Finite Group Databasebeta

← C2×D4×C3⋊D15 #13089507

Subgroups — C2×D4×C3⋊D15 #13089507

Order 1440.

1416 conjugacy classes of subgroups; only the 287 normal subgroups are shown.

normal subgroups only

This group has 1416 conjugacy classes of subgroups — too many to draw. Only its 287 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
1C23×C3⋊D15C212yesmaximal, complemented
2C2×C32×C5×D4C211yesmaximal, characteristic, complemented
3C2×#67184C212yesmaximal, complemented
4D4×C3⋊D15C218yesmaximal, direct product factor
5C2×C4⋊(C3⋊D15)C211yesmaximal, characteristic, complemented
6C2×C4×C3⋊D15C211yesmaximal, characteristic, complemented
7C2×D4×D15—34nomaximal
8C23×C32×C5C2212yescomplemented
9C22×C3⋊D15—28no—
10C22×C3⋊D15C2211yescharacteristic
11C22×C3⋊D15C2218yescomplemented
12C22×C3⋊D15C2212yescomplemented
13C32×C5×D4C2214yescomplemented
14C2×C32×C4×C5C2211yescharacteristic, complemented
15#67184C2218yescomplemented
16C2×C3⋊Dic15C2211yescharacteristic, complemented
17C4⋊(C3⋊D15)C2214yescomplemented
18C4×C3⋊D15C2214yescomplemented
19C2×D4×C3⋊D3—51nomaximal, Hall
20C23×D15—38no—
21C2×C3×C5×D4D314yescomplemented
22C2×#1220—38no—
23D4×D15—332no—
24C2×D60—34no—
25C2×C4×D15—34no—
26C22×C32×C5—24no—
27C22×C32×C5C2311yescharacteristic
28C22×C32×C5C2314yescomplemented
29C2×C3⋊D15—24no—
30C2×C3⋊D15—216no—
31C2×C3⋊D15D414yesdirect product factor
32C2×C3⋊D15C2312yes—
33C2×C3⋊D15C2314yescomplemented
34C32×C4×C5C2312yescomplemented
35C3⋊Dic15C2312yescomplemented
36C2×D4×D5—91noHall
37C23×C3⋊D3—52no—
38C2×C32×D4D511yescharacteristic, complemented
39C2×#638—52no—
40D4×C3⋊D3—58no—
41C2×C4⋊(C3⋊D3)—51no—
42C2×C4×C3⋊D3—51no—
43C23×C3×C5C2×D318yescomplemented
44C22×D15—34no—
45C22×D15—38no—
46C22×D15—332no—
47C22×D15—632no—
48C3×C5×D4C2×D3116yescomplemented
49C2×C3×C4×C5C2×D314yescomplemented
50#1220—332no—
51C2×Dic15—34no—
52D60—316no—
53C4×D15—316no—
54C2×D3×D4—154no—
55C2×C32×C5—24no—
56C2×C32×C5C2×D412yescomplemented
57C2×C32×C5C2411yescharacteristic
58C3⋊D15—24no—
59C3⋊D15C2×D414yesdirect product factor
60C23×D5—92no—
61C2×C5×D4C3⋊D311yescharacteristic, complemented
62C2×C22⋊D5—92no—
63D4×D5—98no—
64C2×D20—91no—
65C2×C4×D5—91no—
66C23×C32C2×D512yescomplemented
67C22×C3⋊D3—51no—
68C22×C3⋊D3—52no—
69C22×C3⋊D3—58no—
70C22×C3⋊D3—108no—
71C32×D4C2×D514yescomplemented
72C2×C32×C4C2×D511yescharacteristic, complemented
73#638—58no—
74C2×C3⋊Dic3—51no—
75C4⋊(C3⋊D3)—54no—
76C4×C3⋊D3—54no—
77C22×C3×C5—216no—
78C22×C3×C5C22×D314yes—
79C22×C3×C5C22×D3116yescomplemented
80C2×D15—316no—
81C2×D15—38no—
82C2×D15—316no—
83C2×D15—664no—
84C2×D15—616no—
85C3×C4×C5C22×D318yescomplemented
86Dic15—38no—
87C23×D3—158no—
88C2×C3×D4D1514yescomplemented
89C2×#67—158no—
90D3×D4—1532no—
91C2×D12—154no—
92C2×C4×D3—154no—
93C32×C5C22×D411yescharacteristic, complemented, Hall
94C23×C5C2×C3⋊D312yescomplemented
95C22×D5—91no—
96C22×D5—92no—
97C22×D5—98no—
98C22×D5—188no—
99C5×D4C2×C3⋊D314yescomplemented
100C2×C4×C5C2×C3⋊D311yescharacteristic, complemented
101C22⋊D5—98no—
102C2×Dic5—91no—
103D20—94no—
104C4×D5—94no—
105C22×C32—24no—
106C22×C32C22×D511yescharacteristic
107C22×C32C22×D514yescomplemented
108C2×C3⋊D3—54no—
109C2×C3⋊D3—52no—
110C2×C3⋊D3—54no—
111C2×C3⋊D3—1016no—
112C2×C3⋊D3—104no—
113C32×C4C22×D512yescomplemented
114C3⋊Dic3—52no—
115C22×D4—451noSylow
116C2×C3×C5—216no—
117C2×C3×C5D3×D418yescomplemented
118C2×C3×C5C23×D314yes—
119D15—316no—
120D15—616no—
121C23×C3C2×D1518yescomplemented
122C22×D3—154no—
123C22×D3—158no—
124C22×D3—1532no—
125C22×D3—3032no—
126C3×D4C2×D15116yescomplemented
127C2×C3×C4C2×D1514yescomplemented
128#67—1532no—
129C2×Dic3—154no—
130D12—1516no—
131C4×D3—1516no—
132C22×C5—24no—
133C22×C5C22×C3⋊D311yescharacteristic
134C22×C5C22×C3⋊D314yescomplemented
135C2×D5—92no—
136C2×D5—94no—
137C2×D5—94no—
138C2×D5—1816no—
139C2×D5—184no—
140C4×C5C22×C3⋊D312yescomplemented
141Dic5—92no—
142C2×C32—24no—
143C2×C32D4×D512yescomplemented
144C2×C32C23×D511yescharacteristic
145C3⋊D3—54no—
146C3⋊D3—104no—
147C24—452no—
148C2×D4—452no—
149C2×D4—458no—
150C2×D4—451no—
151C2×D4C3⋊D1511yescharacteristic, direct product factor
152C22×C4—451no—
153C3×C5C2×D3×D414yescomplemented
154C22×C3—216no—
155C22×C3C22×D1514yes—
156C22×C3C22×D15116yescomplemented
157C2×D3—1516no—
158C2×D3—158no—
159C2×D3—1516no—
160C2×D3—3064no—
161C2×D3—3016no—
162C3×C4C22×D1518yescomplemented
163Dic3—158no—
164C2×C5—24no—
165C2×C5D4×C3⋊D312yescomplemented
166C2×C5C23×C3⋊D311yescharacteristic
167D5—94no—
168D5—184no—
169C32C2×D4×D511yescharacteristic, complemented, Sylow
170C23—451no—
171C23—452no—
172C23—458no—
173C23—908no—
174C23C2×C3⋊D1512yescomplemented
175D4—458no—
176D4—454no—
177D4C2×C3⋊D1514yesdirect product factor
178C2×C4—451no—
179C2×C4—454no—
180C2×C4C2×C3⋊D1511yescharacteristic, complemented
181C2×C3—216no—
182C2×C3D4×D1518yescomplemented
183C2×C3C23×D1514yes—
184D3—1516no—
185D3—3016no—
186C5C2×D4×C3⋊D311yescharacteristic, complemented, Sylow
187C22—24no—
188C22—454no—
189C22—452no—
190C22—454no—
191C22—9016no—
192C22—904no—
193C22C22×C3⋊D1511yescharacteristic
194C22C22×C3⋊D1514yescomplemented
195C4—452no—
196C4C22×C3⋊D1512yescomplemented
197C3C2×D4×D1514yescomplemented
198C2—24no—
199C2—454no—
200C2—904no—
201C2D4×C3⋊D1512yesdirect product factor
202C2C23×C3⋊D1511yescharacteristic
subgroupG/H
centerC22C22×C3⋊D15
commutator, cosocleC2×C32×C5C24
FrattiniC2C23×C3⋊D15
FittingC2×C32×C5×D4C2
socleC22×C32×C5C23
hypercenterC2×D4C3⋊D15
hypocenterC32×C5C22×D4
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C23×C3⋊D15C2semidirect
2. C2×C32×C5×D4C2semidirect
3. C2×#67184C2semidirect
4. D4×C3⋊D15C2direct (N × H)
5. C2×C4⋊(C3⋊D15)C2semidirect
6. C2×C4×C3⋊D15C2semidirect
8. C23×C32×C5C22semidirect
11. C22×C3⋊D15C22semidirect
12. C22×C3⋊D15C22semidirect
13. C32×C5×D4C22semidirect
14. C2×C32×C4×C5C22semidirect
15. #67184C22semidirect
16. C2×C3⋊Dic15C22semidirect
17. C4⋊(C3⋊D15)C22semidirect
18. C4×C3⋊D15C22semidirect
21. C2×C3×C5×D4D3semidirect
28. C22×C32×C5C23semidirect
31. C2×C3⋊D15D4direct (N × H)
33. C2×C3⋊D15C23semidirect
34. C32×C4×C5C23semidirect
35. C3⋊Dic15C23semidirect
38. C2×C32×D4D5semidirect
43. C23×C3×C5C2×D3semidirect
48. C3×C5×D4C2×D3semidirect
49. C2×C3×C4×C5C2×D3semidirect
56. C2×C32×C5C2×D4semidirect
59. C3⋊D15C2×D4direct (N × H)
61. C2×C5×D4C3⋊D3semidirect
66. C23×C32C2×D5semidirect
71. C32×D4C2×D5semidirect
72. C2×C32×C4C2×D5semidirect
79. C22×C3×C5C22×D3semidirect
85. C3×C4×C5C22×D3semidirect
88. C2×C3×D4D15semidirect
93. C32×C5C22×D4semidirect
94. C23×C5C2×C3⋊D3semidirect
99. C5×D4C2×C3⋊D3semidirect
100. C2×C4×C5C2×C3⋊D3semidirect
107. C22×C32C22×D5semidirect
113. C32×C4C22×D5semidirect
117. C2×C3×C5D3×D4semidirect
121. C23×C3C2×D15semidirect
126. C3×D4C2×D15semidirect
127. C2×C3×C4C2×D15semidirect
134. C22×C5C22×C3⋊D3semidirect
140. C4×C5C22×C3⋊D3semidirect
143. C2×C32D4×D5semidirect
151. C2×D4C3⋊D15direct (N × H)
153. C3×C5C2×D3×D4semidirect
156. C22×C3C22×D15semidirect
162. C3×C4C22×D15semidirect
165. C2×C5D4×C3⋊D3semidirect
169. C32C2×D4×D5semidirect
174. C23C2×C3⋊D15semidirect
177. D4C2×C3⋊D15direct (N × H)
180. C2×C4C2×C3⋊D15semidirect
182. C2×C3D4×D15semidirect
186. C5C2×D4×C3⋊D3semidirect
194. C22C22×C3⋊D15semidirect
196. C4C22×C3⋊D15semidirect
197. C3C2×D4×D15semidirect
201. C2D4×C3⋊D15direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3⋊D152
C2×C32×C5×D42
C2×#671842
D4×C3⋊D152
C2×C4⋊(C3⋊D15)2
C2×C4×C3⋊D152
C2×D4×D153
C2×D4×C3⋊D35