Finite Group Databasebeta

← #13089514

Subgroups — #13089514

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
1C32×C5×#41C211yesmaximal, characteristic, complemented
2#10624287C212yesmaximal, complemented
3D4×C3⋊D15C216yesmaximal, complemented
4#10624283C213yesmaximal, complemented
5C2×C4⋊(C3⋊D15)C213yesmaximal, complemented
6#92100—34nomaximal
7C22×C3⋊D15C2216yescomplemented
8C32×C5×Q8C2211yescharacteristic, complemented
9C32×C5×D4C2213yescomplemented
10C2×C32×C4×C5C2213yescomplemented
11#67184C2216yescomplemented
12C4⋊(C3⋊D15)C2213yescomplemented
13C4⋊(C3⋊D15)C2216yescomplemented
14C4×C3⋊D15C2216yescomplemented
15#67180C2211yescharacteristic, complemented
16#64366—51nomaximal, Hall
17C3×C5×#41D314yescomplemented
18#6821—38no—
19D4×D15—324no—
20#6817—312no—
21C2×D60—312no—
22C22×C32×C5C2313yes—
23C2×C3⋊D15—46no—
24C2×C3⋊D15C2316yes—
25C32×C4×C5C2311yescharacteristic
26C32×C4×C5C2313yes—
27C3⋊Dic15C2312yes—
28#4149—91noHall
29C32×#41D511yescharacteristic, complemented
30#3832—52no—
31D4×C3⋊D3—56no—
32#3828—53no—
33C2×C4⋊(C3⋊D3)—53no—
34C22×D15—324no—
35C3×C5×Q8C2×D314yescomplemented
36C3×C5×D4C2×D3112yescomplemented
37C2×C3×C4×C5C2×D3112yescomplemented
38#1220—324no—
39D60—312no—
40D60—324no—
41C4×D15—324no—
42Dic30—34no—
43#1009—154no—
44C2×C32×C5—23no—
45C2×C32×C5C2411yescharacteristic
46C3⋊D15—26no—
47C5×#41C3⋊D311yescharacteristic, complemented
48#713—92no—
49D4×D5—96no—
50#709—93no—
51C2×D20—93no—
52C22×C3⋊D3—56no—
53C32×Q8C2×D511yescharacteristic, complemented
54C32×D4C2×D513yescomplemented
55C2×C32×C4C2×D513yescomplemented
56#638—56no—
57C4⋊(C3⋊D3)—53no—
58C4⋊(C3⋊D3)—56no—
59C4×C3⋊D3—56no—
60#634—51no—
61C22×C3×C5C22×D3112yes—
62C2×D15—324no—
63C2×D15—1224no—
64C3×C4×C5C22×D314yes—
65C3×C4×C5C22×D3112yes—
66Dic15—38no—
67C3×#41D1514yescomplemented
68#239—158no—
69D3×D4—1524no—
70#235—1512no—
71C2×D12—1512no—
72C32×C5H(5,𝔽2)11yescharacteristic, complemented, Hall
73C22×D5—96no—
74C5×Q8C2×C3⋊D311yescharacteristic, complemented
75C5×D4C2×C3⋊D313yescomplemented
76C2×C4×C5C2×C3⋊D313yescomplemented
77C22⋊D5—96no—
78D20—93no—
79D20—96no—
80C4×D5—96no—
81Dic10—91no—
82C22×C32C22×D513yes—
83C2×C3⋊D3—56no—
84C2×C3⋊D3—206no—
85C32×C4C22×D511yescharacteristic
86C32×C4C22×D513yes—
87C3⋊Dic3—52no—
88H(5,𝔽2)—451noSylow
89C2×C3×C5—212no—
90C2×C3×C5C23×D314yes—
91D15—624no—
92C22×D3—1524no—
93C3×Q8C2×D1514yescomplemented
94C3×D4C2×D15112yescomplemented
95C2×C3×C4C2×D15112yescomplemented
96#67—1524no—
97D12—1512no—
98D12—1524no—
99C4×D3—1524no—
100Dic6—154no—
101C22×C5C22×C3⋊D313yes—
102C2×D5—96no—
103C2×D5—366no—
104C4×C5C22×C3⋊D311yescharacteristic
105C4×C5C22×C3⋊D313yes—
106Dic5—92no—
107C2×C32—23no—
108C2×C32C23×D511yescharacteristic
109C3⋊D3—106no—
110#41—452no—
111#41—453no—
112#41C3⋊D1511yescharacteristic, complemented
113C2×D4—456no—
114C2×D4—453no—
115C3×C5#100914yescomplemented
116C22×C3C22×D15112yes—
117C2×D3—1524no—
118C2×D3—6024no—
119C3×C4C22×D1514yes—
120C3×C4C22×D15112yes—
121Dic3—158no—
122C2×C5—23no—
123C2×C5C23×C3⋊D311yescharacteristic
124D5—186no—
125C32#414911yescharacteristic, complemented, Sylow
126C23—456no—
127Q8—451no—
128Q8C2×C3⋊D1511yescharacteristic, complemented
129D4—456no—
130D4—456no—
131D4—453no—
132D4C2×C3⋊D1513yescomplemented
133C2×C4—456no—
134C2×C4C2×C3⋊D1513yescomplemented
135C2×C3—212no—
136C2×C3C23×D1514yes—
137D3—3024no—
138C5#6436611yescharacteristic, complemented, Sylow
139C22—456no—
140C22—1806no—
141C22C22×C3⋊D1513yes—
142C4—452no—
143C4C22×C3⋊D1513yes—
144C4C22×C3⋊D1511yescharacteristic
145C3#9210014yescomplemented
146C2—23no—
147C2—906no—
148C2C23×C3⋊D1511yescharacteristic
subgroupG/H
center, FrattiniC2C23×C3⋊D15
commutator, socle, cosocleC2×C32×C5C24
FittingC32×C5×#41C2
hypercenter#41C3⋊D15
hypocenterC32×C5H(5,𝔽2)
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C2 ◁ #41

Complements

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

NH ≅ G/Ntype
1. C32×C5×#41C2semidirect
2. #10624287C2semidirect
3. D4×C3⋊D15C2semidirect
4. #10624283C2semidirect
5. C2×C4⋊(C3⋊D15)C2semidirect
7. C22×C3⋊D15C22semidirect
8. C32×C5×Q8C22semidirect
9. C32×C5×D4C22semidirect
10. C2×C32×C4×C5C22semidirect
11. #67184C22semidirect
12. C4⋊(C3⋊D15)C22semidirect
13. C4⋊(C3⋊D15)C22semidirect
14. C4×C3⋊D15C22semidirect
15. #67180C22semidirect
17. C3×C5×#41D3semidirect
29. C32×#41D5semidirect
35. C3×C5×Q8C2×D3semidirect
36. C3×C5×D4C2×D3semidirect
37. C2×C3×C4×C5C2×D3semidirect
47. C5×#41C3⋊D3semidirect
53. C32×Q8C2×D5semidirect
54. C32×D4C2×D5semidirect
55. C2×C32×C4C2×D5semidirect
67. C3×#41D15semidirect
72. C32×C5H(5,𝔽2)semidirect
74. C5×Q8C2×C3⋊D3semidirect
75. C5×D4C2×C3⋊D3semidirect
76. C2×C4×C5C2×C3⋊D3semidirect
93. C3×Q8C2×D15semidirect
94. C3×D4C2×D15semidirect
95. C2×C3×C4C2×D15semidirect
112. #41C3⋊D15semidirect
115. C3×C5#1009semidirect
125. C32#4149semidirect
128. Q8C2×C3⋊D15semidirect
132. D4C2×C3⋊D15semidirect
134. C2×C4C2×C3⋊D15semidirect
138. C5#64366semidirect
145. C3#92100semidirect

Maximal subgroups

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

subgroupindex
C32×C5×#412
#106242872
D4×C3⋊D152
#106242832
C2×C4⋊(C3⋊D15)2
#921003
#643665