Finite Group Databasebeta

← C3×#22576491 #39908145

Subgroups — C3×#22576491 #39908145

Order 26100.

224 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 50 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×C29×C5⋊D5C211yesmaximal, characteristic, complemented
2C3×C5×D435C212yesmaximal, complemented
3#22576491C311yesmaximal, characteristic, direct product factor
4C3×(C5⋊D5)⋊D29—31nomaximal
5C32×C52×C29C2211yescharacteristic, complemented, Hall
6C3×D5×D87—52nomaximal
7C5×D435C2×C312yescomplemented
8C3×C29×C5⋊D5—21no—
9C3×C29×C5⋊D5D311yescharacteristic, complemented
10C3×C29×C5⋊D5C2×C311yescharacteristic, complemented
11C3×C5×D145—32no—
12(C5⋊D5)⋊D29—31noHall
13C3×D435D512yescomplemented
14C3×C5×D87—52no—
15C32×D5×C29—52no—
16C32×D5×C29—102no—
17C3×C52×C29—21no—
18C3×C52×C29C2×D311yescharacteristic, complemented
19C3×C52×C29C22×C311yescharacteristic, complemented
20D5×D87—52no—
21C3×D5×D29—152no—
22C29×C5⋊D5C3×D311yescharacteristic, complemented
23C5×D145—32no—
24C32×C5×C29—22no—
25C32×C5×C29C2×D512yescomplemented
26C2×C3×D87—251noHall
27C3×D15⋊D5—291nomaximal, Hall
28D435C3×D512yescomplemented
29C5×D87—52no—
30C3×D145—32no—
31C3×D5×C29—52no—
32C3×D5×C29—52no—
33C3×D5×C29—102no—
34C3×D5×C29—102no—
35C3×D5×C29—102no—
36C3×D5×C29—104no—
37C3×C5×D29—152no—
38C52×C29C2×C3×D311yescharacteristic, complemented, Hall
39D5×D29—152no—
40C2×C32×C29—251no—
41C3×D87—52no—
42C3×C5×D15—292no—
43C32×C5⋊D5D2911yescharacteristic, complemented
44C3×C5×C29—24no—
45C3×C5×C29—22no—
46C3×C5×C29—22no—
47C3×C5×C29—22no—
48C3×C5×C29D3×D512yescomplemented
49C3×C5×C29C2×C3×D512yescomplemented
50C2×D87—251no—
51C2×C3×D29—751no—
52D15⋊D5—291no—
53C3×D52—871no—
54D145—32no—
55C5×D29—152no—
56D5×C29—52no—
57D5×C29—102no—
58C32×C29D5211yescharacteristic, complemented, Hall
59C32×C52C2×D2911yescharacteristic, complemented, Hall
60C3×D3×D5—1452no—
61C2×C3×C29—251no—
62C2×C3×C29—251no—
63C2×C3×C29—501no—
64D87—52no—
65C3×D29—152no—
66C5×D15—292no—
67C3×C5⋊D5—21no—
68C3×C5⋊D5C3×D2911yescharacteristic, complemented
69C3×C5⋊D5D8711yescharacteristic, complemented
70C3×C5×D5—872no—
71C5×C29—22no—
72C5×C29C3×D3×D512yescomplemented
73C2×D29—751noHall
74D52—871noHall
75C3×D15—292no—
76C3×C5×D3—1452no—
77C32×D5—52no—
78C32×D5—102no—
79C3×C29—21no—
80C3×C29C3×D5211yescharacteristic, complemented
81C3×C29D15⋊D511yescharacteristic, complemented
82C3×C52—21no—
83C3×C52C2×C3×D2911yescharacteristic, complemented
84C3×C52C2×D8711yescharacteristic, complemented
85C2×C3×D5—4352no—
86D3×D5—1452no—
87C2×C29—251no—
88D29—152no—
89C5⋊D5C3×D8711yescharacteristic, complemented
90C5×D5—872no—
91C32×C5—22no—
92C32×C5D5×D2912yescomplemented
93C2×C3×D3—7251noHall
94C2×C3×C5—4352no—
95D15—292no—
96C3×D5—52no—
97C3×D5—52no—
98C3×D5—102no—
99C3×D5—102no—
100C3×D5—102no—
101C3×D5—104no—
102C3×D5—872no—
103C5×D3—1452no—
104C29C3×D15⋊D511yescharacteristic, complemented, Sylow
105C52C2×C3×D8711yescharacteristic, complemented, Sylow
106C2×D5—4352no—
107C2×C32—251no—
108C3×D3—1452no—
109C3×C5—24no—
110C3×C5—22no—
111C3×C5—22no—
112C3×C5—22no—
113C3×C5C3×D5×D2912yescomplemented
114C3×C5D5×D8712yescomplemented
115C22×C3—21751no—
116C2×D3—7251no—
117C2×C5—4352no—
118D5—52no—
119D5—102no—
120D5—872no—
121C32(C5⋊D5)⋊D2911yescharacteristic, complemented, Sylow
122C2×C3—251no—
123C2×C3—251no—
124C2×C3—501no—
125C2×C3—4352no—
126D3—1452no—
127C5—22no—
128C5C3×D5×D8712yescomplemented
129C22—21751noSylow
130C3—21no—
131C3C3×(C5⋊D5)⋊D2911yescharacteristic, complemented
132C3#2257649111yescharacteristic, direct product factor
133C2—251no—
134C2—4352no—
subgroupG/H
center, hypercenterC3#22576491
commutator, cosocle, hypocenterC3×C52×C29C22×C3
FrattiniC1G
Fitting, socleC32×C52×C29C22
LCSG ▷ C3×C52×C29
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C32×C29×C5⋊D5C2semidirect
2. C3×C5×D435C2semidirect
3. #22576491C3direct (N × H)
5. C32×C52×C29C22semidirect
7. C5×D435C2×C3semidirect
9. C3×C29×C5⋊D5D3semidirect
10. C3×C29×C5⋊D5C2×C3semidirect
13. C3×D435D5semidirect
18. C3×C52×C29C2×D3semidirect
19. C3×C52×C29C22×C3semidirect
22. C29×C5⋊D5C3×D3semidirect
25. C32×C5×C29C2×D5semidirect
28. D435C3×D5semidirect
38. C52×C29C2×C3×D3semidirect
43. C32×C5⋊D5D29semidirect
48. C3×C5×C29D3×D5semidirect
49. C3×C5×C29C2×C3×D5semidirect
58. C32×C29D52semidirect
59. C32×C52C2×D29semidirect
68. C3×C5⋊D5C3×D29semidirect
69. C3×C5⋊D5D87semidirect
72. C5×C29C3×D3×D5semidirect
80. C3×C29C3×D52semidirect
81. C3×C29D15⋊D5semidirect
83. C3×C52C2×C3×D29semidirect
84. C3×C52C2×D87semidirect
89. C5⋊D5C3×D87semidirect
92. C32×C5D5×D29semidirect
104. C29C3×D15⋊D5semidirect
105. C52C2×C3×D87semidirect
113. C3×C5C3×D5×D29semidirect
114. C3×C5D5×D87semidirect
121. C32(C5⋊D5)⋊D29semidirect
128. C5C3×D5×D87semidirect
131. C3C3×(C5⋊D5)⋊D29semidirect
132. C3#22576491direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C29×C5⋊D52
C3×C5×D4352
#225764913
C3×(C5⋊D5)⋊D293
C3×D5×D875
C3×D15⋊D529