Finite Group Databasebeta

← C2×D4×D45 #13085348

Subgroups — C2×D4×D45 #13085348

Order 1440.

708 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 708 conjugacy classes of subgroups — too many to draw. Only its 173 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×D45C212yesmaximal, complemented
2C2×C5×D4×C9C211yesmaximal, characteristic, complemented
3C2×#67099C212yesmaximal, complemented
4D4×D45C218yesmaximal, direct product factor
5C2×D180C211yesmaximal, characteristic, complemented
6C2×C4×D45C211yesmaximal, characteristic, complemented
7C2×D4×D15—31nomaximal
8C23×C5×C9C2212yescomplemented
9C22×D45—28no—
10C22×D45C2211yescharacteristic
11C22×D45C2218yescomplemented
12C22×D45C2212yescomplemented
13C5×D4×C9C2214yescomplemented
14C2×C4×C5×C9C2211yescharacteristic, complemented
15#67099C2218yescomplemented
16C2×Dic45C2211yescharacteristic, complemented
17D180C2214yescomplemented
18C4×D45C2214yescomplemented
19C2×D4×D9—51nomaximal, Hall
20C23×D15—32no—
21C2×C3×C5×D4D311yescharacteristic
22C2×#1220—32no—
23D4×D15—38no—
24C2×D60—31no—
25C2×C4×D15—31no—
26C22×C5×C9—24no—
27C22×C5×C9C2311yescharacteristic
28C22×C5×C9C2314yescomplemented
29C2×D45—24no—
30C2×D45—216no—
31C2×D45D414yesdirect product factor
32C2×D45C2312yes—
33C2×D45C2314yescomplemented
34C4×C5×C9C2312yescomplemented
35Dic45C2312yescomplemented
36C2×D4×D5—91noHall
37C23×D9—52no—
38C2×D4×C9D511yescharacteristic, complemented
39C2×#611—52no—
40D4×D9—58no—
41C2×D36—51no—
42C2×C4×D9—51no—
43C23×C3×C5C2×D312yes—
44C22×D15—31no—
45C22×D15—32no—
46C22×D15—38no—
47C22×D15—68no—
48C3×C5×D4C2×D314yes—
49C2×C3×C4×C5C2×D311yescharacteristic
50#1220—38no—
51C2×Dic15—31no—
52D60—34no—
53C4×D15—34no—
54C2×D3×D4—151no—
55C2×C5×C9—24no—
56C2×C5×C9C2×D412yescomplemented
57C2×C5×C9C2411yescharacteristic
58D45—24no—
59D45C2×D414yesdirect product factor
60C23×D5—92no—
61C2×C5×D4D911yescharacteristic, complemented
62C2×C22⋊D5—92no—
63D4×D5—98no—
64C2×D20—91no—
65C2×C4×D5—91no—
66C23×C9C2×D512yescomplemented
67C22×D9—51no—
68C22×D9—52no—
69C22×D9—58no—
70C22×D9—108no—
71D4×C9C2×D514yescomplemented
72C2×C4×C9C2×D511yescharacteristic, complemented
73#611—58no—
74C2×Dic9—51no—
75D36—54no—
76C4×D9—54no—
77C22×C3×C5—24no—
78C22×C3×C5C22×D311yescharacteristic
79C22×C3×C5C22×D314yes—
80C2×D15—34no—
81C2×D15—32no—
82C2×D15—34no—
83C2×D15—616no—
84C2×D15—64no—
85C3×C4×C5C22×D312yes—
86Dic15—32no—
87C23×D3—152no—
88C2×C3×D4D1511yescharacteristic
89C2×#67—152no—
90D3×D4—158no—
91C2×D12—151no—
92C2×C4×D3—151no—
93C5×C9C22×D411yescharacteristic, complemented, Hall
94C23×C5C2×D912yescomplemented
95C22×D5—91no—
96C22×D5—92no—
97C22×D5—98no—
98C22×D5—188no—
99C5×D4C2×D914yescomplemented
100C2×C4×C5C2×D911yescharacteristic, complemented
101C22⋊D5—98no—
102C2×Dic5—91no—
103D20—94no—
104C4×D5—94no—
105C22×C9—24no—
106C22×C9C22×D511yescharacteristic
107C22×C9C22×D514yescomplemented
108C2×D9—54no—
109C2×D9—52no—
110C2×D9—54no—
111C2×D9—1016no—
112C2×D9—104no—
113C4×C9C22×D512yescomplemented
114Dic9—52no—
115C22×D4—451noSylow
116C2×C3×C5—24no—
117C2×C3×C5D3×D412yes—
118C2×C3×C5C23×D311yescharacteristic
119D15—34no—
120D15—64no—
121C23×C3C2×D1512yes—
122C22×D3—151no—
123C22×D3—152no—
124C22×D3—158no—
125C22×D3—308no—
126C3×D4C2×D1514yes—
127C2×C3×C4C2×D1511yescharacteristic
128#67—158no—
129C2×Dic3—151no—
130D12—154no—
131C4×D3—154no—
132C22×C5—24no—
133C22×C5C22×D911yescharacteristic
134C22×C5C22×D914yescomplemented
135C2×D5—94no—
136C2×D5—92no—
137C2×D5—94no—
138C2×D5—1816no—
139C2×D5—184no—
140C4×C5C22×D912yescomplemented
141Dic5—92no—
142C2×C9—24no—
143C2×C9D4×D512yescomplemented
144C2×C9C23×D511yescharacteristic
145D9—54no—
146D9—104no—
147C24—452no—
148C2×D4—452no—
149C2×D4—458no—
150C2×D4—451no—
151C2×D4D4511yescharacteristic, direct product factor
152C22×C4—451no—
153C3×C5C2×D3×D411yescharacteristic
154C22×C3—24no—
155C22×C3C22×D1511yescharacteristic
156C22×C3C22×D1514yes—
157C2×D3—154no—
158C2×D3—152no—
159C2×D3—154no—
160C2×D3—3016no—
161C2×D3—304no—
162C3×C4C22×D1512yes—
163Dic3—152no—
164C2×C5—24no—
165C2×C5D4×D912yescomplemented
166C2×C5C23×D911yescharacteristic
167D5—94no—
168D5—184no—
169C9C2×D4×D511yescharacteristic, complemented, Sylow
170C23—451no—
171C23—452no—
172C23—458no—
173C23—908no—
174C23C2×D4512yescomplemented
175D4—458no—
176D4—454no—
177D4C2×D4514yesdirect product factor
178C2×C4—451no—
179C2×C4—454no—
180C2×C4C2×D4511yescharacteristic, complemented
181C2×C3—24no—
182C2×C3D4×D1512yes—
183C2×C3C23×D1511yescharacteristic
184D3—154no—
185D3—304no—
186C5C2×D4×D911yescharacteristic, complemented, Sylow
187C22—24no—
188C22—452no—
189C22—454no—
190C22—454no—
191C22—9016no—
192C22—904no—
193C22C22×D4511yescharacteristic
194C22C22×D4514yescomplemented
195C4—452no—
196C4C22×D4512yescomplemented
197C3C2×D4×D1511yescharacteristic
198C2—24no—
199C2—454no—
200C2—904no—
201C2D4×D4512yesdirect product factor
202C2C23×D4511yescharacteristic
subgroupG/H
centerC22C22×D45
commutator, cosocleC2×C5×C9C24
FrattiniC2×C3C23×D15
FittingC2×C5×D4×C9C2
socleC22×C3×C5C22×D3
hypercenterC2×D4D45
hypocenterC5×C9C22×D4
LCSG ▷ C2×C5×C9 ▷ C5×C9
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C23×D45C2semidirect
2. C2×C5×D4×C9C2semidirect
3. C2×#67099C2semidirect
4. D4×D45C2direct (N × H)
5. C2×D180C2semidirect
6. C2×C4×D45C2semidirect
8. C23×C5×C9C22semidirect
11. C22×D45C22semidirect
12. C22×D45C22semidirect
13. C5×D4×C9C22semidirect
14. C2×C4×C5×C9C22semidirect
15. #67099C22semidirect
16. C2×Dic45C22semidirect
17. D180C22semidirect
18. C4×D45C22semidirect
28. C22×C5×C9C23semidirect
31. C2×D45D4direct (N × H)
33. C2×D45C23semidirect
34. C4×C5×C9C23semidirect
35. Dic45C23semidirect
38. C2×D4×C9D5semidirect
56. C2×C5×C9C2×D4semidirect
59. D45C2×D4direct (N × H)
61. C2×C5×D4D9semidirect
66. C23×C9C2×D5semidirect
71. D4×C9C2×D5semidirect
72. C2×C4×C9C2×D5semidirect
93. C5×C9C22×D4semidirect
94. C23×C5C2×D9semidirect
99. C5×D4C2×D9semidirect
100. C2×C4×C5C2×D9semidirect
107. C22×C9C22×D5semidirect
113. C4×C9C22×D5semidirect
134. C22×C5C22×D9semidirect
140. C4×C5C22×D9semidirect
143. C2×C9D4×D5semidirect
151. C2×D4D45direct (N × H)
165. C2×C5D4×D9semidirect
169. C9C2×D4×D5semidirect
174. C23C2×D45semidirect
177. D4C2×D45direct (N × H)
180. C2×C4C2×D45semidirect
186. C5C2×D4×D9semidirect
194. C22C22×D45semidirect
196. C4C22×D45semidirect
201. C2D4×D45direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D452
C2×C5×D4×C92
C2×#670992
D4×D452
C2×D1802
C2×C4×D452
C2×D4×D153
C2×D4×D95