Finite Group Databasebeta

← D5×C29×D45 #39907970

Subgroups — D5×C29×D45 #39907970

Order 26100.

144 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 44 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
1C29×C5⋊D45C211yesmaximal, characteristic, complemented
2C5×C29×D45C211yesmaximal, characteristic, complemented
3C5×C9×D5×C29C211yesmaximal, characteristic, complemented
4D5×C29×D15—31nomaximal
5C52×C9×C29C2211yescharacteristic, complemented, Hall
6C2×C29×D45—51nomaximal
7D5×D9×C29—51nomaximal
8C29×C3⋊(C5⋊D5)—31no—
9C5×C29×D15—31no—
10C3×C5×D5×C29D311yescharacteristic
11D52×C29—91noHall
12C29×D45—51no—
13C29×D45—51no—
14C29×D45—102no—
15C29×D45D511yescharacteristic, direct product factor
16C5×D9×C29—51no—
17C9×D5×C29D511yescharacteristic, complemented
18C2×C5×C9×C29—51no—
19C3×C52×C29C2×D311yescharacteristic
20C2×C29×D15—151no—
21D3×D5×C29—151no—
22C29×C5⋊D5—91no—
23C5×D5×C29—91no—
24C5×D5×C29D911yescharacteristic, complemented
25C5×C9×C29—22no—
26C5×C9×C29C2×D511yescharacteristic, complemented
27C5×C9×C29C2×D511yescharacteristic, complemented
28C2×D9×C29—251noHall
29D5×D45C2911yesmaximal, characteristic, direct product factor, Hall
30C2×C3×C5×C29—51no—
31C29×D15—31no—
32C29×D15—151no—
33C29×D15—151no—
34C29×D15—302no—
35C5×D3×C29—151no—
36C3×D5×C29D1511yescharacteristic
37C52×C29C2×D911yescharacteristic, complemented, Hall
38C2×D5×C29—451no—
39C2×D5×C29—451no—
40C2×C9×C29—51no—
41D9×C29—51no—
42D9×C29—251no—
43C5⋊D45C2×C2911yescharacteristic, complemented
44C5×D45C2×C2911yescharacteristic, complemented
45C5×C9×D5C2×C2911yescharacteristic, complemented
46C3×C5×C29—22no—
47C3×C5×C29D3×D511yescharacteristic
48C3×C5×C29C2×D1511yescharacteristic
49C2×D3×C29—751no—
50D5×D15—31no—
51C2×C5×C29—51no—
52C2×C5×C29—451no—
53D5×C29—91no—
54D5×C29—451no—
55D5×C29—451no—
56D5×C29—902no—
57D5×C29D4511yescharacteristic, direct product factor
58C9×C29D5211yescharacteristic, complemented, Hall
59C52×C9C22×C2911yescharacteristic, complemented, Hall
60C2×D45—51no—
61D5×D9—51no—
62C2×C3×C29—51no—
63D3×C29—151no—
64D3×C29—751no—
65C3⋊(C5⋊D5)—31no—
66C5×D15—31no—
67C3×C5×D5D3×C2911yescharacteristic
68C5×C29—22no—
69C5×C29D5×D911yescharacteristic, complemented
70C5×C29C2×D4511yescharacteristic, complemented
71C22×C29—2251noHall
72D52—91noHall
73C2×C5×C9—51no—
74D45—51no—
75D45—51no—
76D45—102no—
77D45D5×C2911yescharacteristic, direct product factor
78C9×D5D5×C2911yescharacteristic, complemented
79C5×D9—51no—
80C3×C29D5×D1511yescharacteristic
81C3×C52C2×D3×C2911yescharacteristic
82C2×D15—151no—
83D3×D5—151no—
84C2×C29—51no—
85C2×C29—451no—
86C2×C29—2251no—
87C5⋊D5—91no—
88C5×D5—91no—
89C5×D5D9×C2911yescharacteristic, complemented
90C5×C9—22no—
91C5×C9C2×D5×C2911yescharacteristic, complemented
92C5×C9C2×D5×C2911yescharacteristic, complemented
93C2×D9—251noHall
94C2×C3×C5—51no—
95D15—31no—
96D15—151no—
97D15—151no—
98D15—302no—
99C3×D5C29×D1511yescharacteristic
100C5×D3—151no—
101C29D5×D4511yescharacteristic, direct product factor, Sylow
102C52C2×D9×C2911yescharacteristic, complemented, Sylow
103C2×D5—451no—
104C2×D5—451no—
105C2×C9—51no—
106D9—51no—
107D9—251no—
108C3×C5—22no—
109C3×C5D3×D5×C2911yescharacteristic
110C3×C5C2×C29×D1511yescharacteristic
111C2×D3—751no—
112C2×C5—51no—
113C2×C5—451no—
114D5—91no—
115D5—451no—
116D5—451no—
117D5—902no—
118D5C29×D4511yescharacteristic, direct product factor
119C9D52×C2911yescharacteristic, complemented, Sylow
120C2×C3—51no—
121D3—151no—
122D3—751no—
123C5—22no—
124C5D5×D9×C2911yescharacteristic, complemented
125C5C2×C29×D4511yescharacteristic, complemented
126C22—2251noSylow
127C3D5×C29×D1511yescharacteristic
128C2—51no—
129C2—451no—
130C2—2251no—
subgroupG/H
center, hypercenterC29D5×D45
commutator, cosocle, hypocenterC52×C9C22×C29
FrattiniC3D5×C29×D15
FittingC52×C9×C29C22
socleC3×C52×C29C2×D3
LCSG ▷ C52×C9
UCSC1 ◁ C29

Complements

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

NH ≅ G/Ntype
1. C29×C5⋊D45C2semidirect
2. C5×C29×D45C2semidirect
3. C5×C9×D5×C29C2semidirect
5. C52×C9×C29C22semidirect
15. C29×D45D5direct (N × H)
17. C9×D5×C29D5semidirect
24. C5×D5×C29D9semidirect
26. C5×C9×C29C2×D5semidirect
27. C5×C9×C29C2×D5semidirect
29. D5×D45C29direct (N × H)
37. C52×C29C2×D9semidirect
43. C5⋊D45C2×C29semidirect
44. C5×D45C2×C29semidirect
45. C5×C9×D5C2×C29semidirect
57. D5×C29D45direct (N × H)
58. C9×C29D52semidirect
59. C52×C9C22×C29semidirect
69. C5×C29D5×D9semidirect
70. C5×C29C2×D45semidirect
77. D45D5×C29direct (N × H)
78. C9×D5D5×C29semidirect
89. C5×D5D9×C29semidirect
91. C5×C9C2×D5×C29semidirect
92. C5×C9C2×D5×C29semidirect
101. C29D5×D45direct (N × H)
102. C52C2×D9×C29semidirect
118. D5C29×D45direct (N × H)
119. C9D52×C29semidirect
124. C5D5×D9×C29semidirect
125. C5C2×C29×D45semidirect

Maximal subgroups

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

subgroupindex
C29×C5⋊D452
C5×C29×D452
C5×C9×D5×C292
D5×C29×D153
C2×C29×D455
D5×D9×C295
D5×D4529