Finite Group Databasebeta

← #13085355

Subgroups — #13085355

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
1C5×C9×#41C211yesmaximal, characteristic, complemented
2#10623713C212yesmaximal, complemented
3D4×D45C216yesmaximal, complemented
4#10623709C213yesmaximal, complemented
5C2×D180C213yesmaximal, complemented
6#92100—31nomaximal
7C22×D45C2216yescomplemented
8C5×Q8×C9C2211yescharacteristic, complemented
9C5×D4×C9C2213yescomplemented
10C2×C4×C5×C9C2213yescomplemented
11#67099C2216yescomplemented
12D180C2213yescomplemented
13D180C2216yescomplemented
14C4×D45C2216yescomplemented
15Dic90C2211yescharacteristic, complemented
16#63715—51nomaximal, Hall
17C3×C5×#41D311yescharacteristic
18#6821—32no—
19D4×D15—36no—
20#6817—33no—
21C2×D60—33no—
22C22×C5×C9C2313yes—
23C2×D45—46no—
24C2×D45C2316yes—
25C4×C5×C9C2311yescharacteristic
26C4×C5×C9C2313yes—
27Dic45C2312yes—
28#4149—91noHall
29C9×#41D511yescharacteristic, complemented
30#3701—52no—
31D4×D9—56no—
32#3697—53no—
33C2×D36—53no—
34C22×D15—36no—
35C3×C5×Q8C2×D311yescharacteristic
36C3×C5×D4C2×D313yes—
37C2×C3×C4×C5C2×D313yes—
38#1220—36no—
39D60—33no—
40D60—36no—
41C4×D15—36no—
42Dic30—31no—
43#1009—151no—
44C2×C5×C9—23no—
45C2×C5×C9C2411yescharacteristic
46D45—26no—
47C5×#41D911yescharacteristic, complemented
48#713—92no—
49D4×D5—96no—
50#709—93no—
51C2×D20—93no—
52C22×D9—56no—
53Q8×C9C2×D511yescharacteristic, complemented
54D4×C9C2×D513yescomplemented
55C2×C4×C9C2×D513yescomplemented
56#611—56no—
57D36—53no—
58D36—56no—
59C4×D9—56no—
60Dic18—51no—
61C22×C3×C5C22×D313yes—
62C2×D15—36no—
63C2×D15—126no—
64C3×C4×C5C22×D311yescharacteristic
65C3×C4×C5C22×D313yes—
66Dic15—32no—
67C3×#41D1511yescharacteristic
68#239—152no—
69D3×D4—156no—
70#235—153no—
71C2×D12—153no—
72C5×C9H(5,𝔽2)11yescharacteristic, complemented, Hall
73C22×D5—96no—
74C5×Q8C2×D911yescharacteristic, complemented
75C5×D4C2×D913yescomplemented
76C2×C4×C5C2×D913yescomplemented
77C22⋊D5—96no—
78D20—93no—
79D20—96no—
80C4×D5—96no—
81Dic10—91no—
82C22×C9C22×D513yes—
83C2×D9—56no—
84C2×D9—206no—
85C4×C9C22×D511yescharacteristic
86C4×C9C22×D513yes—
87Dic9—52no—
88H(5,𝔽2)—451noSylow
89C2×C3×C5—23no—
90C2×C3×C5C23×D311yescharacteristic
91D15—66no—
92C22×D3—156no—
93C3×Q8C2×D1511yescharacteristic
94C3×D4C2×D1513yes—
95C2×C3×C4C2×D1513yes—
96#67—156no—
97D12—153no—
98D12—156no—
99C4×D3—156no—
100Dic6—151no—
101C22×C5C22×D913yes—
102C2×D5—96no—
103C2×D5—366no—
104C4×C5C22×D911yescharacteristic
105C4×C5C22×D913yes—
106Dic5—92no—
107C2×C9—23no—
108C2×C9C23×D511yescharacteristic
109D9—106no—
110#41—452no—
111#41—453no—
112#41D4511yescharacteristic, complemented
113C2×D4—456no—
114C2×D4—453no—
115C3×C5#100911yescharacteristic
116C22×C3C22×D1513yes—
117C2×D3—156no—
118C2×D3—606no—
119C3×C4C22×D1511yescharacteristic
120C3×C4C22×D1513yes—
121Dic3—152no—
122C2×C5—23no—
123C2×C5C23×D911yescharacteristic
124D5—186no—
125C9#414911yescharacteristic, complemented, Sylow
126C23—456no—
127Q8—451no—
128Q8C2×D4511yescharacteristic, complemented
129D4—456no—
130D4—456no—
131D4—453no—
132D4C2×D4513yescomplemented
133C2×C4—456no—
134C2×C4C2×D4513yescomplemented
135C2×C3—23no—
136C2×C3C23×D1511yescharacteristic
137D3—306no—
138C5#6371511yescharacteristic, complemented, Sylow
139C22—456no—
140C22—1806no—
141C22C22×D4513yes—
142C4—452no—
143C4C22×D4513yes—
144C4C22×D4511yescharacteristic
145C3#9210011yescharacteristic
146C2—23no—
147C2—906no—
148C2C23×D4511yescharacteristic
subgroupG/H
centerC2C23×D45
commutator, cosocleC2×C5×C9C24
FrattiniC2×C3C23×D15
FittingC5×C9×#41C2
socleC2×C3×C5C23×D3
hypercenter#41D45
hypocenterC5×C9H(5,𝔽2)
LCSG ▷ C2×C5×C9 ▷ C5×C9
UCSC1 ◁ C2 ◁ #41

Complements

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

NH ≅ G/Ntype
1. C5×C9×#41C2semidirect
2. #10623713C2semidirect
3. D4×D45C2semidirect
4. #10623709C2semidirect
5. C2×D180C2semidirect
7. C22×D45C22semidirect
8. C5×Q8×C9C22semidirect
9. C5×D4×C9C22semidirect
10. C2×C4×C5×C9C22semidirect
11. #67099C22semidirect
12. D180C22semidirect
13. D180C22semidirect
14. C4×D45C22semidirect
15. Dic90C22semidirect
29. C9×#41D5semidirect
47. C5×#41D9semidirect
53. Q8×C9C2×D5semidirect
54. D4×C9C2×D5semidirect
55. C2×C4×C9C2×D5semidirect
72. C5×C9H(5,𝔽2)semidirect
74. C5×Q8C2×D9semidirect
75. C5×D4C2×D9semidirect
76. C2×C4×C5C2×D9semidirect
112. #41D45semidirect
125. C9#4149semidirect
128. Q8C2×D45semidirect
132. D4C2×D45semidirect
134. C2×C4C2×D45semidirect
138. C5#63715semidirect

Maximal subgroups

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

subgroupindex
C5×C9×#412
#106237132
D4×D452
#106237092
C2×D1802
#921003
#637155