Finite Group Databasebeta

← C5×D155⋊(C3⋊D3) #42124952

Subgroups — C5×D155⋊(C3⋊D3) #42124952

Order 27900.

288 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 70 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
2C52×C3⋊D93C211yesmaximal, characteristic, complemented
3C5×C31×C3⋊D15C211yesmaximal, characteristic, complemented
4C5×D15⋊D31—34nomaximal
5C32×C52×C31C2211yescharacteristic, complemented, Hall
6D155⋊(C3⋊D3)C511yesmaximal, characteristic, direct product factor
7C5×C3⋊D3×D31—51nomaximal
8C5×D15×C31—34no—
9C52×D93—34no—
10C3×C5×D155D314yescomplemented
11C5×D5×D31—91noHall
12C31×C3⋊D15C2×C511yescharacteristic, complemented
13C5×C3⋊D93—22no—
14C5×C3⋊D93D511yescharacteristic, complemented
15C5×C3⋊D93C2×C511yescharacteristic, complemented
16C5×C3⋊D3×C31—51no—
17C32×D155C2×C511yescharacteristic, complemented
18C32×C5×D31—51no—
19C3×C52×C31C2×D314yescomplemented
20D15⋊D31—34no—
21C5×D3×D31—154no—
22C5×D155C3⋊D311yescharacteristic, complemented
23C5×D5×C31—91no—
24C52×D31—91no—
25C32×C5×C31—22no—
26C32×C5×C31C2×D511yescharacteristic, complemented
27C32×C5×C31C22×C511yescharacteristic, complemented
28C3⋊D3×D31—51noHall
29D15×C31—34no—
30C5×D93—34no—
31C5×D93—34no—
32C5×D93—68no—
33C5×D3×C31—154no—
34C3×D155C5×D314yescomplemented
35C3×C5×D31—54no—
36C5×D5×C3⋊D3—311nomaximal, Hall
37C52×C31C2×C3⋊D311yescharacteristic, complemented, Hall
38C2×C5×D31—451no—
39D5×D31—91no—
40C3⋊D93C5×D511yescharacteristic, complemented
41C3⋊D3×C31—51no—
42C32×D31—51no—
43C3×C5×C31—28no—
44C3×C5×C31D3×D514yescomplemented
45C3×C5×C31C2×C5×D314yescomplemented
46C5×C3⋊D15D3111yescharacteristic, complemented
47C52×C3⋊D3—311no—
48C32×C5×D5—311no—
49D3×D31—154no—
50C2×C5×C31—451no—
51D155C5×C3⋊D311yescharacteristic, complemented
52C5×D31—51no—
53C5×D31—91no—
54C5×D31—91no—
55C5×D31—182no—
56D5×C31—91no—
57C5×D3×D5—934no—
58C32×C31C2×C5×D511yescharacteristic, complemented, Hall
59C32×C52C2×D3111yescharacteristic, complemented, Hall
60D93—34no—
61C3×D31—54no—
62D3×C31—154no—
63C2×C5×C3⋊D3—1551no—
64D5×C3⋊D3—311no—
65C5×C31—22no—
66C5×C31D5×C3⋊D311yescharacteristic, complemented
67C5×C31C2×C5×C3⋊D311yescharacteristic, complemented
68C5×D15—34no—
69C52×D3—934no—
70C3×C5×D5—314no—
71C2×D31—451noHall
72C2×C5×D5—2791noHall
73C3×C31C5×D3×D514yescomplemented
74C2×C32×C5—1551no—
75C3⋊D15C5×D3111yescharacteristic, complemented
76C5×C3⋊D3—51no—
77C5×C3⋊D3—311no—
78C5×C3⋊D3—311no—
79C5×C3⋊D3—622no—
80C32×D5—311no—
81C3×C52D3×D3114yescomplemented
82C2×C31—451no—
83D31—51no—
84D31—91no—
85C2×C5×D3—4654no—
86D3×D5—934no—
87C2×C52—2791no—
88C5×D5—91no—
89C5×D5—311no—
90C32×C5—22no—
91C32×C5D5×D3111yescharacteristic, complemented
92C32×C5C2×C5×D3111yescharacteristic, complemented
93C2×C3⋊D3—1551noHall
94C31C5×D5×C3⋊D311yescharacteristic, complemented, Sylow
95C2×C3×C5—1554no—
96D15—34no—
97C3×D5—314no—
98C5×D3—154no—
99C5×D3—934no—
100C5×D3—934no—
101C5×D3—1868no—
102C52C3⋊D3×D3111yescharacteristic, complemented, Sylow
103C22×C5—13951no—
104C2×D5—2791no—
105C2×C32—1551no—
106C3⋊D3—51no—
107C3⋊D3—311no—
108C3×C5—28no—
109C3×C5C5×D3×D3114yescomplemented
110C3×C5D15⋊D3114yescomplemented
111C2×D3—4654no—
112C2×C5—2791no—
113C2×C5—2791no—
114C2×C5—451no—
115C2×C5—5582no—
116C2×C5—1551no—
117D5—91no—
118D5—311no—
119C32C5×D5×D3111yescharacteristic, complemented, Sylow
120C2×C3—1554no—
121D3—154no—
122D3—934no—
123C5—22no—
124C5C5×C3⋊D3×D3111yescharacteristic, complemented
125C5D155⋊(C3⋊D3)11yescharacteristic, direct product factor
126C22—13951noSylow
127C3C5×D15⋊D3114yescomplemented
128C2—2791no—
129C2—451no—
130C2—1551no—
subgroupG/H
center, hypercenterC5D155⋊(C3⋊D3)
commutator, cosocle, hypocenterC32×C5×C31C22×C5
FrattiniC1G
Fitting, socleC32×C52×C31C22
LCSG ▷ C32×C5×C31
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
1. C32×C5×D155C2semidirect
2. C52×C3⋊D93C2semidirect
3. C5×C31×C3⋊D15C2semidirect
5. C32×C52×C31C22semidirect
6. D155⋊(C3⋊D3)C5direct (N × H)
10. C3×C5×D155D3semidirect
12. C31×C3⋊D15C2×C5semidirect
14. C5×C3⋊D93D5semidirect
15. C5×C3⋊D93C2×C5semidirect
17. C32×D155C2×C5semidirect
19. C3×C52×C31C2×D3semidirect
22. C5×D155C3⋊D3semidirect
26. C32×C5×C31C2×D5semidirect
27. C32×C5×C31C22×C5semidirect
34. C3×D155C5×D3semidirect
37. C52×C31C2×C3⋊D3semidirect
40. C3⋊D93C5×D5semidirect
44. C3×C5×C31D3×D5semidirect
45. C3×C5×C31C2×C5×D3semidirect
46. C5×C3⋊D15D31semidirect
51. D155C5×C3⋊D3semidirect
58. C32×C31C2×C5×D5semidirect
59. C32×C52C2×D31semidirect
66. C5×C31D5×C3⋊D3semidirect
67. C5×C31C2×C5×C3⋊D3semidirect
73. C3×C31C5×D3×D5semidirect
75. C3⋊D15C5×D31semidirect
81. C3×C52D3×D31semidirect
91. C32×C5D5×D31semidirect
92. C32×C5C2×C5×D31semidirect
94. C31C5×D5×C3⋊D3semidirect
102. C52C3⋊D3×D31semidirect
109. C3×C5C5×D3×D31semidirect
110. C3×C5D15⋊D31semidirect
119. C32C5×D5×D31semidirect
124. C5C5×C3⋊D3×D31semidirect
125. C5D155⋊(C3⋊D3)direct (N × H)
127. C3C5×D15⋊D31semidirect

Maximal subgroups

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

subgroupindex
C32×C5×D1552
C52×C3⋊D932
C5×C31×C3⋊D152
C5×D15⋊D313
D155⋊(C3⋊D3)5
C5×C3⋊D3×D315
C5×D5×C3⋊D331