Finite Group Databasebeta

← #39908172

Subgroups — #39908172

Order 26100.

224 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 43 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×C5×D435C212yesmaximal, complemented
2C29×C3⋊(C3⋊(C5⋊D5))C211yesmaximal, characteristic, complemented
3D145⋊D15—32nomaximal
4C32×C52×C29C2211yescharacteristic, complemented, Hall
5D87⋊D15—52nomaximal
6C29×C3⋊(C5⋊D5)—32no—
7C29×C3⋊(C5⋊D5)—61no—
8C5×D435D312yescomplemented
9C3×C5×D145—32no—
10(C5⋊D5)⋊D29—91noHall
11C29×C3⋊D15—52no—
12C29×C3⋊D15—102no—
13C3×D435D512yescomplemented
14C3×C5×D87—52no—
15C3×C52×C29—21no—
16C3×C52×C29C2×D312yescomplemented
17D15⋊D29—152no—
18D15×D29—152no—
19C29×C5⋊D5—91no—
20C5×D145—32no—
21C32×C5×C29—22no—
22C32×C5×C29C2×D512yescomplemented
23(C3⋊D3)⋊D29—251noHall
24D152—291nomaximal, Hall
25D435D1512yescomplemented
26C29×D15—152no—
27C29×D15—152no—
28C29×D15—302no—
29C29×D15—304no—
30C29×D15—304no—
31C5×D87—52no—
32C3×D145—32no—
33C3×C5×D29—152no—
34C52×C29D3211yescharacteristic, complemented, Hall
35D5×D29—452no—
36C3⋊D3×C29—251no—
37C3×D87—52no—
38C3⋊(C3⋊(C5⋊D5))D2911yescharacteristic, complemented
39C3×C5×D15—292no—
40C3×C5×C29—24no—
41C3×C5×C29—24no—
42C3×C5×C29—22no—
43C3×C5×C29D3×D512yescomplemented
44C3×C5×C29C2×D1512yescomplemented
45D3×D29—752no—
46D5×D15—872no—
47D145—32no—
48C5×D29—152no—
49D5×C29—452no—
50D5×C29—902no—
51C32×C29D5211yescharacteristic, complemented, Hall
52C32×C52C2×D2911yescharacteristic, complemented, Hall
53D3×D15—1452no—
54D87—52no—
55C3×D29—152no—
56D3×C29—752no—
57D3×C29—1501no—
58C3⋊(C5⋊D5)—32no—
59C3⋊(C5⋊D5)—61no—
60C5×D15—292no—
61C3×C5×D5—872no—
62C5×C29—22no—
63C5×C29D3×D1512yescomplemented
64C2×D29—2251noHall
65D52—2611noHall
66C3⋊D15—52no—
67C3⋊D15—102no—
68C3×D15—292no—
69C3×C5×D3—1452no—
70C3×C29—21no—
71C3×C29D5×D1512yescomplemented
72C3×C52—21no—
73C3×C52D3×D2912yescomplemented
74C2×D15—4352no—
75D3×D5—4352no—
76C2×C29—2251no—
77D29—152no—
78C5⋊D5—91no—
79C5×D5—872no—
80C32×C5—22no—
81C32×C5D5×D2912yescomplemented
82D32—7251noHall
83C2×C3×C5—4352no—
84D15—152no—
85D15—152no—
86D15—292no—
87D15—304no—
88D15—302no—
89D15—304no—
90C3×D5—872no—
91C5×D3—1452no—
92C29D15211yescharacteristic, complemented, Sylow
93C52(C3⋊D3)⋊D2911yescharacteristic, complemented, Sylow
94C2×D5—13052no—
95C3⋊D3—251no—
96C3×D3—1452no—
97C3×C5—24no—
98C3×C5—22no—
99C3×C5—24no—
100C3×C5D15×D2912yescomplemented
101C3×C5D15⋊D2912yescomplemented
102C2×D3—21752no—
103C2×C5—4352no—
104D5—452no—
105D5—872no—
106D5—902no—
107C32(C5⋊D5)⋊D2911yescharacteristic, complemented, Sylow
108C2×C3—4352no—
109D3—752no—
110D3—1452no—
111D3—1501no—
112C5—22no—
113C5D87⋊D1512yescomplemented
114C22—65251noSylow
115C3—21no—
116C3D145⋊D1512yescomplemented
117C2—4352no—
118C2—2251no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C52×C29C22
LCSG ▷ C32×C52×C29
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C5×D435C2semidirect
2. C29×C3⋊(C3⋊(C5⋊D5))C2semidirect
4. C32×C52×C29C22semidirect
8. C5×D435D3semidirect
13. C3×D435D5semidirect
16. C3×C52×C29C2×D3semidirect
22. C32×C5×C29C2×D5semidirect
25. D435D15semidirect
34. C52×C29D32semidirect
38. C3⋊(C3⋊(C5⋊D5))D29semidirect
43. C3×C5×C29D3×D5semidirect
44. C3×C5×C29C2×D15semidirect
51. C32×C29D52semidirect
52. C32×C52C2×D29semidirect
63. C5×C29D3×D15semidirect
71. C3×C29D5×D15semidirect
73. C3×C52D3×D29semidirect
81. C32×C5D5×D29semidirect
92. C29D152semidirect
93. C52(C3⋊D3)⋊D29semidirect
100. C3×C5D15×D29semidirect
101. C3×C5D15⋊D29semidirect
107. C32(C5⋊D5)⋊D29semidirect
113. C5D87⋊D15semidirect
116. C3D145⋊D15semidirect

Maximal subgroups

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

subgroupindex
C3×C5×D4352
C29×C3⋊(C3⋊(C5⋊D5))2
D145⋊D153
D87⋊D155
D15229