Finite Group Databasebeta

← D155⋊(C3⋊D15) #42124960

Subgroups — D155⋊(C3⋊D15) #42124960

Order 27900.

288 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 65 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×D155C211yesmaximal, characteristic, complemented
2C5×C3⋊D465C211yesmaximal, characteristic, complemented
3C31×C3⋊(C3⋊(C5⋊D5))C211yesmaximal, characteristic, complemented
4D155⋊D15—34nomaximal
5C32×C52×C31C2211yescharacteristic, complemented, Hall
6D155⋊(C3⋊D3)—51nomaximal
7D31×C3⋊D15—51nomaximal
8C31×C3⋊(C5⋊D5)—34no—
9C5×D465—34no—
10C3×C5×D155D314yescomplemented
11(C5⋊D5)⋊D31—91noHall
12C3⋊D465D511yescharacteristic, complemented
13C31×C3⋊D15—51no—
14C31×C3⋊D15—51no—
15C31×C3⋊D15—102no—
16C5×C3⋊D93—51no—
17C32×D155D511yescharacteristic, complemented
18C32×C5×D31—51no—
19C3×C52×C31C2×D314yescomplemented
20D15⋊D31—154no—
21D15×D31—154no—
22C31×C5⋊D5—91no—
23C5×D155—91no—
24C5×D155C3⋊D311yescharacteristic, complemented
25C32×C5×C31—22no—
26C32×C5×C31C2×D511yescharacteristic, complemented
27C32×C5×C31C2×D511yescharacteristic, complemented
28C3⋊D3×D31—251noHall
29D465—34no—
30D15×C31—154no—
31D15×C31—154no—
32D15×C31—308no—
33C5×D93—154no—
34C3×D155D1514yescomplemented
35C3×C5×D31—54no—
36D5×C3⋊D15—311nomaximal, Hall
37C52×C31C2×C3⋊D311yescharacteristic, complemented, Hall
38D5×D31—451no—
39D5×D31—451no—
40C3⋊D93—51no—
41C3⋊D3×C31—251no—
42C32×D31—51no—
43C3×C5×C31—28no—
44C3×C5×C31D3×D514yescomplemented
45C3×C5×C31C2×D1514yescomplemented
46C3⋊(C3⋊(C5⋊D5))D3111yescharacteristic, complemented
47C5×C3⋊D15—311no—
48C32×C5×D5—311no—
49D3×D31—754no—
50D155—91no—
51D155C3⋊D1511yescharacteristic, complemented
52C5×D31—51no—
53C5×D31—451no—
54D5×C31—451no—
55D5×C31—451no—
56D5×C31—902no—
57D5×D15—934no—
58C32×C31D5211yescharacteristic, complemented, Hall
59C32×C52C2×D3111yescharacteristic, complemented, Hall
60D93—154no—
61C3×D31—54no—
62D3×C31—754no—
63C2×C3⋊D15—1551no—
64D5×C3⋊D3—1551no—
65C5×C31—22no—
66C5×C31D5×C3⋊D311yescharacteristic, complemented
67C5×C31C2×C3⋊D1511yescharacteristic, complemented
68C3⋊(C5⋊D5)—34no—
69C5×D15—934no—
70C3×C5×D5—314no—
71C2×D31—2251noHall
72D52—2791noHall
73C3×C31D5×D1514yescomplemented
74C2×C32×C5—1551no—
75C3⋊D15—51no—
76C3⋊D15—51no—
77C3⋊D15—102no—
78C3⋊D15—311no—
79C5×C3⋊D3—1551no—
80C32×D5—311no—
81C3×C52D3×D3114yescomplemented
82C2×C31—2251no—
83D31—51no—
84D31—451no—
85C2×D15—4654no—
86D3×D5—4654no—
87C5⋊D5—91no—
88C5×D5—2791no—
89C5×D5—311no—
90C32×C5—22no—
91C32×C5D5×D3111yescharacteristic, complemented
92C32×C5D5×D3111yescharacteristic, complemented
93C2×C3⋊D3—7751noHall
94C31D5×C3⋊D1511yescharacteristic, complemented, Sylow
95C2×C3×C5—1554no—
96D15—154no—
97D15—154no—
98D15—308no—
99D15—934no—
100C3×D5—314no—
101C5×D3—4654no—
102C52C3⋊D3×D3111yescharacteristic, complemented, Sylow
103C2×D5—13951no—
104C2×D5—13951no—
105C2×C32—1551no—
106C3⋊D3—251no—
107C3⋊D3—1551no—
108C3×C5—28no—
109C3×C5D15×D3114yescomplemented
110C3×C5D15⋊D3114yescomplemented
111C2×D3—23254no—
112C2×C5—13951no—
113C2×C5—1551no—
114D5—2791no—
115D5—311no—
116D5—451no—
117D5—451no—
118D5—902no—
119C32(C5⋊D5)⋊D3111yescharacteristic, complemented, Sylow
120C2×C3—1554no—
121D3—754no—
122D3—4654no—
123C5—22no—
124C5D31×C3⋊D1511yescharacteristic, complemented
125C5D155⋊(C3⋊D3)11yescharacteristic, complemented
126C22—69751noSylow
127C3D155⋊D1514yescomplemented
128C2—13951no—
129C2—1551no—
130C2—2251no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C52×C31C22
LCSG ▷ C32×C52×C31
UCSC1

Complements

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

NH ≅ G/Ntype
1. C32×C5×D155C2semidirect
2. C5×C3⋊D465C2semidirect
3. C31×C3⋊(C3⋊(C5⋊D5))C2semidirect
5. C32×C52×C31C22semidirect
10. C3×C5×D155D3semidirect
12. C3⋊D465D5semidirect
17. C32×D155D5semidirect
19. C3×C52×C31C2×D3semidirect
24. C5×D155C3⋊D3semidirect
26. C32×C5×C31C2×D5semidirect
27. C32×C5×C31C2×D5semidirect
34. C3×D155D15semidirect
37. C52×C31C2×C3⋊D3semidirect
44. C3×C5×C31D3×D5semidirect
45. C3×C5×C31C2×D15semidirect
46. C3⋊(C3⋊(C5⋊D5))D31semidirect
51. D155C3⋊D15semidirect
58. C32×C31D52semidirect
59. C32×C52C2×D31semidirect
66. C5×C31D5×C3⋊D3semidirect
67. C5×C31C2×C3⋊D15semidirect
73. C3×C31D5×D15semidirect
81. C3×C52D3×D31semidirect
91. C32×C5D5×D31semidirect
92. C32×C5D5×D31semidirect
94. C31D5×C3⋊D15semidirect
102. C52C3⋊D3×D31semidirect
109. C3×C5D15×D31semidirect
110. C3×C5D15⋊D31semidirect
119. C32(C5⋊D5)⋊D31semidirect
124. C5D31×C3⋊D15semidirect
125. C5D155⋊(C3⋊D3)semidirect
127. C3D155⋊D15semidirect

Maximal subgroups

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

subgroupindex
C32×C5×D1552
C5×C3⋊D4652
C31×C3⋊(C3⋊(C5⋊D5))2
D155⋊D153
D155⋊(C3⋊D3)5
D31×C3⋊D155
D5×C3⋊D1531