Finite Group Databasebeta

← #39908064

Subgroups — #39908064

Order 26100.

160 conjugacy classes of subgroups; only the 26 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 26 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
2C29×C3⋊#3874C211yesmaximal, characteristic, complemented
3C3×C29⋊((C5⋊D5)⋊C3)C211yesmaximal, characteristic, complemented
4D15⋊D145—31nomaximal
5#3874⋊D29—31nomaximal
6#3874⋊D29—31nomaximal
7#3874⋊D29—31nomaximal
8C3×C29×C52⋊C3C2211yescharacteristic, complemented, Hall
9C5×D435—31no—
10C5×C29×D15—31no—
11C3×C5⋊D145D311yescharacteristic, complemented
12C29⋊((C5⋊D5)⋊C3)D311yescharacteristic, complemented
13C29⋊((C5⋊D5)⋊C3)D311yescharacteristic, complemented
14C29⋊((C5⋊D5)⋊C3)D311yescharacteristic, complemented
15C29⋊#3874—31no—
16C29⋊#3874—31no—
17C29⋊#3874—31no—
18C29×#3874—31no—
19C29×#3874—31no—
20C29×#3874—31no—
21D5×D145—91noHall
22C29×C52⋊C3C2×D311yescharacteristic, complemented
23C29×C52⋊C3C2×D311yescharacteristic, complemented
24C29×C52⋊C3C2×D311yescharacteristic, complemented
25C3×C52×C29C2×D311yescharacteristic, complemented
26D15⋊D29—151no—
27D3×D145—151no—
28C5⋊D145C3⋊D311yescharacteristic, complemented
29C5×D145—91no—
30C5×D5×C29—91no—
31C3⋊D3×D29—251nomaximal, Hall
32((C5⋊D5)⋊C3)⋊D3—291nomaximal, Hall
33D435—31no—
34C29×D15—31no—
35C5×D87—151no—
36C5×D3×C29—151no—
37C3×D145—301no—
38C3×D145—301no—
39C52×C29C2×C3⋊D311yescharacteristic, complemented, Hall
40C2×D145—451no—
41D5×D29—451no—
42C3⋊D87—501no—
43C3⋊D3×C29—501no—
44C32×D29—251no—
45C3×(C5⋊D5)⋊C3—291no—
46C3⋊#3874—291no—
47C3⋊#3874D2911yescharacteristic, complemented
48C3×C5×C29—61no—
49C3×C5×C29—61no—
50D3×D29—751no—
51D3×D29—751no—
52D3×D29—751no—
53D3×D29—751no—
54D15⋊D5—871no—
55#3874⋊C2—871no—
56#3874⋊C2—871no—
57#3874⋊C2—871no—
58C2×C5×C29—451no—
59D145—91no—
60D145—151no—
61D145—301no—
62C5×D29—451no—
63D5×C29—91no—
64C32×C29—1001noHall
65C3×C52⋊C3C2×D2911yescharacteristic, complemented, Hall
66D87—151no—
67D87—1501no—
68D87—1501no—
69D87—1501no—
70C3×D29—251no—
71C3×D29—251no—
72C3×D29—251no—
73C3×D29—251no—
74D3×C29—151no—
75D3×C29—1501no—
76D3×C29—1501no—
77D3×C29—1501no—
78C5×D15—31no—
79C5×D15—871no—
80C3×C5⋊D5—291no—
81(C5⋊D5)⋊C3—291no—
82(C5⋊D5)⋊C3—291no—
83(C5⋊D5)⋊C3—291no—
84#3874—31no—
85#3874—31no—
86#3874—31no—
87#3874—871no—
88#3874—871no—
89#3874—871no—
90C5×C29—31no—
91C5×C29—61no—
92C2×D29—2251noHall
93D52—2611noHall
94C3×C29—501no—
95C3×C29—501no—
96C3×C29—1001no—
97C3×C29#3874⋊C211yescharacteristic, complemented
98C3×C52D3×D2911yescharacteristic, complemented
99C52⋊C3D3×D2911yescharacteristic, complemented
100C52⋊C3D3×D2911yescharacteristic, complemented
101C52⋊C3D3×D2911yescharacteristic, complemented
102D3×D5—4351no—
103D3×D5—4351no—
104C2×C29—451no—
105D29—251no—
106D29—451no—
107C5⋊D5—291no—
108C5×D5—2611no—
109C5×D5—91no—
110C2×C3⋊D3—7251noHall
111D15—31no—
112D15—871no—
113C3×D5—4351no—
114C3×D5—4351no—
115C5×D3—151no—
116C5×D3—4351no—
117C29((C5⋊D5)⋊C3)⋊D311yescharacteristic, complemented, Sylow
118C52C3⋊D3×D2911yescharacteristic, complemented, Sylow
119C2×D5—13051no—
120C2×D5—13051no—
121C2×C32—7251no—
122C3⋊D3—501no—
123C3⋊D3—14501no—
124C3×C5—31no—
125C3×C5—31no—
126C2×D3—21751no—
127C2×D3—21751no—
128C2×D3—21751no—
129C2×D3—21751no—
130C2×C5—13051no—
131C2×C5—451no—
132D5—2611no—
133D5—91no—
134D5—8701no—
135D5—4351no—
136C32—1001noSylow
137C2×C3—7251no—
138C2×C3—7251no—
139C2×C3—7251no—
140C2×C3—7251no—
141D3—151no—
142D3—21751no—
143D3—1501no—
144D3—1501no—
145D3—1501no—
146D3—4351no—
147D3—43501no—
148D3—43501no—
149C5—31no—
150C5—61no—
151C22—65251noSylow
152C3—501no—
153C3—1001no—
154C3—1001no—
155C3#3874⋊D2911yescharacteristic, complemented
156C2—13051no—
157C2—451no—
158C2—7251no—
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. C29×C3⋊#3874C2semidirect
3. C3×C29⋊((C5⋊D5)⋊C3)C2semidirect
8. C3×C29×C52⋊C3C22semidirect
11. C3×C5⋊D145D3semidirect
12. C29⋊((C5⋊D5)⋊C3)D3semidirect
13. C29⋊((C5⋊D5)⋊C3)D3semidirect
14. C29⋊((C5⋊D5)⋊C3)D3semidirect
22. C29×C52⋊C3C2×D3semidirect
23. C29×C52⋊C3C2×D3semidirect
24. C29×C52⋊C3C2×D3semidirect
25. C3×C52×C29C2×D3semidirect
28. C5⋊D145C3⋊D3semidirect
39. C52×C29C2×C3⋊D3semidirect
47. C3⋊#3874D29semidirect
65. C3×C52⋊C3C2×D29semidirect
97. C3×C29#3874⋊C2semidirect
98. C3×C52D3×D29semidirect
99. C52⋊C3D3×D29semidirect
100. C52⋊C3D3×D29semidirect
101. C52⋊C3D3×D29semidirect
117. C29((C5⋊D5)⋊C3)⋊D3semidirect
118. C52C3⋊D3×D29semidirect
155. C3#3874⋊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
C29×C3⋊#38742
C3×C29⋊((C5⋊D5)⋊C3)2
D15⋊D1453
#3874⋊D293
C3⋊D3×D2925
((C5⋊D5)⋊C3)⋊D329