Finite Group Databasebeta

← #16839189⋊C3 #26043638

Subgroups — #16839189⋊C3 #26043638

Order 11700.

224 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 40 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⋊(C5⋊(D13⋊C3))C212yesmaximal, complemented
2C3×C13⋊C3×C5⋊D5C211yesmaximal, characteristic, complemented
3#16839189C311yesmaximal, characteristic, complemented
4(C5⋊(D13⋊C3))⋊D5—31nomaximal
5C3×C52×C13⋊C3C2211yescharacteristic, complemented, Hall
6D5×C3⋊(D13⋊C3)—52nomaximal
7C5×D195C2×C312yescomplemented
8C3×C13×C5⋊D5C2×C311yescharacteristic, complemented
9C13⋊C3×C5⋊D5—21no—
10C13⋊C3×C5⋊D5D311yescharacteristic, complemented
11C5×C5⋊(D13⋊C3)—32no—
12(C5⋊D5)⋊D13—31noHall
13C3⋊(C5⋊(D13⋊C3))D512yescomplemented
14C5×C3⋊(D13⋊C3)—52no—
15C3×D5×C13⋊C3—52no—
16C3×D5×C13⋊C3—102no—
17C3×C52×C13C22×C311yescharacteristic, complemented
18C52×C13⋊C3—21no—
19C52×C13⋊C3C2×D311yescharacteristic, complemented
20C3×D15⋊D5—131nomaximal, Hall
21D5×D39—52no—
22D5×D13⋊C3—152no—
23C13×C5⋊D5C3×D311yescharacteristic, complemented
24C5×D65—32no—
25C3×C5×C13⋊C3—22no—
26C3×C5×C13⋊C3C2×D512yescomplemented
27C2×C3⋊(D13⋊C3)—251noHall
28C3×C5×D15—132no—
29C32×C5⋊D5—131no—
30D195C3×D512yescomplemented
31C5×D39—52no—
32C3×D5×C13—52no—
33C3×D5×C13—102no—
34C5⋊(D13⋊C3)—32no—
35D5×C13⋊C3—52no—
36D5×C13⋊C3—102no—
37D5×C13⋊C3—102no—
38D5×C13⋊C3—104no—
39C5×D13⋊C3—152no—
40C52×C13C2×C3×D311yescharacteristic, complemented, Hall
41D15⋊D5—131no—
42C3×D52—391no—
43D5×D13—152no—
44C2×C3×C13⋊C3—251no—
45C3⋊(D13⋊C3)—52no—
46C32×C52—131noHall
47C3×C5×C13—22no—
48C3×C5×C13C2×C3×D512yescomplemented
49C5×C13⋊C3—24no—
50C5×C13⋊C3—22no—
51C5×C13⋊C3—22no—
52C5×C13⋊C3D3×D512yescomplemented
53C3×D3×D5—652no—
54C2×D39—251no—
55C2×D13⋊C3—751no—
56C5×D15—132no—
57C3×C5⋊D5—131no—
58C3×C5⋊D5—261no—
59C3×C5⋊D5D13⋊C311yescharacteristic, complemented
60C3×C5×D5—392no—
61D65—32no—
62C5×D13—152no—
63D5×C13—52no—
64D5×C13—102no—
65C3×C13⋊C3D5211yescharacteristic, complemented, Hall
66D52—391noHall
67C3×D15—132no—
68C3×C5×D3—652no—
69C32×D5—652no—
70C32×D5—1302no—
71C2×C3×C13—251no—
72D39—52no—
73C2×C13⋊C3—251no—
74C2×C13⋊C3—501no—
75D13⋊C3—152no—
76C3×C52—131no—
77C3×C52—261no—
78C3×C52C2×D13⋊C311yescharacteristic, complemented
79C5×C13—22no—
80C5×C13C3×D3×D512yescomplemented
81C2×C3×D5—1952no—
82D3×D5—652no—
83C2×D13—751noHall
84C5⋊D5C3⋊(D13⋊C3)11yescharacteristic, complemented
85C5×D5—392no—
86C32×C5—132no—
87C32×C5—262no—
88C3×C13C3×D5211yescharacteristic, complemented
89C13⋊C3—21no—
90C13⋊C3D15⋊D511yescharacteristic, complemented
91C2×C3×D3—3251noHall
92C2×C3×C5—1952no—
93D15—132no—
94C3×D5—52no—
95C3×D5—102no—
96C3×D5—392no—
97C3×D5—652no—
98C3×D5—1302no—
99C3×D5—1302no—
100C3×D5—1304no—
101C5×D3—652no—
102C2×C13—251no—
103D13—152no—
104C52C2×C3⋊(D13⋊C3)11yescharacteristic, complemented, Sylow
105C2×D5—1952no—
106C2×C32—3251no—
107C3×D3—652no—
108C3×C5—22no—
109C3×C5—132no—
110C3×C5—262no—
111C3×C5—264no—
112C3×C5—262no—
113C3×C5D5×D13⋊C312yescomplemented
114C13C3×D15⋊D511yescharacteristic, complemented, Sylow
115C22×C3—9751no—
116C2×D3—3251no—
117C2×C5—1952no—
118D5—52no—
119D5—102no—
120D5—392no—
121C32—131noSylow
122C2×C3—251no—
123C2×C3—3251no—
124C2×C3—6501no—
125C2×C3—1952no—
126D3—652no—
127C5—22no—
128C5D5×C3⋊(D13⋊C3)12yescomplemented
129C22—9751noSylow
130C3—131no—
131C3—261no—
132C3(C5⋊(D13⋊C3))⋊D511yescharacteristic, complemented
133C2—251no—
134C2—1952no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C52×C13C22×C3
LCSG ▷ C3×C52×C13
UCSC1

Complements

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

NH ≅ G/Ntype
1. C5×C3⋊(C5⋊(D13⋊C3))C2semidirect
2. C3×C13⋊C3×C5⋊D5C2semidirect
3. #16839189C3semidirect
5. C3×C52×C13⋊C3C22semidirect
7. C5×D195C2×C3semidirect
8. C3×C13×C5⋊D5C2×C3semidirect
10. C13⋊C3×C5⋊D5D3semidirect
13. C3⋊(C5⋊(D13⋊C3))D5semidirect
17. C3×C52×C13C22×C3semidirect
19. C52×C13⋊C3C2×D3semidirect
23. C13×C5⋊D5C3×D3semidirect
26. C3×C5×C13⋊C3C2×D5semidirect
30. D195C3×D5semidirect
40. C52×C13C2×C3×D3semidirect
48. C3×C5×C13C2×C3×D5semidirect
52. C5×C13⋊C3D3×D5semidirect
59. C3×C5⋊D5D13⋊C3semidirect
65. C3×C13⋊C3D52semidirect
78. C3×C52C2×D13⋊C3semidirect
80. C5×C13C3×D3×D5semidirect
84. C5⋊D5C3⋊(D13⋊C3)semidirect
88. C3×C13C3×D52semidirect
90. C13⋊C3D15⋊D5semidirect
104. C52C2×C3⋊(D13⋊C3)semidirect
113. C3×C5D5×D13⋊C3semidirect
114. C13C3×D15⋊D5semidirect
128. C5D5×C3⋊(D13⋊C3)semidirect
132. C3(C5⋊(D13⋊C3))⋊D5semidirect

Maximal subgroups

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

subgroupindex
C5×C3⋊(C5⋊(D13⋊C3))2
C3×C13⋊C3×C5⋊D52
#168391893
(C5⋊(D13⋊C3))⋊D53
D5×C3⋊(D13⋊C3)5
C3×D15⋊D513