Finite Group Databasebeta

← ((C5⋊D5)⋊C3)⋊D87 #39908063

Subgroups — ((C5⋊D5)⋊C3)⋊D87 #39908063

Order 26100.

160 conjugacy classes of subgroups; only the 31 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 31 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⋊(C29⋊#3874)C211yesmaximal, characteristic, complemented
2C3⋊(C29⋊#3874)C211yesmaximal, characteristic, complemented
3C3×C29×(C5⋊D5)⋊C3C211yesmaximal, characteristic, complemented
4#22576491—31nomaximal
5((C5⋊D5)⋊C3)⋊D29—31nomaximal
6((C5⋊D5)⋊C3)⋊D29—31nomaximal
7((C5⋊D5)⋊C3)⋊D29—31nomaximal
8C3×C29×C52⋊C3C2211yescharacteristic, complemented, Hall
9C5×D435—31no—
10C5×D435—31no—
11C3×C29×C5⋊D5D311yescharacteristic, complemented
12C29×(C5⋊D5)⋊C3D311yescharacteristic, complemented
13C29×(C5⋊D5)⋊C3D311yescharacteristic, complemented
14C29×(C5⋊D5)⋊C3D311yescharacteristic, complemented
15C29⋊#3874—31no—
16C29⋊#3874—31no—
17C29⋊#3874—31no—
18C29⋊#3874—31no—
19C29⋊#3874—31no—
20C29⋊#3874—31no—
21(C5⋊D5)⋊D29—91noHall
22C29×C52⋊C3C2×D311yescharacteristic, complemented
23C29×C52⋊C3C2×D311yescharacteristic, complemented
24C29×C52⋊C3C2×D311yescharacteristic, complemented
25C3×C52×C29C2×D311yescharacteristic, complemented
26D5×D87—151no—
27D5×D87—151no—
28C29×C5⋊D5C3⋊D311yescharacteristic, complemented
29C5×D145—91no—
30C5×D145—91no—
31C2×C3⋊D87—251nomaximal, Hall
32((C5⋊D5)⋊C3)⋊D3—291nomaximal, Hall
33D435—31no—
34D435—31no—
35C5×D87—151no—
36C5×D87—151no—
37C3×D5×C29—301no—
38C3×D5×C29—301no—
39C52×C29C2×C3⋊D311yescharacteristic, complemented, Hall
40D5×D29—451no—
41D5×D29—451no—
42C2×C32×C29—251no—
43C3⋊D87—251no—
44C3⋊D87—501no—
45C3×(C5⋊D5)⋊C3D2911yescharacteristic, complemented
46C3⋊#3874—291no—
47C3⋊#3874—291no—
48C3×C5×C29—61no—
49C3×C5×C29—61no—
50C2×D87—751no—
51C2×D87—751no—
52C2×D87—751no—
53C2×D87—751no—
54D15⋊D5—871no—
55#3874⋊C2—871no—
56#3874⋊C2—871no—
57#3874⋊C2—871no—
58D145—91no—
59D145—91no—
60C5×D29—451no—
61C5×D29—451no—
62D5×C29—301no—
63D5×C29—301no—
64C32×C29—1001noHall
65C3×C52⋊C3C2×D2911yescharacteristic, complemented, Hall
66C2×C3×C29—251no—
67C2×C3×C29—251no—
68C2×C3×C29—251no—
69C2×C3×C29—251no—
70D87—151no—
71D87—151no—
72D87—751no—
73D87—1501no—
74D87—1501no—
75D87—1501no—
76D87—1501no—
77D87—1501no—
78C5×D15—871no—
79C5×D15—871no—
80C3×C5⋊D5D8711yescharacteristic, complemented
81(C5⋊D5)⋊C3D8711yescharacteristic, complemented
82(C5⋊D5)⋊C3D8711yescharacteristic, complemented
83(C5⋊D5)⋊C3D8711yescharacteristic, complemented
84#3874—871no—
85#3874—871no—
86#3874—871no—
87#3874—871no—
88#3874—871no—
89#3874—871no—
90C5×C29—61no—
91C5×C29—61no—
92C2×D29—2251noHall
93D52—2611noHall
94C3×C29—501no—
95C3×C29—1001no—
96C3×C29—1001no—
97C3×C29#3874⋊C211yescharacteristic, complemented
98C3×C52C2×D8711yescharacteristic, complemented
99C52⋊C3C2×D8711yescharacteristic, complemented
100C52⋊C3C2×D8711yescharacteristic, complemented
101C52⋊C3C2×D8711yescharacteristic, complemented
102D3×D5—4351no—
103D3×D5—4351no—
104C2×C29—251no—
105D29—451no—
106D29—451no—
107C5⋊D5C3⋊D8711yescharacteristic, complemented
108C5×D5—2611no—
109C5×D5—2611no—
110C2×C3⋊D3—7251noHall
111D15—871no—
112D15—871no—
113C3×D5—151no—
114C3×D5—301no—
115C5×D3—4351no—
116C5×D3—4351no—
117C29((C5⋊D5)⋊C3)⋊D311yescharacteristic, complemented, Sylow
118C52C2×C3⋊D8711yescharacteristic, complemented, Sylow
119C2×D5—13051no—
120C2×D5—13051no—
121C2×C32—251no—
122C3⋊D3—14501no—
123C3⋊D3—14501no—
124C3×C5—31no—
125C3×C5—61no—
126C2×D3—21751no—
127C2×D3—21751no—
128C2×D3—21751no—
129C2×D3—21751no—
130C2×C5—13051no—
131C2×C5—13051no—
132D5—2611no—
133D5—2611no—
134D5—151no—
135D5—301no—
136C32—1001noSylow
137C2×C3—251no—
138C2×C3—251no—
139C2×C3—251no—
140C2×C3—251no—
141D3—21751no—
142D3—21751no—
143D3—21751no—
144D3—4351no—
145D3—4351no—
146D3—43501no—
147D3—43501no—
148D3—43501no—
149C5—31no—
150C5—61no—
151C22—65251noSylow
152C3—501no—
153C3—1001no—
154C3—1001no—
155C3((C5⋊D5)⋊C3)⋊D2911yescharacteristic, complemented
156C2—251no—
157C2—13051no—
158C2—13051no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, cosocle, hypocenterC3×C29×C52⋊C3C22
Fitting, socleC3×C52×C29C2×D3
LCSG ▷ C3×C29×C52⋊C3
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3⋊(C29⋊#3874)C2semidirect
2. C3⋊(C29⋊#3874)C2semidirect
3. C3×C29×(C5⋊D5)⋊C3C2semidirect
8. C3×C29×C52⋊C3C22semidirect
11. C3×C29×C5⋊D5D3semidirect
12. C29×(C5⋊D5)⋊C3D3semidirect
13. C29×(C5⋊D5)⋊C3D3semidirect
14. C29×(C5⋊D5)⋊C3D3semidirect
22. C29×C52⋊C3C2×D3semidirect
23. C29×C52⋊C3C2×D3semidirect
24. C29×C52⋊C3C2×D3semidirect
25. C3×C52×C29C2×D3semidirect
28. C29×C5⋊D5C3⋊D3semidirect
39. C52×C29C2×C3⋊D3semidirect
45. C3×(C5⋊D5)⋊C3D29semidirect
65. C3×C52⋊C3C2×D29semidirect
80. C3×C5⋊D5D87semidirect
81. (C5⋊D5)⋊C3D87semidirect
82. (C5⋊D5)⋊C3D87semidirect
83. (C5⋊D5)⋊C3D87semidirect
97. C3×C29#3874⋊C2semidirect
98. C3×C52C2×D87semidirect
99. C52⋊C3C2×D87semidirect
100. C52⋊C3C2×D87semidirect
101. C52⋊C3C2×D87semidirect
107. C5⋊D5C3⋊D87semidirect
117. C29((C5⋊D5)⋊C3)⋊D3semidirect
118. C52C2×C3⋊D87semidirect
155. C3((C5⋊D5)⋊C3)⋊D29semidirect

Maximal subgroups

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

subgroupindex
C3⋊(C29⋊#3874)2
C3×C29×(C5⋊D5)⋊C32
#225764913
((C5⋊D5)⋊C3)⋊D293
C2×C3⋊D8725
((C5⋊D5)⋊C3)⋊D329