Finite Group Databasebeta

← #39908176

Subgroups — #39908176

Order 26100.

212 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 43 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×C5×D435C211yesmaximal, characteristic, complemented
2C3×C29×C3⋊(C5⋊D5)C211yesmaximal, characteristic, complemented
3C5×C3⋊D435C211yesmaximal, characteristic, complemented
4#22576491—31nomaximal
5D145⋊D15—31nomaximal
6C32×C52×C29C2211yescharacteristic, complemented, Hall
7D15⋊D87—51nomaximal
8D15×D87—51nomaximal
9C29×C3⋊(C5⋊D5)D311yescharacteristic, complemented
10C5×D435—31no—
11C5×D435—31no—
12C5×D435—61no—
13C5×D435D311yescharacteristic, complemented
14C3×C29×C5⋊D5—31no—
15C3×C5×D145—31no—
16(C5⋊D5)⋊D29—91noHall
17C3⋊D435D511yescharacteristic, complemented
18C5×C3⋊D87—51no—
19C3×D435D511yescharacteristic, complemented
20C3×C29×D15—51no—
21C3×C29×D15—51no—
22C3×C29×D15—102no—
23C3×C5×D87—51no—
24C3×C52×C29—21no—
25C3×C52×C29C2×D311yescharacteristic, complemented
26C3×C52×C29C2×D311yescharacteristic, complemented
27D15⋊D29—151no—
28D5×D87—151no—
29D5×D87—151no—
30D15×D29—151no—
31C29×C5⋊D5—31no—
32C5×D145—31no—
33C5×D145—91no—
34C32×C5×C29—22no—
35C32×C5×C29C2×D511yescharacteristic, complemented
36C32×C5×C29C2×D511yescharacteristic, complemented
37D3×D87—251noHall
38D15⋊D15—291nomaximal, Hall
39D435—31no—
40D435—31no—
41D435—61no—
42D435D1511yescharacteristic, complemented
43C29×D15—51no—
44C29×D15—51no—
45C29×D15—102no—
46C5×D87—51no—
47C5×D87—151no—
48C5×D87—151no—
49C5×D87—301no—
50C3×D145—31no—
51C3×D5×C29—151no—
52C3×D5×C29—151no—
53C3×D5×C29—302no—
54C3×C5×D29—151no—
55C52×C29D3211yescharacteristic, complemented, Hall
56D5×D29—451no—
57D5×D29—451no—
58C3⋊D87—51no—
59C3×D87—51no—
60C3×D3×C29—251no—
61C5×C3⋊D15—291no—
62C3×C3⋊(C5⋊D5)D2911yescharacteristic, complemented
63C3×C5×D15—291no—
64C3×C5×C29—22no—
65C3×C5×C29—22no—
66C3×C5×C29—21no—
67C3×C5×C29—21no—
68C3×C5×C29—42no—
69C3×C5×C29D3×D511yescharacteristic, complemented
70C3×C5×C29D3×D511yescharacteristic, complemented
71C3×C5×C29D3×D511yescharacteristic, complemented
72C3×C5×C29C2×D1511yescharacteristic, complemented
73C2×D87—751no—
74D3×D29—751no—
75D15⋊D5—871no—
76D5×D15—871no—
77D145—31no—
78D145—91no—
79C5×D29—151no—
80C5×D29—451no—
81D5×C29—151no—
82D5×C29—151no—
83D5×C29—302no—
84C32×C29D5211yescharacteristic, complemented, Hall
85C32×C52C2×D2911yescharacteristic, complemented, Hall
86(C3⋊D3)⋊D5—1451no—
87D3×D15—1451no—
88C2×C3×C29—751no—
89D87—51no—
90D87—151no—
91D87—151no—
92D87—301no—
93C3×D29—151no—
94D3×C29—251no—
95C3⋊(C5⋊D5)D8711yescharacteristic, complemented
96C5×D15—291no—
97C5×D15—871no—
98C5×D15—871no—
99C5×D15—1741no—
100C3×C5⋊D5—31no—
101C3×C5×D5—871no—
102C5×C29—22no—
103C5×C29D3×D1511yescharacteristic, complemented
104C5×C29(C3⋊D3)⋊D511yescharacteristic, complemented
105C2×D29—2251noHall
106D52—2611noHall
107C3⋊D15—291no—
108C5×C3⋊D3—1451no—
109C3×D15—51no—
110C3×D15—51no—
111C3×D15—102no—
112C3×D15—291no—
113C3×C5×D3—1451no—
114C3×C29—21no—
115C3×C29D5×D1511yescharacteristic, complemented
116C3×C29D15⋊D511yescharacteristic, complemented
117C3×C52—21no—
118C3×C52D3×D2911yescharacteristic, complemented
119C3×C52C2×D8711yescharacteristic, complemented
120C2×D15—4351no—
121D3×D5—4351no—
122D3×D5—4351no—
123D3×D5—4351no—
124C2×C29—751no—
125D29—151no—
126D29—451no—
127C5⋊D5—31no—
128C5×D5—2611no—
129C5×D5—871no—
130C32×C5—22no—
131C32×C5D5×D2911yescharacteristic, complemented
132C32×C5D5×D2911yescharacteristic, complemented
133D32—7251noHall
134C2×C3×C5—4351no—
135D15—51no—
136D15—51no—
137D15—102no—
138D15—291no—
139D15—871no—
140D15—871no—
141D15—1741no—
142C3×D5—151no—
143C3×D5—151no—
144C3×D5—302no—
145C3×D5—871no—
146C5×D3—8701no—
147C5×D3—1451no—
148C5×D3—4351no—
149C5×D3—4351no—
150C29D15⋊D1511yescharacteristic, complemented, Sylow
151C52D3×D8711yescharacteristic, complemented, Sylow
152C2×D5—13051no—
153C2×D5—13051no—
154C3⋊D3—1451no—
155C3×D3—251no—
156C3×D3—1451no—
157C3×C5—21no—
158C3×C5—21no—
159C3×C5—22no—
160C3×C5—22no—
161C3×C5—42no—
162C3×C5D15×D2911yescharacteristic, complemented
163C3×C5D5×D8711yescharacteristic, complemented
164C3×C5D5×D8711yescharacteristic, complemented
165C3×C5D15⋊D2911yescharacteristic, complemented
166C2×D3—21751no—
167C2×D3—21751no—
168C2×C5—13051no—
169C2×C5—4351no—
170D5—2611no—
171D5—151no—
172D5—151no—
173D5—302no—
174D5—871no—
175C32(C5⋊D5)⋊D2911yescharacteristic, complemented, Sylow
176C2×C3—751no—
177C2×C3—4351no—
178D3—251no—
179D3—8701no—
180D3—1451no—
181D3—4351no—
182D3—4351no—
183C5—22no—
184C5D15×D8711yescharacteristic, complemented
185C5D15⋊D8711yescharacteristic, complemented
186C22—65251noSylow
187C3—21no—
188C3D145⋊D1511yescharacteristic, complemented
189C3#2257649111yescharacteristic, complemented
190C2—13051no—
191C2—751no—
192C2—4351no—
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. C3×C5×D435C2semidirect
2. C3×C29×C3⋊(C5⋊D5)C2semidirect
3. C5×C3⋊D435C2semidirect
6. C32×C52×C29C22semidirect
9. C29×C3⋊(C5⋊D5)D3semidirect
13. C5×D435D3semidirect
17. C3⋊D435D5semidirect
19. C3×D435D5semidirect
25. C3×C52×C29C2×D3semidirect
26. C3×C52×C29C2×D3semidirect
35. C32×C5×C29C2×D5semidirect
36. C32×C5×C29C2×D5semidirect
42. D435D15semidirect
55. C52×C29D32semidirect
62. C3×C3⋊(C5⋊D5)D29semidirect
69. C3×C5×C29D3×D5semidirect
70. C3×C5×C29D3×D5semidirect
71. C3×C5×C29D3×D5semidirect
72. C3×C5×C29C2×D15semidirect
84. C32×C29D52semidirect
85. C32×C52C2×D29semidirect
95. C3⋊(C5⋊D5)D87semidirect
103. C5×C29D3×D15semidirect
104. C5×C29(C3⋊D3)⋊D5semidirect
115. C3×C29D5×D15semidirect
116. C3×C29D15⋊D5semidirect
118. C3×C52D3×D29semidirect
119. C3×C52C2×D87semidirect
131. C32×C5D5×D29semidirect
132. C32×C5D5×D29semidirect
150. C29D15⋊D15semidirect
151. C52D3×D87semidirect
162. C3×C5D15×D29semidirect
163. C3×C5D5×D87semidirect
164. C3×C5D5×D87semidirect
165. C3×C5D15⋊D29semidirect
175. C32(C5⋊D5)⋊D29semidirect
184. C5D15×D87semidirect
185. C5D15⋊D87semidirect
188. C3D145⋊D15semidirect
189. C3#22576491semidirect

Maximal subgroups

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

subgroupindex
C3×C5×D4352
C3×C29×C3⋊(C5⋊D5)2
C5×C3⋊D4352
#225764913
D145⋊D153
D15⋊D875
D15×D875
D15⋊D1529