Finite Group Databasebeta

← D3×D1365 #30655729

Subgroups — D3×D1365 #30655729

Order 16380.

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

normal subgroups only

This group has 176 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⋊D1365C211yesmaximal, characteristic, complemented
2C3×D1365C211yesmaximal, characteristic, complemented
3C3×C5×D3×C7×C13C211yesmaximal, characteristic, complemented
4C2×D1365—31nomaximal
5D3×D455—31nomaximal
6C32×C5×C7×C13C2211yescharacteristic, complemented, Hall
7D3×D273—51nomaximal, Hall
8D1365—31no—
9D1365—31no—
10D1365—61no—
11D1365D311yescharacteristic, direct product factor
12C5×D3×C7×C13D311yescharacteristic, complemented
13C3×D455—31no—
14C2×C3×C5×C7×C13—31no—
15D3×D195—71nomaximal, Hall
16C2×D455—91noHall
17C3⋊D273—51no—
18C3×D273—51no—
19C3×D3×C7×C13D511yescharacteristic, complemented
20C3×C5×C7×C13—21no—
21C3×C5×C7×C13C2×D311yescharacteristic, complemented
22C3×C5×C7×C13C2×D311yescharacteristic, complemented
23D3×D105—131nomaximal, Hall
24C3⋊D195—71no—
25C3×D195—71no—
26C3×C5×D3×C13D711yescharacteristic, complemented
27C2×D273—151no—
28D3×D91—151no—
29C2×C5×C7×C13—31no—
30D455—31no—
31D455—91no—
32C32×C7×C13C2×D511yescharacteristic, complemented, Hall
33C2×D195—211no—
34D3×D65—211no—
35C3⋊D105—131no—
36C3×D105—131no—
37C3×C5×D3×C7D1311yescharacteristic, complemented
38C32×C5×C13C2×D711yescharacteristic, complemented, Hall
39C2×C3×C7×C13—31no—
40D273—51no—
41D273—151no—
42D273—151no—
43D273—301no—
44D3×C7×C13D1511yescharacteristic, complemented
45C3×D91—151no—
46D3×D39—351noHall
47C5×C7×C13D3211yescharacteristic, complemented, Hall
48C2×D105—391no—
49D3×D35—391no—
50C2×C3×C5×C13—31no—
51D195—71no—
52D195—211no—
53D195—211no—
54D195—421no—
55C5×D3×C13D2111yescharacteristic, complemented
56C3×D65—211no—
57C2×D91—451noHall
58C32×C5×C7C2×D1311yescharacteristic, complemented, Hall
59C3×C7×C13—21no—
60C3×C7×C13D3×D511yescharacteristic, complemented
61C3×C7×C13C2×D1511yescharacteristic, complemented
62C2×D65—631noHall
63D3×D21—651noHall
64C3⋊D39—351no—
65C3×D39—351no—
66C3×D3×C13D3511yescharacteristic, complemented
67C2×C3×C5×C7—31no—
68D105—131no—
69D105—391no—
70D105—391no—
71D105—781no—
72C5×D3×C7D3911yescharacteristic, complemented
73C3×D35—391no—
74C3×C5×C13—21no—
75C3×C5×C13D3×D711yescharacteristic, complemented
76C3×C5×C13C2×D2111yescharacteristic, complemented
77C2×C7×C13—31no—
78D91—151no—
79D91—451no—
80D3×D15—911noHall
81C2×D39—1051no—
82D3×D13—1051no—
83C2×D35—1171noHall
84C2×C5×C13—31no—
85D65—211no—
86D65—631no—
87C3⋊D21—651no—
88C3×D21—651no—
89C3×D3×C7D6511yescharacteristic, complemented
90C32×C13C2×D3511yescharacteristic, complemented, Hall
91C3×C5×C7—21no—
92C3×C5×C7D3×D1311yescharacteristic, complemented
93C3×C5×C7C2×D3911yescharacteristic, complemented
94C7×C13D3×D1511yescharacteristic, complemented, Hall
95C3⋊D15—911no—
96C3×D15—911no—
97C3×C5×D3D9111yescharacteristic, complemented
98C2×D21—1951no—
99D3×D7—1951no—
100C2×C3×C13—31no—
101D39—351no—
102D39—1051no—
103D39—1051no—
104D39—2101no—
105C3×D13—1051no—
106D3×C13D10511yescharacteristic, complemented
107C2×C5×C7—31no—
108D35—391no—
109D35—1171no—
110C5×C13D3×D2111yescharacteristic, complemented, Hall
111C32×C7C2×D6511yescharacteristic, complemented, Hall
112C2×D15—2731no—
113D3×D5—2731no—
114C2×D13—3151noHall
115C32×C5C2×D9111yescharacteristic, complemented, Hall
116C2×C3×C7—31no—
117D21—651no—
118D21—3901no—
119D21—1951no—
120D21—1951no—
121C3×D7—1951no—
122D3×C7D19511yescharacteristic, complemented
123C3×C13—21no—
124C3×C13D3×D3511yescharacteristic, complemented
125C3×C13C2×D10511yescharacteristic, complemented
126D32—4551noHall
127C5×C7D3×D3911yescharacteristic, complemented, Hall
128C2×C3×C5—31no—
129D15—2731no—
130D15—2731no—
131D15—5461no—
132D15—911no—
133C3×D5—2731no—
134C5×D3D27311yescharacteristic, complemented
135C2×D7—5851noHall
136C2×C13—31no—
137D13—3151no—
138D13—1051no—
139C3×C7—21no—
140C3×C7D3×D6511yescharacteristic, complemented
141C3×C7C2×D19511yescharacteristic, complemented
142C2×D5—8191noHall
143C3⋊D3—4551no—
144C3×D3—4551no—
145C3×D3D45511yescharacteristic, complemented
146C3×C5—21no—
147C3×C5D3×D9111yescharacteristic, complemented
148C3×C5C2×D27311yescharacteristic, complemented
149C2×C7—31no—
150D7—5851no—
151D7—1951no—
152C13D3×D10511yescharacteristic, complemented, Sylow
153C2×D3—13651no—
154C2×D3—13651no—
155C2×C5—31no—
156D5—2731no—
157D5—8191no—
158C32C2×D45511yescharacteristic, complemented, Sylow
159C7D3×D19511yescharacteristic, complemented, Sylow
160C2×C3—31no—
161C2×C3—13651no—
162D3—13651no—
163D3—13651no—
164D3—27301no—
165D3—4551no—
166D3D136511yescharacteristic, direct product factor
167C5D3×D27311yescharacteristic, complemented, Sylow
168C22—40951noSylow
169C3—21no—
170C3D3×D45511yescharacteristic, complemented
171C3C2×D136511yescharacteristic, complemented
172C2—31no—
173C2—13651no—
174C2—40951no—
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. C3⋊D1365C2semidirect
2. C3×D1365C2semidirect
3. C3×C5×D3×C7×C13C2semidirect
6. C32×C5×C7×C13C22semidirect
11. D1365D3direct (N × H)
12. C5×D3×C7×C13D3semidirect
19. C3×D3×C7×C13D5semidirect
21. C3×C5×C7×C13C2×D3semidirect
22. C3×C5×C7×C13C2×D3semidirect
26. C3×C5×D3×C13D7semidirect
32. C32×C7×C13C2×D5semidirect
37. C3×C5×D3×C7D13semidirect
38. C32×C5×C13C2×D7semidirect
44. D3×C7×C13D15semidirect
47. C5×C7×C13D32semidirect
55. C5×D3×C13D21semidirect
58. C32×C5×C7C2×D13semidirect
60. C3×C7×C13D3×D5semidirect
61. C3×C7×C13C2×D15semidirect
66. C3×D3×C13D35semidirect
72. C5×D3×C7D39semidirect
75. C3×C5×C13D3×D7semidirect
76. C3×C5×C13C2×D21semidirect
89. C3×D3×C7D65semidirect
90. C32×C13C2×D35semidirect
92. C3×C5×C7D3×D13semidirect
93. C3×C5×C7C2×D39semidirect
94. C7×C13D3×D15semidirect
97. C3×C5×D3D91semidirect
106. D3×C13D105semidirect
110. C5×C13D3×D21semidirect
111. C32×C7C2×D65semidirect
115. C32×C5C2×D91semidirect
122. D3×C7D195semidirect
124. C3×C13D3×D35semidirect
125. C3×C13C2×D105semidirect
127. C5×C7D3×D39semidirect
134. C5×D3D273semidirect
140. C3×C7D3×D65semidirect
141. C3×C7C2×D195semidirect
145. C3×D3D455semidirect
147. C3×C5D3×D91semidirect
148. C3×C5C2×D273semidirect
152. C13D3×D105semidirect
158. C32C2×D455semidirect
159. C7D3×D195semidirect
166. D3D1365direct (N × H)
167. C5D3×D273semidirect
170. C3D3×D455semidirect
171. C3C2×D1365semidirect

Maximal subgroups

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

subgroupindex
C3⋊D13652
C3×D13652
C3×C5×D3×C7×C132
C2×D13653
D3×D4553
D3×D2735
D3×D1957
D3×D10513