Finite Group Databasebeta

← #13089509

Subgroups — #13089509

Order 1440.

996 conjugacy classes of subgroups; only the 255 normal subgroups are shown.

normal subgroups only

This group has 996 conjugacy classes of subgroups — too many to draw. Only its 255 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×C32×C5×D4C211yesmaximal, characteristic, complemented
2C2×#67184C214yesmaximal, complemented
3#10624285C214yesmaximal, complemented
4D4×C3⋊D15C214yesmaximal, complemented
5#10624283C212yesmaximal, complemented
6#92095—34nomaximal
7C23×C32×C5C2212yescomplemented
8C22×C3⋊D15C2214yescomplemented
9C32×C5×D4C2214yescomplemented
10C2×C32×C4×C5C2211yescharacteristic, complemented
11#67184C2214yescomplemented
12#67184C2218yescomplemented
13C2×C3⋊Dic15C2214yescomplemented
14C4⋊(C3⋊D15)C2212yescomplemented
15C4×C3⋊D15C2214yescomplemented
16#67180C2212yescomplemented
17#64361—51nomaximal, Hall
18C2×C3×C5×D4D314yescomplemented
19C2×#1220—316no—
20#6819—316no—
21D4×D15—316no—
22#6817—38no—
23C22×C32×C5—42no—
24C22×C32×C5C2314yes—
25C22×C32×C5C2311yescharacteristic
26C2×C3⋊D15—44no—
27C2×C3⋊D15C2314yes—
28C32×C4×C5C2312yes—
29C3⋊Dic15C2314yes—
30#4144—91noHall
31C2×C32×D4D511yescharacteristic, complemented
32C2×#638—54no—
33#3830—54no—
34D4×C3⋊D3—54no—
35#3828—52no—
36C23×C3×C5C2×D318yescomplemented
37C22×D15—316no—
38C3×C5×D4C2×D3116yescomplemented
39C2×C3×C4×C5C2×D314yescomplemented
40#1220—316no—
41#1220—332no—
42C2×Dic15—316no—
43D60—38no—
44C4×D15—316no—
45Dic30—38no—
46#1004—154no—
47C2×C32×C5—24no—
48C2×C32×C5—21no—
49C2×C32×C5C2411yescharacteristic
50C3⋊D15—24no—
51C2×C5×D4C3⋊D311yescharacteristic, complemented
52C2×C22⋊D5—94no—
53#711—94no—
54D4×D5—94no—
55#709—92no—
56C23×C32C2×D512yescomplemented
57C22×C3⋊D3—54no—
58C32×D4C2×D514yescomplemented
59C2×C32×C4C2×D511yescharacteristic, complemented
60#638—54no—
61#638—58no—
62C2×C3⋊Dic3—54no—
63C4⋊(C3⋊D3)—52no—
64C4×C3⋊D3—54no—
65#634—52no—
66C22×C3×C5—48no—
67C22×C3×C5C22×D3116yes—
68C22×C3×C5C22×D314yes—
69C2×D15—316no—
70C2×D15—1216no—
71C3×C4×C5C22×D318yes—
72Dic15—316no—
73C2×C3×D4D1514yescomplemented
74C2×#67—1516no—
75#237—1516no—
76D3×D4—1516no—
77#235—158no—
78C32×C5H(5,𝔽2)11yescharacteristic, complemented, Hall
79C23×C5C2×C3⋊D312yescomplemented
80C22×D5—94no—
81C5×D4C2×C3⋊D314yescomplemented
82C2×C4×C5C2×C3⋊D311yescharacteristic, complemented
83C22⋊D5—94no—
84C22⋊D5—98no—
85C2×Dic5—94no—
86D20—92no—
87C4×D5—94no—
88Dic10—92no—
89C22×C32—42no—
90C22×C32C22×D514yes—
91C22×C32C22×D511yescharacteristic
92C2×C3⋊D3—54no—
93C2×C3⋊D3—204no—
94C32×C4C22×D512yes—
95C3⋊Dic3—54no—
96H(5,𝔽2)—451noSylow
97C2×C3×C5—216no—
98C2×C3×C5—24no—
99C2×C3×C5C23×D314yes—
100D15—616no—
101C23×C3C2×D1518yescomplemented
102C22×D3—1516no—
103C3×D4C2×D15116yescomplemented
104C2×C3×C4C2×D1514yescomplemented
105#67—1516no—
106#67—1532no—
107C2×Dic3—1516no—
108D12—158no—
109C4×D3—1516no—
110Dic6—158no—
111C22×C5—42no—
112C22×C5C22×C3⋊D314yes—
113C22×C5C22×C3⋊D311yescharacteristic
114C2×D5—94no—
115C2×D5—364no—
116C4×C5C22×C3⋊D312yes—
117Dic5—94no—
118C2×C32—24no—
119C2×C32—21no—
120C2×C32C23×D511yescharacteristic
121C3⋊D3—104no—
122#41—454no—
123#41—452no—
124C2×D4—454no—
125C2×D4—454no—
126C2×D4C3⋊D1511yescharacteristic, complemented
127C3×C5#100414yescomplemented
128C22×C3—48no—
129C22×C3C22×D15116yes—
130C22×C3C22×D1514yes—
131C2×D3—1516no—
132C2×D3—6016no—
133C3×C4C22×D1518yes—
134Dic3—1516no—
135C2×C5—24no—
136C2×C5—21no—
137C2×C5C23×C3⋊D311yescharacteristic
138D5—184no—
139C32#414411yescharacteristic, complemented, Sylow
140C23—454no—
141C23C2×C3⋊D1512yescomplemented
142Q8—452no—
143D4—458no—
144D4—454no—
145D4—452no—
146D4C2×C3⋊D1514yescomplemented
147C2×C4—454no—
148C2×C4—454no—
149C2×C4C2×C3⋊D1511yescharacteristic, complemented
150C2×C3—216no—
151C2×C3—24no—
152C2×C3C23×D1514yes—
153D3—3016no—
154C5#6436111yescharacteristic, complemented, Sylow
155C22—42no—
156C22—454no—
157C22—1804no—
158C22C22×C3⋊D1514yes—
159C22C22×C3⋊D1511yescharacteristic
160C4—454no—
161C4C22×C3⋊D1512yes—
162C3#9209514yescomplemented
163C2—21no—
164C2—24no—
165C2—904no—
166C2C23×C3⋊D1511yescharacteristic
subgroupG/H
center, FrattiniC2C23×C3⋊D15
commutator, socle, cosocleC2×C32×C5C24
FittingC2×C32×C5×D4C2
hypercenterC2×D4C3⋊D15
hypocenterC32×C5H(5,𝔽2)
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C2 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×C32×C5×D4C2semidirect
2. C2×#67184C2semidirect
3. #10624285C2semidirect
4. D4×C3⋊D15C2semidirect
5. #10624283C2semidirect
7. C23×C32×C5C22semidirect
8. C22×C3⋊D15C22semidirect
9. C32×C5×D4C22semidirect
10. C2×C32×C4×C5C22semidirect
11. #67184C22semidirect
12. #67184C22semidirect
13. C2×C3⋊Dic15C22semidirect
14. C4⋊(C3⋊D15)C22semidirect
15. C4×C3⋊D15C22semidirect
16. #67180C22semidirect
18. C2×C3×C5×D4D3semidirect
31. C2×C32×D4D5semidirect
36. C23×C3×C5C2×D3semidirect
38. C3×C5×D4C2×D3semidirect
39. C2×C3×C4×C5C2×D3semidirect
51. C2×C5×D4C3⋊D3semidirect
56. C23×C32C2×D5semidirect
58. C32×D4C2×D5semidirect
59. C2×C32×C4C2×D5semidirect
73. C2×C3×D4D15semidirect
78. C32×C5H(5,𝔽2)semidirect
79. C23×C5C2×C3⋊D3semidirect
81. C5×D4C2×C3⋊D3semidirect
82. C2×C4×C5C2×C3⋊D3semidirect
101. C23×C3C2×D15semidirect
103. C3×D4C2×D15semidirect
104. C2×C3×C4C2×D15semidirect
126. C2×D4C3⋊D15semidirect
127. C3×C5#1004semidirect
139. C32#4144semidirect
141. C23C2×C3⋊D15semidirect
146. D4C2×C3⋊D15semidirect
149. C2×C4C2×C3⋊D15semidirect
154. C5#64361semidirect
162. C3#92095semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C5×D42
C2×#671842
#106242852
D4×C3⋊D152
#106242832
#920953
#643615