Finite Group Databasebeta

← #13089512

Subgroups — #13089512

Order 1440.

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

normal subgroups only

This group has 876 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×Q8C211yesmaximal, characteristic, complemented
2#10624287C214yesmaximal, complemented
3Q8×C3⋊D15C214yesmaximal, complemented
4#10624283C216yesmaximal, complemented
5#92098—34nomaximal
6C32×C5×Q8C2214yes—
7C2×C32×C4×C5C2213yes—
8#67184C2214yes—
9C4⋊(C3⋊D15)C2216yes—
10C4×C3⋊D15C22112yes—
11#67180C2216yes—
12#64364—51nomaximal, Hall
13C2×C3×C5×Q8D314yescomplemented
14#6821—316no—
15Q8×D15—316no—
16#6817—324no—
17C22×C32×C5C2311yescharacteristic
18C2×C3⋊D15C2314yes—
19C32×C4×C5C2316yes—
20C3⋊Dic15C2314yes—
21#4147—91noHall
22C2×C32×Q8D511yescharacteristic, complemented
23#3832—54no—
24Q8×C3⋊D3—54no—
25#3828—56no—
26C3×C5×Q8C2×D3116yes—
27C2×C3×C4×C5C2×D3112yes—
28#1220—316no—
29D60—324no—
30C4×D15—348no—
31Dic30—324no—
32#1007—154no—
33C2×C32×C5—21no—
34C2×C32×C5C2411yescharacteristic
35C3⋊D15—24no—
36C2×C5×Q8C3⋊D311yescharacteristic, complemented
37#713—94no—
38Q8×D5—94no—
39#709—96no—
40C32×Q8C2×D514yes—
41C2×C32×C4C2×D513yes—
42#638—54no—
43C4⋊(C3⋊D3)—56no—
44C4×C3⋊D3—512no—
45#634—56no—
46C22×C3×C5C22×D314yes—
47C2×D15—316no—
48C3×C4×C5C22×D3124yes—
49Dic15—316no—
50C2×C3×Q8D1514yescomplemented
51#239—1516no—
52D3×Q8—1516no—
53#235—1524no—
54C32×C52−1+411yescharacteristic, complemented, Hall
55C5×Q8C2×C3⋊D314yes—
56C2×C4×C5C2×C3⋊D313yes—
57C22⋊D5—94no—
58D20—96no—
59C4×D5—912no—
60Dic10—96no—
61C22×C32C22×D511yescharacteristic
62C2×C3⋊D3—54no—
63C32×C4C22×D516yes—
64C3⋊Dic3—54no—
652−1+4—451noSylow
66C2×C3×C5—24no—
67C2×C3×C5C23×D314yes—
68D15—616no—
69C3×Q8C2×D15116yes—
70C2×C3×C4C2×D15112yes—
71#67—1516no—
72D12—1524no—
73C4×D3—1548no—
74Dic6—1524no—
75C22×C5C22×C3⋊D311yescharacteristic
76C2×D5—94no—
77C4×C5C22×C3⋊D316yes—
78Dic5—94no—
79C2×C32—21no—
80C2×C32C23×D511yescharacteristic
81C3⋊D3—104no—
82#41—454no—
83#41—456no—
84C2×Q8—454no—
85C2×Q8C3⋊D1511yescharacteristic, complemented
86C3×C5#100714yescomplemented
87C22×C3C22×D1514yes—
88C2×D3—1516no—
89C3×C4C22×D15124yes—
90Dic3—1516no—
91C2×C5—21no—
92C2×C5C23×C3⋊D311yescharacteristic
93D5—184no—
94C32#414711yescharacteristic, complemented, Sylow
95Q8—456no—
96Q8C2×C3⋊D1514yes—
97D4—454no—
98D4—456no—
99C2×C4—4512no—
100C2×C4C2×C3⋊D1513yes—
101C2×C3—24no—
102C2×C3C23×D1514yes—
103D3—3016no—
104C5#6436411yescharacteristic, complemented, Sylow
105C22—454no—
106C22C22×C3⋊D1511yescharacteristic
107C4—454no—
108C4C22×C3⋊D1516yes—
109C3#9209814yescomplemented
110C2—21no—
111C2—904no—
112C2C23×C3⋊D1511yescharacteristic
subgroupG/H
center, FrattiniC2C23×C3⋊D15
commutator, socle, cosocleC2×C32×C5C24
FittingC2×C32×C5×Q8C2
hypercenterC2×Q8C3⋊D15
hypocenterC32×C52−1+4
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C2 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C32×C5×Q8C2semidirect
2. #10624287C2semidirect
3. Q8×C3⋊D15C2semidirect
4. #10624283C2semidirect
13. C2×C3×C5×Q8D3semidirect
22. C2×C32×Q8D5semidirect
36. C2×C5×Q8C3⋊D3semidirect
50. C2×C3×Q8D15semidirect
54. C32×C52−1+4semidirect
85. C2×Q8C3⋊D15semidirect
86. C3×C5#1007semidirect
94. C32#4147semidirect
104. C5#64364semidirect
109. C3#92098semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C5×Q82
#106242872
Q8×C3⋊D152
#106242832
#920983
#643645