8. D1365D3semidirect
12. C5×C7×D39D3semidirect
19. C3×C7×D39D5semidirect
21. C3×C5×C7×C13C2×D3semidirect
22. C3×C5×C7×C13C2×D3semidirect
26. C3×C5×D39D7semidirect
32. C32×C7×C13C2×D5semidirect
35. C3⋊D105D13semidirect
38. C32×C5×C13C2×D7semidirect
43. C7×D39D15semidirect
47. C5×C7×C13D32semidirect
54. C5×D39D21semidirect
58. C32×C5×C7C2×D13semidirect
60. C3×C7×C13D3×D5semidirect
61. C3×C7×C13C2×D15semidirect
66. C3×D39D35semidirect
75. C3×C5×C13D3×D7semidirect
76. C3×C5×C13C2×D21semidirect
90. C32×C13C2×D35semidirect
92. C3×C5×C7D3×D13semidirect
93. C3×C5×C7D3×D13semidirect
94. C7×C13D3×D15semidirect
101. D39D105semidirect
110. C5×C13D3×D21semidirect
111. C32×C7D5×D13semidirect
115. C32×C5D7×D13semidirect
124. C3×C13D3×D35semidirect
125. C3×C13C2×D105semidirect
127. C5×C7(C3⋊D3)⋊D13semidirect
140. C3×C7D13×D15semidirect
141. C3×C7D15⋊D13semidirect
147. C3×C5D13×D21semidirect
148. C3×C5D21⋊D13semidirect
152. C13D3×D105semidirect
158. C32D13×D35semidirect
159. C7D39⋊D15semidirect
167. C5D39⋊D21semidirect
170. C3D13×D105semidirect
171. C3D39⋊D35semidirect

Maximal subgroups

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

subgroupindex
C13×C3⋊D1052
C3×D13652
C3×C5×C7×D392
D39⋊D353
D13×D1053
D39⋊D215
D39⋊D157
D3×D10513