Finite Group Databasebeta

← C3×D5×D273 #30655663

Subgroups — C3×D5×D273 #30655663

Order 16380.

176 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 56 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×C5×D273C211yesmaximal, characteristic, complemented
3C32×C7×D5×C13C211yesmaximal, characteristic, complemented
4D5×D273C311yesmaximal, characteristic, direct product factor
5C3×D5×D91—31nomaximal
6C32×C5×C7×C13C2211yescharacteristic, complemented, Hall
7C2×C3×D273—51nomaximal, Hall
8D1365C2×C311yescharacteristic, complemented
9C5×D273C2×C311yescharacteristic, complemented
10C3×D455—31no—
11C3×C7×D5×C13—21no—
12C3×C7×D5×C13D311yescharacteristic, complemented
13C3×C7×D5×C13C2×C311yescharacteristic, complemented
14C3×C5×D91—31no—
15C3×D5×D39—71nomaximal, Hall
16D5×D91—31noHall
17C2×C32×C7×C13—51no—
18C3×D273—51no—
19C3×D273D511yescharacteristic, direct product factor
20C3×C5×C7×C13—21no—
21C3×C5×C7×C13C2×D311yescharacteristic, complemented
22C3×C5×C7×C13C22×C311yescharacteristic, complemented
23C3×D5×D21—131nomaximal, Hall
24C3×D195—71no—
25C3×C5×D39—71no—
26C32×D5×C13D711yescharacteristic, complemented
27C2×D273—51no—
28C2×C3×D91—151no—
29D455—31no—
30C7×D5×C13C3×D311yescharacteristic, complemented
31C5×D91—31no—
32C32×C7×C13C2×D511yescharacteristic, complemented, Hall
33D5×D39—71no—
34C3×D5×D13—211no—
35C3×D105—131no—
36C3×C5×D21—131no—
37C32×C7×D5D1311yescharacteristic, complemented
38C32×C5×C13C2×D711yescharacteristic, complemented, Hall
39C2×C3×C7×C13—51no—
40C2×C3×C7×C13—51no—
41C2×C3×C7×C13—101no—
42D273—51no—
43D273C3×D511yescharacteristic, direct product factor
44C3×D91—31no—
45C3×D91—151no—
46C2×C3×D39—351noHall
47C5×C7×C13C2×C3×D311yescharacteristic, complemented, Hall
48D5×D21—131no—
49C3×D5×D7—391no—
50D195—71no—
51C5×D39—71no—
52C3×D65—211no—
53C3×D5×C13—21no—
54C3×D5×C13C3×D711yescharacteristic, complemented
55C3×D5×C13D2111yescharacteristic, complemented
56C3×C5×D13—211no—
57C2×D91—151noHall
58C32×C5×C7C2×D1311yescharacteristic, complemented, Hall
59C3×C7×C13—21no—
60C3×C7×C13D3×D511yescharacteristic, complemented
61C3×C7×C13C2×C3×D511yescharacteristic, complemented
62D5×D13—211noHall
63C2×C3×D21—651noHall
64C2×C32×C13—51no—
65C3×D39—71no—
66C3×D39—351no—
67D105—131no—
68C5×D21—131no—
69C3×D35—391no—
70C3×C7×D5—21no—
71C3×C7×D5C3×D1311yescharacteristic, complemented
72C3×C7×D5D3911yescharacteristic, complemented
73C3×C5×D7—391no—
74C3×C5×C13—21no—
75C3×C5×C13C2×C3×D711yescharacteristic, complemented
76C3×C5×C13C2×D2111yescharacteristic, complemented
77C2×C7×C13—51no—
78D91—31no—
79D91—151no—
80C3×D3×D5—911noHall
81C2×D39—351no—
82C2×C3×D13—1051no—
83D5×D7—391noHall
84D65—211no—
85C5×D13—211no—
86D5×C13C3×D2111yescharacteristic, complemented
87C2×C32×C7—51no—
88C3×D21—131no—
89C3×D21—651no—
90C32×C13D5×D711yescharacteristic, complemented, Hall
91C3×C5×C7—21no—
92C3×C5×C7C2×C3×D1311yescharacteristic, complemented
93C3×C5×C7C2×D3911yescharacteristic, complemented
94C7×C13C3×D3×D511yescharacteristic, complemented, Hall
95C3×D15—911no—
96C3×C5×D3—911no—
97C32×D5D9111yescharacteristic, complemented
98C2×D21—651no—
99C2×C3×D7—1951no—
100C2×C3×C13—51no—
101C2×C3×C13—51no—
102C2×C3×C13—101no—
103D39—71no—
104D39—351no—
105C3×D13—211no—
106C3×D13—1051no—
107D35—391no—
108C5×D7—391no—
109C7×D5C3×D3911yescharacteristic, complemented
110C5×C13C2×C3×D2111yescharacteristic, complemented, Hall
111C32×C7D5×D1311yescharacteristic, complemented, Hall
112C2×C3×D5—2731no—
113D3×D5—911no—
114C2×D13—1051noHall
115C32×C5C2×D9111yescharacteristic, complemented, Hall
116C2×C3×C7—51no—
117C2×C3×C7—51no—
118C2×C3×C7—101no—
119D21—131no—
120D21—651no—
121C3×D7—391no—
122C3×D7—1951no—
123C3×C13—21no—
124C3×C13C3×D5×D711yescharacteristic, complemented
125C3×C13D5×D2111yescharacteristic, complemented
126C2×C3×D3—4551noHall
127C5×C7C2×C3×D3911yescharacteristic, complemented, Hall
128C2×C3×C5—2731no—
129D15—911no—
130C3×D5—21no—
131C3×D5—2731no—
132C3×D5C3×D9111yescharacteristic, complemented
133C3×D5D27311yescharacteristic, direct product factor
134C5×D3—911no—
135C2×D7—1951noHall
136C2×C13—51no—
137D13—211no—
138D13—1051no—
139C3×C7—21no—
140C3×C7C3×D5×D1311yescharacteristic, complemented
141C3×C7D5×D3911yescharacteristic, complemented
142C2×D5—2731noHall
143C2×C32—51no—
144C3×D3—911no—
145C3×D3—4551no—
146C3×C5—21no—
147C3×C5C2×C3×D9111yescharacteristic, complemented
148C3×C5C2×D27311yescharacteristic, complemented
149C2×C7—51no—
150D7—391no—
151D7—1951no—
152C13C3×D5×D2111yescharacteristic, complemented, Sylow
153C22×C3—13651no—
154C2×D3—4551no—
155C2×C5—2731no—
156D5—2731no—
157D5C3×D27311yescharacteristic, direct product factor
158C32D5×D9111yescharacteristic, complemented, Sylow
159C7C3×D5×D3911yescharacteristic, complemented, Sylow
160C2×C3—51no—
161C2×C3—51no—
162C2×C3—101no—
163C2×C3—2731no—
164C2×C3—13651no—
165D3—911no—
166D3—4551no—
167C5C2×C3×D27311yescharacteristic, complemented, Sylow
168C22—13651noSylow
169C3—21no—
170C3C3×D5×D9111yescharacteristic, complemented
171C3D5×D27311yescharacteristic, direct product factor
172C2—51no—
173C2—2731no—
174C2—13651no—
subgroupG/H
center, hypercenterC3D5×D273
commutator, cosocle, hypocenterC3×C5×C7×C13C22×C3
FrattiniC1G
Fitting, socleC32×C5×C7×C13C22
LCSG ▷ C3×C5×C7×C13
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×D1365C2semidirect
2. C3×C5×D273C2semidirect
3. C32×C7×D5×C13C2semidirect
4. D5×D273C3direct (N × H)
6. C32×C5×C7×C13C22semidirect
8. D1365C2×C3semidirect
9. C5×D273C2×C3semidirect
12. C3×C7×D5×C13D3semidirect
13. C3×C7×D5×C13C2×C3semidirect
19. C3×D273D5direct (N × H)
21. C3×C5×C7×C13C2×D3semidirect
22. C3×C5×C7×C13C22×C3semidirect
26. C32×D5×C13D7semidirect
30. C7×D5×C13C3×D3semidirect
32. C32×C7×C13C2×D5semidirect
37. C32×C7×D5D13semidirect
38. C32×C5×C13C2×D7semidirect
43. D273C3×D5direct (N × H)
47. C5×C7×C13C2×C3×D3semidirect
54. C3×D5×C13C3×D7semidirect
55. C3×D5×C13D21semidirect
58. C32×C5×C7C2×D13semidirect
60. C3×C7×C13D3×D5semidirect
61. C3×C7×C13C2×C3×D5semidirect
71. C3×C7×D5C3×D13semidirect
72. C3×C7×D5D39semidirect
75. C3×C5×C13C2×C3×D7semidirect
76. C3×C5×C13C2×D21semidirect
86. D5×C13C3×D21semidirect
90. C32×C13D5×D7semidirect
92. C3×C5×C7C2×C3×D13semidirect
93. C3×C5×C7C2×D39semidirect
94. C7×C13C3×D3×D5semidirect
97. C32×D5D91semidirect
109. C7×D5C3×D39semidirect
110. C5×C13C2×C3×D21semidirect
111. C32×C7D5×D13semidirect
115. C32×C5C2×D91semidirect
124. C3×C13C3×D5×D7semidirect
125. C3×C13D5×D21semidirect
127. C5×C7C2×C3×D39semidirect
132. C3×D5C3×D91semidirect
133. C3×D5D273direct (N × H)
140. C3×C7C3×D5×D13semidirect
141. C3×C7D5×D39semidirect
147. C3×C5C2×C3×D91semidirect
148. C3×C5C2×D273semidirect
152. C13C3×D5×D21semidirect
157. D5C3×D273direct (N × H)
158. C32D5×D91semidirect
159. C7C3×D5×D39semidirect
167. C5C2×C3×D273semidirect
170. C3C3×D5×D91semidirect
171. C3D5×D273direct (N × H)

Maximal subgroups

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

subgroupindex
C3×D13652
C3×C5×D2732
C32×C7×D5×C132
D5×D2733
C3×D5×D913
C2×C3×D2735
C3×D5×D397
C3×D5×D2113