Finite Group Databasebeta

← C3⋊D15×D155 #42124959

Subgroups — C3⋊D15×D155 #42124959

Order 27900.

288 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 66 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×C31×C3⋊D15C211yesmaximal, characteristic, complemented
3C3⋊(C3⋊(C5⋊D155))C211yesmaximal, characteristic, complemented
4D15×D155—34nomaximal
5C32×C52×C31C2211yescharacteristic, complemented, Hall
6C3⋊D3×D155—51nomaximal
7D31×C3⋊D15—51nomaximal
8C3⋊(C5⋊D155)—34no—
9C5×D15×C31—34no—
10C3×C5×D155D314yescomplemented
11D5×D155—91noHall
12C3⋊D465—51no—
13C3⋊D465—51no—
14C3⋊D465—102no—
15C31×C3⋊D15D511yescharacteristic, complemented
16C5×C3⋊D3×C31—51no—
17C32×D155D511yescharacteristic, complemented
18C32×C5×D31—51no—
19C3×C52×C31C2×D314yescomplemented
20D3×D155—154no—
21D15×D31—154no—
22C5⋊D155—91no—
23C5×D155C3⋊D311yescharacteristic, complemented
24C5×D5×C31—91no—
25C32×C5×C31—22no—
26C32×C5×C31C2×D511yescharacteristic, complemented
27C32×C5×C31C2×D511yescharacteristic, complemented
28C3⋊D3×D31—251noHall
29D465—154no—
30D465—154no—
31D465—308no—
32D15×C31—34no—
33C5×D3×C31—154no—
34C3×D155D1514yescomplemented
35C3×C5×D31—54no—
36D5×C3⋊D15—311nomaximal, Hall
37C52×C31C2×C3⋊D311yescharacteristic, complemented, Hall
38C2×D155—451no—
39D5×D31—451no—
40C3⋊D93—251no—
41C3⋊D3×C31—51no—
42C32×D31—51no—
43C3×C5×C31—28no—
44C3×C5×C31D3×D514yescomplemented
45C3×C5×C31C2×D1514yescomplemented
46C3⋊(C3⋊(C5⋊D5))—311no—
47C5×C3⋊D15D3111yescharacteristic, complemented
48C32×C5×D5—311no—
49D3×D31—754no—
50C2×C5×C31—451no—
51D155—451no—
52D155—451no—
53D155—902no—
54D155C3⋊D1511yescharacteristic, direct product factor
55C5×D31—51no—
56D5×C31—91no—
57D5×D15—934no—
58C32×C31D5211yescharacteristic, complemented, Hall
59C32×C52C2×D3111yescharacteristic, complemented, Hall
60D93—754no—
61C3×D31—54no—
62D3×C31—154no—
63C2×C3⋊D15—1551no—
64D5×C3⋊D3—1551no—
65C5×C31—22no—
66C5×C31D5×C3⋊D311yescharacteristic, complemented
67C5×C31C2×C3⋊D1511yescharacteristic, complemented
68C3⋊(C5⋊D5)—934no—
69C5×D15—34no—
70C3×C5×D5—314no—
71C2×D31—2251noHall
72D52—2791noHall
73C3×C31D5×D1514yescomplemented
74C2×C32×C5—1551no—
75C3⋊D15—3102no—
76C3⋊D15—1551no—
77C3⋊D15—1551no—
78C3⋊D15D15511yescharacteristic, direct product factor
79C5×C3⋊D3—51no—
80C32×D5—311no—
81C3×C52D3×D3114yescomplemented
82C2×C31—451no—
83D31—51no—
84D31—2251no—
85C2×D15—4654no—
86D3×D5—4654no—
87C5⋊D5—2791no—
88C5×D5—91no—
89C5×D5—311no—
90C32×C5—22no—
91C32×C5D5×D3111yescharacteristic, complemented
92C32×C5C2×D15511yescharacteristic, complemented
93C2×C3⋊D3—7751noHall
94C31D5×C3⋊D1511yescharacteristic, complemented, Sylow
95C2×C3×C5—1554no—
96D15—34no—
97D15—9308no—
98D15—4654no—
99D15—4654no—
100C3×D5—314no—
101C5×D3—154no—
102C52C3⋊D3×D3111yescharacteristic, complemented, Sylow
103C2×D5—13951no—
104C2×D5—13951no—
105C2×C32—1551no—
106C3⋊D3—51no—
107C3⋊D3—7751no—
108C3×C5—28no—
109C3×C5D15×D3114yescomplemented
110C3×C5D3×D15514yescomplemented
111C2×D3—23254no—
112C2×C5—451no—
113C2×C5—1551no—
114D5—91no—
115D5—311no—
116D5—13951no—
117D5—13951no—
118D5—27902no—
119C32D5×D15511yescharacteristic, complemented, Sylow
120C2×C3—1554no—
121D3—154no—
122D3—23254no—
123C5—22no—
124C5D31×C3⋊D1511yescharacteristic, complemented
125C5C3⋊D3×D15511yescharacteristic, complemented
126C22—69751noSylow
127C3D15×D15514yescomplemented
128C2—451no—
129C2—69751no—
130C2—1551no—
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×C31×C3⋊D15C2semidirect
3. C3⋊(C3⋊(C5⋊D155))C2semidirect
5. C32×C52×C31C22semidirect
10. C3×C5×D155D3semidirect
15. C31×C3⋊D15D5semidirect
17. C32×D155D5semidirect
19. C3×C52×C31C2×D3semidirect
23. 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
47. C5×C3⋊D15D31semidirect
54. D155C3⋊D15direct (N × H)
58. C32×C31D52semidirect
59. C32×C52C2×D31semidirect
66. C5×C31D5×C3⋊D3semidirect
67. C5×C31C2×C3⋊D15semidirect
73. C3×C31D5×D15semidirect
78. C3⋊D15D155direct (N × H)
81. C3×C52D3×D31semidirect
91. C32×C5D5×D31semidirect
92. C32×C5C2×D155semidirect
94. C31D5×C3⋊D15semidirect
102. C52C3⋊D3×D31semidirect
109. C3×C5D15×D31semidirect
110. C3×C5D3×D155semidirect
119. C32D5×D155semidirect
124. C5D31×C3⋊D15semidirect
125. C5C3⋊D3×D155semidirect
127. C3D15×D155semidirect

Maximal subgroups

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

subgroupindex
C32×C5×D1552
C5×C31×C3⋊D152
C3⋊(C3⋊(C5⋊D155))2
D15×D1553
C3⋊D3×D1555
D31×C3⋊D155
D5×C3⋊D1531