Finite Group Databasebeta

← C5×C3⋊D3×D155 #42124951

Subgroups — C5×C3⋊D3×D155 #42124951

Order 27900.

288 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 72 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⋊D3×C31C211yesmaximal, characteristic, complemented
3C5×C3⋊D465C211yesmaximal, characteristic, complemented
4C5×D3×D155—34nomaximal
5C32×C52×C31C2211yescharacteristic, complemented, Hall
6C3⋊D3×D155C511yesmaximal, characteristic, direct product factor
7C5×C3⋊D3×D31—51nomaximal
8C5×D465—34no—
9C52×D3×C31—34no—
10C3×C5×D155D314yescomplemented
11C2×C5×D155—91noHall
12C3⋊D465C2×C511yescharacteristic, complemented
13C5×C3⋊D93—51no—
14C5×C3⋊D3×C31—22no—
15C5×C3⋊D3×C31D511yescharacteristic, complemented
16C5×C3⋊D3×C31C2×C511yescharacteristic, complemented
17C32×D155C2×C511yescharacteristic, complemented
18C32×C5×D31—51no—
19C3×C52×C31C2×D314yescomplemented
20D3×D155—34no—
21C5×D3×D31—154no—
22C2×C52×C31—91no—
23C5×D155—91no—
24C5×D155C3⋊D311yescharacteristic, direct product factor
25C32×C5×C31—22no—
26C32×C5×C31C2×D511yescharacteristic, complemented
27C32×C5×C31C22×C511yescharacteristic, complemented
28C3⋊D3×D31—51noHall
29D465—34no—
30C5×D93—154no—
31C5×D3×C31—34no—
32C5×D3×C31—34no—
33C5×D3×C31—68no—
34C3×D155C5×D314yescomplemented
35C3×C5×D31—54no—
36C5×D5×C3⋊D3—311nomaximal, Hall
37C52×C31C2×C3⋊D311yescharacteristic, complemented, Hall
38C2×D155—91no—
39C2×C5×D31—451no—
40C3⋊D93—51no—
41C3⋊D3×C31C5×D511yescharacteristic, complemented
42C32×D31—51no—
43C3×C5×C31—28no—
44C3×C5×C31D3×D514yescomplemented
45C3×C5×C31C2×C5×D314yescomplemented
46C5×C3⋊D15—311no—
47C52×C3⋊D3D3111yescharacteristic, complemented
48C32×C5×D5—311no—
49D3×D31—154no—
50C2×C5×C31—91no—
51C2×C5×C31—91no—
52C2×C5×C31—182no—
53D155—91no—
54D155C5×C3⋊D311yescharacteristic, direct product factor
55C5×D31—51no—
56C5×D31—451no—
57C5×D3×D5—934no—
58C32×C31C2×C5×D511yescharacteristic, complemented, Hall
59C32×C52C2×D3111yescharacteristic, complemented, Hall
60D93—154no—
61C3×D31—54no—
62D3×C31—34no—
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—934no—
69C52×D3—34no—
70C3×C5×D5—314no—
71C2×D31—451noHall
72C2×C5×D5—2791noHall
73C3×C31C5×D3×D514yescomplemented
74C2×C32×C5—1551no—
75C3⋊D15—311no—
76C5×C3⋊D3—22no—
77C5×C3⋊D3—1551no—
78C5×C3⋊D3C5×D3111yescharacteristic, complemented
79C5×C3⋊D3D15511yescharacteristic, direct product factor
80C32×D5—311no—
81C3×C52D3×D3114yescomplemented
82C2×C31—91no—
83D31—51no—
84D31—451no—
85C2×C5×D3—4654no—
86D3×D5—934no—
87C2×C52—91no—
88C5×D5—2791no—
89C5×D5—311no—
90C32×C5—22no—
91C32×C5C2×C5×D3111yescharacteristic, complemented
92C32×C5C2×D15511yescharacteristic, complemented
93C2×C3⋊D3—1551noHall
94C31C5×D5×C3⋊D311yescharacteristic, complemented, Sylow
95C2×C3×C5—1554no—
96D15—934no—
97C3×D5—314no—
98C5×D3—34no—
99C5×D3—34no—
100C5×D3—68no—
101C5×D3—4654no—
102C52C3⋊D3×D3111yescharacteristic, complemented, Sylow
103C22×C5—13951no—
104C2×D5—2791no—
105C2×C32—1551no—
106C3⋊D3—1551no—
107C3⋊D3C5×D15511yescharacteristic, direct product factor
108C3×C5—28no—
109C3×C5C5×D3×D3114yescomplemented
110C3×C5D3×D15514yescomplemented
111C2×D3—4654no—
112C2×C5—91no—
113C2×C5—91no—
114C2×C5—182no—
115C2×C5—13951no—
116C2×C5—1551no—
117D5—2791no—
118D5—311no—
119C32C2×C5×D15511yescharacteristic, complemented, Sylow
120C2×C3—1554no—
121D3—34no—
122D3—4654no—
123C5—22no—
124C5C5×C3⋊D3×D3111yescharacteristic, complemented
125C5C3⋊D3×D15511yescharacteristic, direct product factor
126C22—13951noSylow
127C3C5×D3×D15514yescomplemented
128C2—91no—
129C2—13951no—
130C2—1551no—
subgroupG/H
center, hypercenterC5C3⋊D3×D155
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⋊D3×C31C2semidirect
3. C5×C3⋊D465C2semidirect
5. C32×C52×C31C22semidirect
6. C3⋊D3×D155C5direct (N × H)
10. C3×C5×D155D3semidirect
12. C3⋊D465C2×C5semidirect
15. C5×C3⋊D3×C31D5semidirect
16. C5×C3⋊D3×C31C2×C5semidirect
17. C32×D155C2×C5semidirect
19. C3×C52×C31C2×D3semidirect
24. C5×D155C3⋊D3direct (N × H)
26. C32×C5×C31C2×D5semidirect
27. C32×C5×C31C22×C5semidirect
34. C3×D155C5×D3semidirect
37. C52×C31C2×C3⋊D3semidirect
41. C3⋊D3×C31C5×D5semidirect
44. C3×C5×C31D3×D5semidirect
45. C3×C5×C31C2×C5×D3semidirect
47. C52×C3⋊D3D31semidirect
54. D155C5×C3⋊D3direct (N × H)
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
78. C5×C3⋊D3C5×D31semidirect
79. C5×C3⋊D3D155direct (N × H)
81. C3×C52D3×D31semidirect
91. C32×C5C2×C5×D31semidirect
92. C32×C5C2×D155semidirect
94. C31C5×D5×C3⋊D3semidirect
102. C52C3⋊D3×D31semidirect
107. C3⋊D3C5×D155direct (N × H)
109. C3×C5C5×D3×D31semidirect
110. C3×C5D3×D155semidirect
119. C32C2×C5×D155semidirect
124. C5C5×C3⋊D3×D31semidirect
125. C5C3⋊D3×D155direct (N × H)
127. C3C5×D3×D155semidirect

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⋊D3×C312
C5×C3⋊D4652
C5×D3×D1553
C3⋊D3×D1555
C5×C3⋊D3×D315
C5×D5×C3⋊D331