Finite Group Databasebeta

← D5×C3⋊D195 #26043806

Subgroups — D5×C3⋊D195 #26043806

Order 11700.

288 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 76 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
1C3⋊(C3⋊(C5⋊D65))C211yesmaximal, characteristic, complemented
2C5×C3⋊D195C211yesmaximal, characteristic, complemented
3C32×C5×D5×C13C211yesmaximal, characteristic, complemented
4D5×D195—34nomaximal
5C32×C52×C13C2211yescharacteristic, complemented, Hall
6C2×C3⋊D195—51nomaximal
7D5×C3⋊D39—51nomaximal
8C3⋊(C5⋊D65)—34no—
9C5×D195—34no—
10C3×C5×D5×C13D314yescomplemented
11D5×D65—91noHall
12C2×C32×C5×C13—51no—
13C3⋊D195—51no—
14C3⋊D195—51no—
15C3⋊D195—102no—
16C3⋊D195D511yescharacteristic, direct product factor
17C5×C3⋊D39—51no—
18C32×D5×C13D511yescharacteristic, complemented
19C3×C52×C13C2×D314yescomplemented
20D5×C3⋊D15—131nomaximal, Hall
21C2×D195—154no—
22D5×D39—154no—
23C5⋊D65—91no—
24C5×D65—91no—
25C5×D5×C13C3⋊D311yescharacteristic, complemented
26C32×C5×C13—22no—
27C32×C5×C13C2×D511yescharacteristic, complemented
28C32×C5×C13C2×D511yescharacteristic, complemented
29C2×C3⋊D39—251noHall
30C3⋊(C3⋊(C5⋊D5))—131no—
31C5×C3⋊D15—131no—
32C32×C5×D5D1311yescharacteristic, complemented
33C2×C3×C5×C13—54no—
34D195—34no—
35D195—154no—
36D195—154no—
37D195—308no—
38C5×D39—154no—
39C3×D5×C13D1514yescomplemented
40C52×C13C2×C3⋊D311yescharacteristic, complemented, Hall
41D5×D15—394no—
42C2×D65—451no—
43D5×D13—451no—
44C2×C32×C13—51no—
45C3⋊D39—51no—
46C3⋊D39—251no—
47C32×C52C2×D1311yescharacteristic, complemented, Hall
48C3×C5×C13—28no—
49C3×C5×C13D3×D514yescomplemented
50C3×C5×C13C2×D1514yescomplemented
51C2×C3⋊D15—651no—
52D5×C3⋊D3—651no—
53C2×D39—754no—
54C3⋊(C5⋊D5)—394no—
55C5×D15—394no—
56C3×C5×D5D3914yescomplemented
57C2×C5×C13—51no—
58D65—91no—
59D65—451no—
60D65—451no—
61D65—902no—
62C5×D13—451no—
63D5×C13C3⋊D1511yescharacteristic, complemented
64C32×C13D5211yescharacteristic, complemented, Hall
65D52—1171noHall
66C2×C32×C5—51no—
67C3⋊D15—131no—
68C3⋊D15—651no—
69C3⋊D15—651no—
70C3⋊D15—1302no—
71C5×C3⋊D3—651no—
72C32×D5D6511yescharacteristic, complemented
73C2×C3×C13—54no—
74D39—154no—
75D39—754no—
76C3×C52C2×D3914yescomplemented
77C5×C13—22no—
78C5×C13D5×C3⋊D311yescharacteristic, complemented
79C5×C13C2×C3⋊D1511yescharacteristic, complemented
80C2×D15—1954no—
81D3×D5—1954no—
82C2×D13—2251noHall
83C5⋊D5—1171no—
84C5×D5—1171no—
85C5×D5C3⋊D3911yescharacteristic, complemented
86C32×C5—22no—
87C32×C5D5×D1311yescharacteristic, complemented
88C32×C5C2×D6511yescharacteristic, complemented
89C3×C13D5×D1514yescomplemented
90C2×C3⋊D3—3251noHall
91C2×C3×C5—54no—
92D15—394no—
93D15—3908no—
94D15—1954no—
95D15—1954no—
96C3×D5D19514yescomplemented
97C5×D3—1954no—
98C2×C13—51no—
99D13—451no—
100D13—2251no—
101C52C2×C3⋊D3911yescharacteristic, complemented, Sylow
102C2×D5—5851no—
103C2×D5—5851no—
104C2×C32—51no—
105C3⋊D3—651no—
106C3⋊D3—3251no—
107C3×C5—28no—
108C3×C5D5×D3914yescomplemented
109C3×C5C2×D19514yescomplemented
110C13D5×C3⋊D1511yescharacteristic, complemented, Sylow
111C2×D3—9754no—
112C2×C5—51no—
113C2×C5—5851no—
114D5—5851no—
115D5—5851no—
116D5—1171no—
117D5—11702no—
118D5C3⋊D19511yescharacteristic, direct product factor
119C32D5×D6511yescharacteristic, complemented, Sylow
120C2×C3—54no—
121D3—1954no—
122D3—9754no—
123C5—22no—
124C5D5×C3⋊D3911yescharacteristic, complemented
125C5C2×C3⋊D19511yescharacteristic, complemented
126C22—29251noSylow
127C3D5×D19514yescomplemented
128C2—51no—
129C2—5851no—
130C2—29251no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C52×C13C22
LCSG ▷ C32×C52×C13
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3⋊(C3⋊(C5⋊D65))C2semidirect
2. C5×C3⋊D195C2semidirect
3. C32×C5×D5×C13C2semidirect
5. C32×C52×C13C22semidirect
10. C3×C5×D5×C13D3semidirect
16. C3⋊D195D5direct (N × H)
18. C32×D5×C13D5semidirect
19. C3×C52×C13C2×D3semidirect
25. C5×D5×C13C3⋊D3semidirect
27. C32×C5×C13C2×D5semidirect
28. C32×C5×C13C2×D5semidirect
32. C32×C5×D5D13semidirect
39. C3×D5×C13D15semidirect
40. C52×C13C2×C3⋊D3semidirect
47. C32×C52C2×D13semidirect
49. C3×C5×C13D3×D5semidirect
50. C3×C5×C13C2×D15semidirect
56. C3×C5×D5D39semidirect
63. D5×C13C3⋊D15semidirect
64. C32×C13D52semidirect
72. C32×D5D65semidirect
76. C3×C52C2×D39semidirect
78. C5×C13D5×C3⋊D3semidirect
79. C5×C13C2×C3⋊D15semidirect
85. C5×D5C3⋊D39semidirect
87. C32×C5D5×D13semidirect
88. C32×C5C2×D65semidirect
89. C3×C13D5×D15semidirect
96. C3×D5D195semidirect
101. C52C2×C3⋊D39semidirect
108. C3×C5D5×D39semidirect
109. C3×C5C2×D195semidirect
110. C13D5×C3⋊D15semidirect
118. D5C3⋊D195direct (N × H)
119. C32D5×D65semidirect
124. C5D5×C3⋊D39semidirect
125. C5C2×C3⋊D195semidirect
127. C3D5×D195semidirect

Maximal subgroups

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

subgroupindex
C3⋊(C3⋊(C5⋊D65))2
C5×C3⋊D1952
C32×C5×D5×C132
D5×D1953
C2×C3⋊D1955
D5×C3⋊D395
D5×C3⋊D1513