Finite Group Databasebeta

← C2×C5×C3⋊D195 #26043869

Subgroups — C2×C5×C3⋊D195 #26043869

Order 11700.

288 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 102 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
1C5×C3⋊D195C212yesmaximal, direct product factor
2C2×C32×C52×C13C211yesmaximal, characteristic, complemented
3C2×C5×D195—34nomaximal
4C32×C52×C13C2211yescharacteristic, complemented, Hall
5C2×C5×C3⋊D39—51nomaximal
6C2×C3⋊D195C511yesmaximal, characteristic, direct product factor
7C2×C3×C52×C13D314yescomplemented
8C5×D195—38no—
9C2×C5×D65—91noHall
10C2×C32×C5×C13—22no—
11C2×C32×C5×C13D511yescharacteristic, complemented
12C2×C32×C5×C13C2×C511yescharacteristic, complemented
13C3⋊D195C2×C512yesdirect product factor
14C5×C3⋊D39—52no—
15C3×C52×C13C2×D314yescomplemented
16C2×C5×C3⋊D15—131nomaximal, Hall
17C2×D195—34no—
18C2×C5×D39—154no—
19C2×C52×C13C3⋊D311yescharacteristic, complemented
20C5×D65—92no—
21C32×C5×C13—22no—
22C32×C5×C13C2×D511yescharacteristic, complemented
23C32×C5×C13C22×C511yescharacteristic, complemented
24C2×C3⋊D39—51noHall
25C2×C32×C52D1311yescharacteristic, complemented
26C5×C3⋊D15—132no—
27C2×C3×C5×C13—28no—
28C2×C3×C5×C13C5×D314yescomplemented
29C2×C3×C5×C13D1514yescomplemented
30D195—38no—
31C5×D39—158no—
32C52×C13C2×C3⋊D311yescharacteristic, complemented, Hall
33C2×C5×D15—394no—
34C2×D65—91no—
35C2×C5×D13—451no—
36C2×C32×C13C5×D511yescharacteristic, complemented
37C3⋊D39—52no—
38C32×C52C2×D1311yescharacteristic, complemented, Hall
39C3×C5×C13—28no—
40C3×C5×C13C2×C5×D314yescomplemented
41C3×C5×C13C2×D1514yescomplemented
42C2×C3⋊D15—131no—
43C2×C5×C3⋊D3—651no—
44C2×D39—154no—
45C2×C3×C52D3914yescomplemented
46C5×D15—398no—
47C2×C5×C13—22no—
48C2×C5×C13C5×C3⋊D311yescharacteristic, complemented
49C2×C5×C13C3⋊D1511yescharacteristic, complemented
50D65—92no—
51C5×D13—452no—
52C32×C13C2×C5×D511yescharacteristic, complemented, Hall
53C2×C5×D5—1171noHall
54C2×C32×C5—22no—
55C2×C32×C5C5×D1311yescharacteristic, complemented
56C2×C32×C5D6511yescharacteristic, complemented
57C3⋊D15—132no—
58C5×C3⋊D3—652no—
59C2×C3×C13C5×D1514yescomplemented
60D39—158no—
61C3×C52C2×D3914yescomplemented
62C5×C13—22no—
63C5×C13C2×C5×C3⋊D311yescharacteristic, complemented
64C5×C13C2×C3⋊D1511yescharacteristic, complemented
65C2×D15—394no—
66C2×C5×D3—1954no—
67C2×D13—451noHall
68C2×C52C3⋊D3911yescharacteristic, complemented
69C5×D5—1172no—
70C32×C5—22no—
71C32×C5C2×C5×D1311yescharacteristic, complemented
72C32×C5C2×D6511yescharacteristic, complemented
73C3×C13C2×C5×D1514yescomplemented
74C2×C3⋊D3—651noHall
75C2×C3×C5—28no—
76C2×C3×C5C5×D3914yescomplemented
77C2×C3×C5D19514yescomplemented
78D15—398no—
79C5×D3—1958no—
80C2×C13C5×C3⋊D1511yescharacteristic, complemented
81D13—452no—
82C52C2×C3⋊D3911yescharacteristic, complemented, Sylow
83C22×C5—5851no—
84C2×D5—1171no—
85C2×C32C5×D6511yescharacteristic, complemented
86C3⋊D3—652no—
87C3×C5—28no—
88C3×C5C2×C5×D3914yescomplemented
89C3×C5C2×D19514yescomplemented
90C13C2×C5×C3⋊D1511yescharacteristic, complemented, Sylow
91C2×D3—1954no—
92C2×C5—22no—
93C2×C5—5852no—
94C2×C5C5×C3⋊D3911yescharacteristic, complemented
95C2×C5C3⋊D19511yescharacteristic, direct product factor
96D5—1172no—
97C32C2×C5×D6511yescharacteristic, complemented, Sylow
98C2×C3C5×D19514yescomplemented
99D3—1958no—
100C5—22no—
101C5C2×C3⋊D19511yescharacteristic, direct product factor
102C5C2×C5×C3⋊D3911yescharacteristic, complemented
103C22—5851noSylow
104C3C2×C5×D19514yescomplemented
105C2—5852no—
106C2C5×C3⋊D19511yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C5C3⋊D195
commutator, cosocle, hypocenterC32×C5×C13C22×C5
FrattiniC1G
Fitting, socleC2×C32×C52×C13C2
LCSG ▷ C32×C5×C13
UCSC1 ◁ C2×C5

Complements

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

NH ≅ G/Ntype
1. C5×C3⋊D195C2direct (N × H)
2. C2×C32×C52×C13C2semidirect
4. C32×C52×C13C22semidirect
6. C2×C3⋊D195C5direct (N × H)
7. C2×C3×C52×C13D3semidirect
11. C2×C32×C5×C13D5semidirect
12. C2×C32×C5×C13C2×C5semidirect
13. C3⋊D195C2×C5direct (N × H)
15. C3×C52×C13C2×D3semidirect
19. C2×C52×C13C3⋊D3semidirect
22. C32×C5×C13C2×D5semidirect
23. C32×C5×C13C22×C5semidirect
25. C2×C32×C52D13semidirect
28. C2×C3×C5×C13C5×D3semidirect
29. C2×C3×C5×C13D15semidirect
32. C52×C13C2×C3⋊D3semidirect
36. C2×C32×C13C5×D5semidirect
38. C32×C52C2×D13semidirect
40. C3×C5×C13C2×C5×D3semidirect
41. C3×C5×C13C2×D15semidirect
45. C2×C3×C52D39semidirect
48. C2×C5×C13C5×C3⋊D3semidirect
49. C2×C5×C13C3⋊D15semidirect
52. C32×C13C2×C5×D5semidirect
55. C2×C32×C5C5×D13semidirect
56. C2×C32×C5D65semidirect
59. C2×C3×C13C5×D15semidirect
61. C3×C52C2×D39semidirect
63. C5×C13C2×C5×C3⋊D3semidirect
64. C5×C13C2×C3⋊D15semidirect
68. C2×C52C3⋊D39semidirect
71. C32×C5C2×C5×D13semidirect
72. C32×C5C2×D65semidirect
73. C3×C13C2×C5×D15semidirect
76. C2×C3×C5C5×D39semidirect
77. C2×C3×C5D195semidirect
80. C2×C13C5×C3⋊D15semidirect
82. C52C2×C3⋊D39semidirect
85. C2×C32C5×D65semidirect
88. C3×C5C2×C5×D39semidirect
89. C3×C5C2×D195semidirect
90. C13C2×C5×C3⋊D15semidirect
94. C2×C5C5×C3⋊D39semidirect
95. C2×C5C3⋊D195direct (N × H)
97. C32C2×C5×D65semidirect
98. C2×C3C5×D195semidirect
101. C5C2×C3⋊D195direct (N × H)
102. C5C2×C5×C3⋊D39semidirect
104. C3C2×C5×D195semidirect
106. C2C5×C3⋊D195direct (N × H)

Maximal subgroups

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

subgroupindex
C5×C3⋊D1952
C2×C32×C52×C132
C2×C5×D1953
C2×C5×C3⋊D395
C2×C3⋊D1955
C2×C5×C3⋊D1513