Finite Group Databasebeta

← D5×C3⋊D435 #39908201

Subgroups — D5×C3⋊D435 #39908201

Order 26100.

288 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 76 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×C5×D5×C29C211yesmaximal, characteristic, complemented
2C5×C3⋊D435C211yesmaximal, characteristic, complemented
3C3⋊(C3⋊(C5⋊D145))C211yesmaximal, characteristic, complemented
4D5×D435—34nomaximal
5C32×C52×C29C2211yescharacteristic, complemented, Hall
6C2×C3⋊D435—51nomaximal
7D5×C3⋊D87—51nomaximal
8C3⋊(C5⋊D145)—34no—
9C5×D435—34no—
10C3×C5×D5×C29D314yescomplemented
11D5×D145—91noHall
12C3⋊D435—51no—
13C3⋊D435—51no—
14C3⋊D435—102no—
15C3⋊D435D511yescharacteristic, direct product factor
16C5×C3⋊D87—51no—
17C32×D5×C29D511yescharacteristic, complemented
18C2×C32×C5×C29—51no—
19C3×C52×C29C2×D314yescomplemented
20C2×D435—154no—
21D5×D87—154no—
22C5⋊D145—91no—
23C5×D145—91no—
24C5×D5×C29C3⋊D311yescharacteristic, complemented
25C32×C5×C29—22no—
26C32×C5×C29C2×D511yescharacteristic, complemented
27C32×C5×C29C2×D511yescharacteristic, complemented
28C2×C3⋊D87—251noHall
29D5×C3⋊D15—291nomaximal, Hall
30C2×C3×C5×C29—54no—
31D435—34no—
32D435—154no—
33D435—154no—
34D435—308no—
35C5×D87—154no—
36C3×D5×C29D1514yescomplemented
37C52×C29C2×C3⋊D311yescharacteristic, complemented, Hall
38C2×D145—451no—
39D5×D29—451no—
40C2×C32×C29—51no—
41C3⋊D87—51no—
42C3⋊D87—251no—
43C3⋊(C3⋊(C5⋊D5))—291no—
44C5×C3⋊D15—291no—
45C32×C5×D5D2911yescharacteristic, complemented
46C3×C5×C29—28no—
47C3×C5×C29D3×D514yescomplemented
48C3×C5×C29C2×D1514yescomplemented
49C2×D87—754no—
50D5×D15—874no—
51C2×C5×C29—51no—
52D145—91no—
53D145—451no—
54D145—451no—
55D145—902no—
56C5×D29—451no—
57D5×C29C3⋊D1511yescharacteristic, complemented
58C32×C29D5211yescharacteristic, complemented, Hall
59C32×C52C2×D2911yescharacteristic, complemented, Hall
60C2×C3⋊D15—1451no—
61D5×C3⋊D3—1451no—
62C2×C3×C29—54no—
63D87—154no—
64D87—754no—
65C3⋊(C5⋊D5)—874no—
66C5×D15—874no—
67C3×C5×D5D8714yescomplemented
68C5×C29—22no—
69C5×C29D5×C3⋊D311yescharacteristic, complemented
70C5×C29C2×C3⋊D1511yescharacteristic, complemented
71C2×D29—2251noHall
72D52—2611noHall
73C2×C32×C5—51no—
74C3⋊D15—291no—
75C3⋊D15—2902no—
76C3⋊D15—1451no—
77C3⋊D15—1451no—
78C5×C3⋊D3—1451no—
79C32×D5D14511yescharacteristic, complemented
80C3×C29D5×D1514yescomplemented
81C3×C52C2×D8714yescomplemented
82C2×D15—4354no—
83D3×D5—4354no—
84C2×C29—51no—
85D29—451no—
86D29—2251no—
87C5⋊D5—2611no—
88C5×D5—2611no—
89C5×D5C3⋊D8711yescharacteristic, complemented
90C32×C5—22no—
91C32×C5D5×D2911yescharacteristic, complemented
92C32×C5C2×D14511yescharacteristic, complemented
93C2×C3⋊D3—7251noHall
94C2×C3×C5—54no—
95D15—874no—
96D15—8708no—
97D15—4354no—
98D15—4354no—
99C3×D5D43514yescomplemented
100C5×D3—4354no—
101C29D5×C3⋊D1511yescharacteristic, complemented, Sylow
102C52C2×C3⋊D8711yescharacteristic, complemented, Sylow
103C2×D5—13051no—
104C2×D5—13051no—
105C2×C32—51no—
106C3⋊D3—1451no—
107C3⋊D3—7251no—
108C3×C5—28no—
109C3×C5D5×D8714yescomplemented
110C3×C5C2×D43514yescomplemented
111C2×D3—21754no—
112C2×C5—51no—
113C2×C5—13051no—
114D5—2611no—
115D5—13051no—
116D5—13051no—
117D5—26102no—
118D5C3⋊D43511yescharacteristic, direct product factor
119C32D5×D14511yescharacteristic, complemented, Sylow
120C2×C3—54no—
121D3—21754no—
122D3—4354no—
123C5—22no—
124C5D5×C3⋊D8711yescharacteristic, complemented
125C5C2×C3⋊D43511yescharacteristic, complemented
126C22—65251noSylow
127C3D5×D43514yescomplemented
128C2—51no—
129C2—13051no—
130C2—65251no—
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. C32×C5×D5×C29C2semidirect
2. C5×C3⋊D435C2semidirect
3. C3⋊(C3⋊(C5⋊D145))C2semidirect
5. C32×C52×C29C22semidirect
10. C3×C5×D5×C29D3semidirect
15. C3⋊D435D5direct (N × H)
17. C32×D5×C29D5semidirect
19. C3×C52×C29C2×D3semidirect
24. C5×D5×C29C3⋊D3semidirect
26. C32×C5×C29C2×D5semidirect
27. C32×C5×C29C2×D5semidirect
36. C3×D5×C29D15semidirect
37. C52×C29C2×C3⋊D3semidirect
45. C32×C5×D5D29semidirect
47. C3×C5×C29D3×D5semidirect
48. C3×C5×C29C2×D15semidirect
57. D5×C29C3⋊D15semidirect
58. C32×C29D52semidirect
59. C32×C52C2×D29semidirect
67. C3×C5×D5D87semidirect
69. C5×C29D5×C3⋊D3semidirect
70. C5×C29C2×C3⋊D15semidirect
79. C32×D5D145semidirect
80. C3×C29D5×D15semidirect
81. C3×C52C2×D87semidirect
89. C5×D5C3⋊D87semidirect
91. C32×C5D5×D29semidirect
92. C32×C5C2×D145semidirect
99. C3×D5D435semidirect
101. C29D5×C3⋊D15semidirect
102. C52C2×C3⋊D87semidirect
109. C3×C5D5×D87semidirect
110. C3×C5C2×D435semidirect
118. D5C3⋊D435direct (N × H)
119. C32D5×D145semidirect
124. C5D5×C3⋊D87semidirect
125. C5C2×C3⋊D435semidirect
127. C3D5×D435semidirect

Maximal subgroups

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

subgroupindex
C32×C5×D5×C292
C5×C3⋊D4352
C3⋊(C3⋊(C5⋊D145))2
D5×D4353
C2×C3⋊D4355
D5×C3⋊D875
D5×C3⋊D1529