Finite Group Databasebeta

← C5×D29×C3⋊D15 #39908187

Subgroups — C5×D29×C3⋊D15 #39908187

Order 26100.

288 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 80 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×C52×D29C211yesmaximal, characteristic, complemented
2C5×C29×C3⋊D15C211yesmaximal, characteristic, complemented
3C5×C3⋊D435C211yesmaximal, characteristic, complemented
4C5×D15×D29—34nomaximal
5C32×C52×C29C2211yescharacteristic, complemented, Hall
6D29×C3⋊D15C511yesmaximal, characteristic, direct product factor
7C5×C3⋊D3×D29—51nomaximal
8C5×D435—34no—
9C5×C29×D15—34no—
10C3×C52×D29D314yescomplemented
11C5×D5×D29—91noHall
12C3⋊D435C2×C511yescharacteristic, complemented
13C29×C3⋊D15C2×C511yescharacteristic, complemented
14C5×C3⋊D87—51no—
15C5×C3⋊D3×C29—51no—
16C32×C5×D29—22no—
17C32×C5×D29D511yescharacteristic, complemented
18C32×C5×D29C2×C511yescharacteristic, complemented
19C3×C52×C29C2×D314yescomplemented
20D15×D29—34no—
21C5×D3×D29—154no—
22C5×D145—91no—
23C5×D5×C29—91no—
24C52×D29C3⋊D311yescharacteristic, complemented
25C32×C5×C29—22no—
26C32×C5×C29C2×D511yescharacteristic, complemented
27C32×C5×C29C22×C511yescharacteristic, complemented
28C3⋊D3×D29—51noHall
29C2×C5×C3⋊D15—291nomaximal, Hall
30D435—34no—
31C29×D15—34no—
32C5×D87—154no—
33C5×D3×C29—154no—
34C3×C5×D29—28no—
35C3×C5×D29C5×D314yescomplemented
36C3×C5×D29D1514yescomplemented
37C52×C29C2×C3⋊D311yescharacteristic, complemented, Hall
38C2×C5×D29—451no—
39D5×D29—91no—
40C3⋊D87—51no—
41C3⋊D3×C29—51no—
42C32×D29C5×D511yescharacteristic, complemented
43C2×C32×C52—291no—
44C5×C3⋊D15—291no—
45C5×C3⋊D15D2911yescharacteristic, direct product factor
46C3×C5×C29—28no—
47C3×C5×C29C2×C5×D314yescomplemented
48C3×C5×C29C2×D1514yescomplemented
49D3×D29—154no—
50C2×C5×D15—874no—
51C2×C5×C29—451no—
52D145—91no—
53C5×D29—22no—
54C5×D29—451no—
55C5×D29C5×C3⋊D311yescharacteristic, complemented
56C5×D29C3⋊D1511yescharacteristic, direct product factor
57D5×C29—91no—
58C32×C29C2×C5×D511yescharacteristic, complemented, Hall
59C32×C52C2×D2911yescharacteristic, complemented, Hall
60C2×C3⋊D15—291no—
61C2×C5×C3⋊D3—1451no—
62D87—154no—
63C3×D29C5×D1514yescomplemented
64D3×C29—154no—
65C2×C3×C52—294no—
66C5×D15—34no—
67C5×D15—874no—
68C5×C29—22no—
69C5×C29C2×C5×C3⋊D311yescharacteristic, complemented
70C5×C29C2×C3⋊D1511yescharacteristic, complemented
71C2×D29—451noHall
72C2×C5×D5—2611noHall
73C2×C32×C5—291no—
74C2×C32×C5—291no—
75C2×C32×C5—582no—
76C3⋊D15—291no—
77C3⋊D15C5×D2911yescharacteristic, direct product factor
78C5×C3⋊D3—51no—
79C5×C3⋊D3—1451no—
80C3×C29C2×C5×D1514yescomplemented
81C3×C52D3×D2914yescomplemented
82C2×D15—874no—
83C2×C5×D3—4354no—
84C2×C29—451no—
85D29—451no—
86D29C5×C3⋊D1511yescharacteristic, direct product factor
87C2×C52—291no—
88C5×D5—2611no—
89C5×D5—91no—
90C32×C5—22no—
91C32×C5D5×D2911yescharacteristic, complemented
92C32×C5C2×C5×D2911yescharacteristic, complemented
93C2×C3⋊D3—1451noHall
94C2×C3×C5—294no—
95C2×C3×C5—294no—
96C2×C3×C5—588no—
97D15—34no—
98D15—874no—
99C5×D3—154no—
100C5×D3—4354no—
101C29C2×C5×C3⋊D1511yescharacteristic, complemented, Sylow
102C52C3⋊D3×D2911yescharacteristic, complemented, Sylow
103C22×C5—13051no—
104C2×D5—2611no—
105C2×C32—291no—
106C3⋊D3—51no—
107C3⋊D3—1451no—
108C3×C5—28no—
109C3×C5C5×D3×D2914yescomplemented
110C3×C5D15×D2914yescomplemented
111C2×D3—4354no—
112C2×C5—13051no—
113C2×C5—291no—
114C2×C5—291no—
115C2×C5—451no—
116C2×C5—582no—
117D5—2611no—
118D5—91no—
119C32C5×D5×D2911yescharacteristic, complemented, Sylow
120C2×C3—294no—
121D3—154no—
122D3—4354no—
123C5—22no—
124C5C5×C3⋊D3×D2911yescharacteristic, complemented
125C5D29×C3⋊D1511yescharacteristic, direct product factor
126C22—13051noSylow
127C3C5×D15×D2914yescomplemented
128C2—13051no—
129C2—291no—
130C2—451no—
subgroupG/H
center, hypercenterC5D29×C3⋊D15
commutator, cosocle, hypocenterC32×C5×C29C22×C5
FrattiniC1G
Fitting, socleC32×C52×C29C22
LCSG ▷ C32×C5×C29
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
1. C32×C52×D29C2semidirect
2. C5×C29×C3⋊D15C2semidirect
3. C5×C3⋊D435C2semidirect
5. C32×C52×C29C22semidirect
6. D29×C3⋊D15C5direct (N × H)
10. C3×C52×D29D3semidirect
12. C3⋊D435C2×C5semidirect
13. C29×C3⋊D15C2×C5semidirect
17. C32×C5×D29D5semidirect
18. C32×C5×D29C2×C5semidirect
19. C3×C52×C29C2×D3semidirect
24. C52×D29C3⋊D3semidirect
26. C32×C5×C29C2×D5semidirect
27. C32×C5×C29C22×C5semidirect
35. C3×C5×D29C5×D3semidirect
36. C3×C5×D29D15semidirect
37. C52×C29C2×C3⋊D3semidirect
42. C32×D29C5×D5semidirect
45. C5×C3⋊D15D29direct (N × H)
47. C3×C5×C29C2×C5×D3semidirect
48. C3×C5×C29C2×D15semidirect
55. C5×D29C5×C3⋊D3semidirect
56. C5×D29C3⋊D15direct (N × H)
58. C32×C29C2×C5×D5semidirect
59. C32×C52C2×D29semidirect
63. C3×D29C5×D15semidirect
69. C5×C29C2×C5×C3⋊D3semidirect
70. C5×C29C2×C3⋊D15semidirect
77. C3⋊D15C5×D29direct (N × H)
80. C3×C29C2×C5×D15semidirect
81. C3×C52D3×D29semidirect
86. D29C5×C3⋊D15direct (N × H)
91. C32×C5D5×D29semidirect
92. C32×C5C2×C5×D29semidirect
101. C29C2×C5×C3⋊D15semidirect
102. C52C3⋊D3×D29semidirect
109. C3×C5C5×D3×D29semidirect
110. C3×C5D15×D29semidirect
119. C32C5×D5×D29semidirect
124. C5C5×C3⋊D3×D29semidirect
125. C5D29×C3⋊D15direct (N × H)
127. C3C5×D15×D29semidirect

Maximal subgroups

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

subgroupindex
C32×C52×D292
C5×C29×C3⋊D152
C5×C3⋊D4352
C5×D15×D293
D29×C3⋊D155
C5×C3⋊D3×D295
C2×C5×C3⋊D1529