Finite Group Databasebeta

← C2×C4×D3×D5 #92010

Subgroups — C2×C4×D3×D5 #92010

Order 480.

472 conjugacy classes of subgroups; only the 180 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 180 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
1C22×D3×D5C211yesmaximal, characteristic
2C2×C4×D15C211yesmaximal, characteristic, complemented
3C2×C4×C5×D3C211yesmaximal, characteristic, complemented
4C2×C3×C4×D5C211yesmaximal, characteristic, complemented
5C2×#1200C211yesmaximal, characteristic, complemented
6C2×D3×Dic5C211yesmaximal, characteristic, complemented
7C2×D5×Dic3C211yesmaximal, characteristic, complemented
8C4×D3×D5C218yesmaximal, direct product factor
9C22×C4×D5—31nomaximal, Hall
10C22×D15C2211yescharacteristic
11C22×C5×D3C2211yescharacteristic
12C22×C3×D5C2211yescharacteristic
13C2×D3×D5C418yesdirect product factor
14C2×D3×D5C2214yes—
15C2×C3×C4×C5C2211yescharacteristic, complemented
16C2×Dic15C2211yescharacteristic, complemented
17C4×D15C2214yescomplemented
18C2×C5×Dic3C2211yescharacteristic, complemented
19C4×C5×D3C2214yescomplemented
20C2×C3×Dic5C2211yescharacteristic, complemented
21C3×C4×D5C2214yescomplemented
22#1200C2214yescomplemented
23D3×Dic5C2214yescomplemented
24D5×Dic3C2214yescomplemented
25C22×C4×D3—51nomaximal, Hall
26C23×D5—31no—
27C22×C4×C5—31no—
28C22×Dic5—31no—
29C2×C4×D5—31no—
30C2×C4×D5—31no—
31C2×C4×D5—31no—
32C2×C4×D5—38no—
33C2×C4×D5D311yescharacteristic, direct product factor
34C22×C3×C5C2311yescharacteristic
35C2×D15C2×C414yescomplemented
36C2×D15C2312yes—
37C2×C5×D3C2×C414yescomplemented
38C2×C5×D3C2312yes—
39C2×C3×D5C2×C414yescomplemented
40C2×C3×D5C2312yes—
41D3×D5C2×C4116yesdirect product factor
42C3×C4×C5C2312yescomplemented
43Dic15C2312yescomplemented
44C3×Dic5C2312yescomplemented
45C5×Dic3C2312yescomplemented
46C23×D3—51no—
47C22×C3×C4—51no—
48C22×Dic3—51no—
49C2×C4×D3—51no—
50C2×C4×D3—51no—
51C2×C4×D3—51no—
52C2×C4×D3—58no—
53C2×C4×D3D511yescharacteristic, direct product factor
54C23×C5—31no—
55C22×D5—31no—
56C22×D5—38no—
57C22×D5—34no—
58C22×D5C2×D311yescharacteristic
59C2×C4×C5—31no—
60C2×C4×C5—34no—
61C2×C4×C5C2×D311yescharacteristic, complemented
62C2×Dic5—31no—
63C2×Dic5—34no—
64C2×Dic5C2×D311yescharacteristic, complemented
65C4×D5—34no—
66C4×D5—34no—
67C4×D5—34no—
68C4×D5C2×D314yesdirect product factor
69C23×C4—151noSylow
70C2×C3×C5C22×C412yescomplemented
71C2×C3×C5C2411yescharacteristic
72D15C22×C414yescomplemented
73C3×D5C22×C414yescomplemented
74C5×D3C22×C414yescomplemented
75C23×C3—51no—
76C22×D3—51no—
77C22×D3—58no—
78C22×D3—54no—
79C22×D3C2×D511yescharacteristic
80C2×C3×C4—51no—
81C2×C3×C4—54no—
82C2×C3×C4C2×D511yescharacteristic, complemented
83C2×Dic3—51no—
84C2×Dic3—54no—
85C2×Dic3C2×D511yescharacteristic, complemented
86C4×D3—54no—
87C4×D3—54no—
88C4×D3—54no—
89C4×D3C2×D514yesdirect product factor
90C22×C5—34no—
91C22×C5—32no—
92C22×C5C22×D311yescharacteristic
93C2×D5—34no—
94C2×D5—32no—
95C2×D5—316no—
96C2×D5C4×D314yesdirect product factor
97C2×D5C22×D312yes—
98C4×C5—32no—
99C4×C5C22×D312yescomplemented
100Dic5—32no—
101Dic5C22×D312yescomplemented
102C24—151no—
103C22×C4—31no—
104C22×C4—51no—
105C22×C4—151no—
106C22×C4—158no—
107C22×C4—151no—
108C22×C4—151no—
109C22×C4—151no—
110C3×C5C23×C411yescharacteristic, complemented, Hall
111C22×C3—54no—
112C22×C3—52no—
113C22×C3C22×D511yescharacteristic
114C2×D3—54no—
115C2×D3—52no—
116C2×D3—516no—
117C2×D3C4×D514yesdirect product factor
118C2×D3C22×D512yes—
119C3×C4—52no—
120C3×C4C22×D512yescomplemented
121Dic3—52no—
122Dic3C22×D512yescomplemented
123C2×C5—34no—
124C2×C5C2×C4×D312yescomplemented
125C2×C5C23×D311yescharacteristic
126D5—34no—
127D5C2×C4×D314yesdirect product factor
128C23—31no—
129C23—51no—
130C23—154no—
131C23—158no—
132C23—151no—
133C2×C4—31no—
134C2×C4—34no—
135C2×C4—51no—
136C2×C4—54no—
137C2×C4—154no—
138C2×C4—154no—
139C2×C4—154no—
140C2×C4—151no—
141C2×C4—154no—
142C2×C4D3×D511yescharacteristic, direct product factor
143C2×C3—54no—
144C2×C3C2×C4×D512yescomplemented
145C2×C3C23×D511yescharacteristic
146D3—54no—
147D3C2×C4×D514yesdirect product factor
148C5C22×C4×D311yescharacteristic, complemented, Sylow
149C22—34no—
150C22—32no—
151C22—54no—
152C22—52no—
153C22—1516no—
154C22—154no—
155C22—152no—
156C22C2×D3×D511yescharacteristic
157C4—32no—
158C4—52no—
159C4—152no—
160C4C2×D3×D512yesdirect product factor
161C3C22×C4×D511yescharacteristic, complemented, Sylow
162C2—34no—
163C2—54no—
164C2—154no—
165C2C4×D3×D512yesdirect product factor
166C2C22×D3×D511yescharacteristic
subgroupG/H
center, hypercenterC2×C4D3×D5
commutator, hypocenterC3×C5C23×C4
FrattiniC2C22×D3×D5
FittingC2×C3×C4×C5C22
socleC22×C3×C5C23
prime radicalC22×D3×D5C2
cosocleC2×C3×C5C24
LCSG ▷ C3×C5
UCSC1 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×D15C2semidirect
3. C2×C4×C5×D3C2semidirect
4. C2×C3×C4×D5C2semidirect
5. C2×#1200C2semidirect
6. C2×D3×Dic5C2semidirect
7. C2×D5×Dic3C2semidirect
8. C4×D3×D5C2direct (N × H)
13. C2×D3×D5C4direct (N × H)
15. C2×C3×C4×C5C22semidirect
16. C2×Dic15C22semidirect
17. C4×D15C22semidirect
18. C2×C5×Dic3C22semidirect
19. C4×C5×D3C22semidirect
20. C2×C3×Dic5C22semidirect
21. C3×C4×D5C22semidirect
22. #1200C22semidirect
23. D3×Dic5C22semidirect
24. D5×Dic3C22semidirect
33. C2×C4×D5D3direct (N × H)
35. C2×D15C2×C4semidirect
37. C2×C5×D3C2×C4semidirect
39. C2×C3×D5C2×C4semidirect
41. D3×D5C2×C4direct (N × H)
42. C3×C4×C5C23semidirect
43. Dic15C23semidirect
44. C3×Dic5C23semidirect
45. C5×Dic3C23semidirect
53. C2×C4×D3D5direct (N × H)
61. C2×C4×C5C2×D3semidirect
64. C2×Dic5C2×D3semidirect
68. C4×D5C2×D3direct (N × H)
70. C2×C3×C5C22×C4semidirect
72. D15C22×C4semidirect
73. C3×D5C22×C4semidirect
74. C5×D3C22×C4semidirect
82. C2×C3×C4C2×D5semidirect
85. C2×Dic3C2×D5semidirect
89. C4×D3C2×D5direct (N × H)
96. C2×D5C4×D3direct (N × H)
99. C4×C5C22×D3semidirect
101. Dic5C22×D3semidirect
110. C3×C5C23×C4semidirect
117. C2×D3C4×D5direct (N × H)
120. C3×C4C22×D5semidirect
122. Dic3C22×D5semidirect
124. C2×C5C2×C4×D3semidirect
127. D5C2×C4×D3direct (N × H)
142. C2×C4D3×D5direct (N × H)
144. C2×C3C2×C4×D5semidirect
147. D3C2×C4×D5direct (N × H)
148. C5C22×C4×D3semidirect
160. C4C2×D3×D5direct (N × H)
161. C3C22×C4×D5semidirect
165. C2C4×D3×D5direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D3×D52
C2×C4×D152
C2×C4×C5×D32
C2×C3×C4×D52
C2×#12002
C2×D3×Dic52
C2×D5×Dic32
C4×D3×D52
C22×C4×D53
C22×C4×D35