Finite Group Databasebeta

← #13085350

Subgroups — #13085350

Order 1440.

498 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 498 conjugacy classes of subgroups — too many to draw. Only its 153 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
1C2×C5×D4×C9C211yesmaximal, characteristic, complemented
2C2×#67099C214yesmaximal, complemented
3#10623711C214yesmaximal, complemented
4D4×D45C214yesmaximal, complemented
5#10623709C212yesmaximal, complemented
6#92095—31nomaximal
7C23×C5×C9C2212yescomplemented
8C22×D45C2214yescomplemented
9C5×D4×C9C2214yescomplemented
10C2×C4×C5×C9C2211yescharacteristic, complemented
11#67099C2214yescomplemented
12#67099C2218yescomplemented
13C2×Dic45C2214yescomplemented
14D180C2212yescomplemented
15C4×D45C2214yescomplemented
16Dic90C2212yescomplemented
17#63710—51nomaximal, Hall
18C2×C3×C5×D4D311yescharacteristic
19C2×#1220—34no—
20#6819—34no—
21D4×D15—34no—
22#6817—32no—
23C22×C5×C9—42no—
24C22×C5×C9C2314yes—
25C22×C5×C9C2311yescharacteristic
26C2×D45—44no—
27C2×D45C2314yes—
28C4×C5×C9C2312yes—
29Dic45C2314yes—
30#4144—91noHall
31C2×D4×C9D511yescharacteristic, complemented
32C2×#611—54no—
33#3699—54no—
34D4×D9—54no—
35#3697—52no—
36C23×C3×C5C2×D312yes—
37C22×D15—34no—
38C3×C5×D4C2×D314yes—
39C2×C3×C4×C5C2×D311yescharacteristic
40#1220—34no—
41#1220—38no—
42C2×Dic15—34no—
43D60—32no—
44C4×D15—34no—
45Dic30—32no—
46#1004—151no—
47C2×C5×C9—24no—
48C2×C5×C9—21no—
49C2×C5×C9C2411yescharacteristic
50D45—24no—
51C2×C5×D4D911yescharacteristic, complemented
52C2×C22⋊D5—94no—
53#711—94no—
54D4×D5—94no—
55#709—92no—
56C23×C9C2×D512yescomplemented
57C22×D9—54no—
58D4×C9C2×D514yescomplemented
59C2×C4×C9C2×D511yescharacteristic, complemented
60#611—54no—
61#611—58no—
62C2×Dic9—54no—
63D36—52no—
64C4×D9—54no—
65Dic18—52no—
66C22×C3×C5—42no—
67C22×C3×C5C22×D314yes—
68C22×C3×C5C22×D311yescharacteristic
69C2×D15—34no—
70C2×D15—124no—
71C3×C4×C5C22×D312yes—
72Dic15—34no—
73C2×C3×D4D1511yescharacteristic
74C2×#67—154no—
75#237—154no—
76D3×D4—154no—
77#235—152no—
78C5×C9H(5,𝔽2)11yescharacteristic, complemented, Hall
79C23×C5C2×D912yescomplemented
80C22×D5—94no—
81C5×D4C2×D914yescomplemented
82C2×C4×C5C2×D911yescharacteristic, complemented
83C22⋊D5—94no—
84C22⋊D5—98no—
85C2×Dic5—94no—
86D20—92no—
87C4×D5—94no—
88Dic10—92no—
89C22×C9—42no—
90C22×C9C22×D514yes—
91C22×C9C22×D511yescharacteristic
92C2×D9—54no—
93C2×D9—204no—
94C4×C9C22×D512yes—
95Dic9—54no—
96H(5,𝔽2)—451noSylow
97C2×C3×C5—24no—
98C2×C3×C5—21no—
99C2×C3×C5C23×D311yescharacteristic
100D15—64no—
101C23×C3C2×D1512yes—
102C22×D3—154no—
103C3×D4C2×D1514yes—
104C2×C3×C4C2×D1511yescharacteristic
105#67—154no—
106#67—158no—
107C2×Dic3—154no—
108D12—152no—
109C4×D3—154no—
110Dic6—152no—
111C22×C5—42no—
112C22×C5C22×D914yes—
113C22×C5C22×D911yescharacteristic
114C2×D5—94no—
115C2×D5—364no—
116C4×C5C22×D912yes—
117Dic5—94no—
118C2×C9—24no—
119C2×C9—21no—
120C2×C9C23×D511yescharacteristic
121D9—104no—
122#41—454no—
123#41—452no—
124C2×D4—454no—
125C2×D4—454no—
126C2×D4D4511yescharacteristic, complemented
127C3×C5#100411yescharacteristic
128C22×C3—42no—
129C22×C3C22×D1514yes—
130C22×C3C22×D1511yescharacteristic
131C2×D3—154no—
132C2×D3—604no—
133C3×C4C22×D1512yes—
134Dic3—154no—
135C2×C5—24no—
136C2×C5—21no—
137C2×C5C23×D911yescharacteristic
138D5—184no—
139C9#414411yescharacteristic, complemented, Sylow
140C23—454no—
141C23C2×D4512yescomplemented
142Q8—452no—
143D4—458no—
144D4—454no—
145D4—452no—
146D4C2×D4514yescomplemented
147C2×C4—454no—
148C2×C4—454no—
149C2×C4C2×D4511yescharacteristic, complemented
150C2×C3—24no—
151C2×C3—21no—
152C2×C3C23×D1511yescharacteristic
153D3—304no—
154C5#6371011yescharacteristic, complemented, Sylow
155C22—42no—
156C22—454no—
157C22—1804no—
158C22C22×D4514yes—
159C22C22×D4511yescharacteristic
160C4—454no—
161C4C22×D4512yes—
162C3#9209511yescharacteristic
163C2—21no—
164C2—24no—
165C2—904no—
166C2C23×D4511yescharacteristic
subgroupG/H
centerC2C23×D45
commutator, cosocleC2×C5×C9C24
FrattiniC2×C3C23×D15
FittingC2×C5×D4×C9C2
socleC2×C3×C5C23×D3
hypercenterC2×D4D45
hypocenterC5×C9H(5,𝔽2)
LCSG ▷ C2×C5×C9 ▷ C5×C9
UCSC1 ◁ C2 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×C5×D4×C9C2semidirect
2. C2×#67099C2semidirect
3. #10623711C2semidirect
4. D4×D45C2semidirect
5. #10623709C2semidirect
7. C23×C5×C9C22semidirect
8. C22×D45C22semidirect
9. C5×D4×C9C22semidirect
10. C2×C4×C5×C9C22semidirect
11. #67099C22semidirect
12. #67099C22semidirect
13. C2×Dic45C22semidirect
14. D180C22semidirect
15. C4×D45C22semidirect
16. Dic90C22semidirect
31. C2×D4×C9D5semidirect
51. C2×C5×D4D9semidirect
56. C23×C9C2×D5semidirect
58. D4×C9C2×D5semidirect
59. C2×C4×C9C2×D5semidirect
78. C5×C9H(5,𝔽2)semidirect
79. C23×C5C2×D9semidirect
81. C5×D4C2×D9semidirect
82. C2×C4×C5C2×D9semidirect
126. C2×D4D45semidirect
139. C9#4144semidirect
141. C23C2×D45semidirect
146. D4C2×D45semidirect
149. C2×C4C2×D45semidirect
154. C5#63710semidirect

Maximal subgroups

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

subgroupindex
C2×C5×D4×C92
C2×#670992
#106237112
D4×D452
#106237092
#920953
#637105