Finite Group Databasebeta

← D5×D15×C13⋊C3 #26043637

Subgroups — D5×D15×C13⋊C3 #26043637

Order 11700.

212 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 48 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
1C13⋊C3×C3⋊(C5⋊D5)C211yesmaximal, characteristic, complemented
2C5×D15×C13⋊C3C211yesmaximal, characteristic, complemented
3C3×C5×D5×C13⋊C3C211yesmaximal, characteristic, complemented
4D5×C13×D15C311yesmaximal, characteristic, complemented
5D52×C13⋊C3—31nomaximal
6C3×C52×C13⋊C3C2211yescharacteristic, complemented, Hall
7C2×D15×C13⋊C3—51nomaximal
8D3×D5×C13⋊C3—51nomaximal
9C13×C3⋊(C5⋊D5)C2×C311yescharacteristic, complemented
10C5×C13×D15C2×C311yescharacteristic, complemented
11C3×C5×D5×C13C2×C311yescharacteristic, complemented
12C13⋊C3×C5⋊D5—31no—
13C5×D5×C13⋊C3—21no—
14C5×D5×C13⋊C3—31no—
15C5×D5×C13⋊C3D311yescharacteristic, complemented
16D52×C13—31noHall
17C2×C3×C5×C13⋊C3—51no—
18D15×C13⋊C3—51no—
19D15×C13⋊C3—51no—
20D15×C13⋊C3—102no—
21D15×C13⋊C3D511yescharacteristic, direct product factor
22C5×D3×C13⋊C3—51no—
23C3×D5×C13⋊C3D511yescharacteristic, complemented
24C3×C52×C13C22×C311yescharacteristic, complemented
25C52×C13⋊C3—21no—
26C52×C13⋊C3C2×D311yescharacteristic, complemented
27C3×D5×D15—131nomaximal, Hall
28C2×C13×D15—51no—
29D3×D5×C13—51no—
30C2×D5×C13⋊C3—151no—
31C2×D5×C13⋊C3—151no—
32C13×C5⋊D5—31no—
33C5×D5×C13—31no—
34C5×D5×C13C3×D311yescharacteristic, complemented
35C3×C5×C13⋊C3—22no—
36C3×C5×C13⋊C3C2×D511yescharacteristic, complemented
37C3×C5×C13⋊C3C2×D511yescharacteristic, complemented
38C2×D3×C13⋊C3—251noHall
39C3×C3⋊(C5⋊D5)—131no—
40C3×C5×D15—131no—
41C32×C5×D5—131no—
42C2×C3×C5×C13—51no—
43C13×D15—51no—
44C13×D15—51no—
45C13×D15—102no—
46C13×D15C3×D511yescharacteristic, complemented
47C5×D3×C13—51no—
48C3×D5×C13C3×D511yescharacteristic, complemented
49C2×C5×C13⋊C3—51no—
50C2×C5×C13⋊C3—101no—
51C2×C5×C13⋊C3—151no—
52D5×C13⋊C3—21no—
53D5×C13⋊C3—31no—
54D5×C13⋊C3—151no—
55D5×C13⋊C3—151no—
56D5×C13⋊C3—302no—
57D5×C13⋊C3D1511yescharacteristic, direct product factor
58C52×C13C2×C3×D311yescharacteristic, complemented, Hall
59D5×D15C13⋊C311yescharacteristic, direct product factor
60C3×D52—391no—
61C2×D5×C13—151no—
62C2×D5×C13—151no—
63C2×C3×C13⋊C3—51no—
64D3×C13⋊C3—51no—
65D3×C13⋊C3—251no—
66C32×C52—131noHall
67C3×C5×C13—22no—
68C3×C5×C13C2×C3×D511yescharacteristic, complemented
69C3×C5×C13C2×C3×D511yescharacteristic, complemented
70C5×C13⋊C3—22no—
71C5×C13⋊C3—21no—
72C5×C13⋊C3—21no—
73C5×C13⋊C3—42no—
74C5×C13⋊C3D3×D511yescharacteristic, complemented
75C5×C13⋊C3C2×D1511yescharacteristic, complemented
76C2×C3×D15—651no—
77C3×D3×D5—651no—
78C2×D3×C13—251no—
79C22×C13⋊C3—751no—
80C3⋊(C5⋊D5)C2×C13⋊C311yescharacteristic, complemented
81C5×D15C2×C13⋊C311yescharacteristic, complemented
82C3×C5⋊D5—391no—
83C3×C5×D5—131no—
84C3×C5×D5—261no—
85C3×C5×D5—391no—
86C3×C5×D5C2×C13⋊C311yescharacteristic, complemented
87C2×C5×C13—51no—
88C2×C5×C13—151no—
89D5×C13—31no—
90D5×C13—151no—
91D5×C13—151no—
92D5×C13—302no—
93D5×C13C3×D1511yescharacteristic, complemented
94C3×C13⋊C3D5211yescharacteristic, complemented, Hall
95D52—31noHall
96C2×C32×C5—651no—
97C3×D15—131no—
98C3×D15—651no—
99C3×D15—651no—
100C3×D15—1302no—
101C3×C5×D3—651no—
102C32×D5—131no—
103C2×C3×C13—51no—
104D3×C13—51no—
105D3×C13—251no—
106C2×C13⋊C3—51no—
107C2×C13⋊C3—101no—
108C2×C13⋊C3—151no—
109C2×C13⋊C3—751no—
110C3×C52—131no—
111C3×C52—261no—
112C3×C52C22×C13⋊C311yescharacteristic, complemented
113C5×C13—22no—
114C5×C13C3×D3×D511yescharacteristic, complemented
115C5×C13C2×C3×D1511yescharacteristic, complemented
116C2×D15—51no—
117C2×C3×D5—1951no—
118C2×C3×D5—1951no—
119D3×D5—51no—
120C22×C13—751noHall
121C5⋊D5—31no—
122C5×D5—31no—
123C5×D5D3×C13⋊C311yescharacteristic, complemented
124C32×C5—131no—
125C32×C5—131no—
126C32×C5—262no—
127C3×C13C3×D5211yescharacteristic, complemented
128C13⋊C3—21no—
129C13⋊C3D5×D1511yescharacteristic, direct product factor
130C2×C3×D3—3251noHall
131C2×C3×C5—51no—
132C2×C3×C5—651no—
133C2×C3×C5—1301no—
134C2×C3×C5—1951no—
135D15—51no—
136D15—51no—
137D15—102no—
138D15D5×C13⋊C311yescharacteristic, direct product factor
139C3×D5—131no—
140C3×D5—261no—
141C3×D5—391no—
142C3×D5—3902no—
143C3×D5—1951no—
144C3×D5—1951no—
145C3×D5D5×C13⋊C311yescharacteristic, complemented
146C5×D3—51no—
147C2×C13—51no—
148C2×C13—151no—
149C2×C13—751no—
150C52C2×D3×C13⋊C311yescharacteristic, complemented, Sylow
151C2×D5—151no—
152C2×D5—151no—
153C2×C32—651no—
154C3×D3—651no—
155C3×D3—3251no—
156C3×C5—22no—
157C3×C5—131no—
158C3×C5—131no—
159C3×C5—262no—
160C3×C5—261no—
161C3×C5—261no—
162C3×C5—522no—
163C3×C5C2×D5×C13⋊C311yescharacteristic, complemented
164C3×C5C2×D5×C13⋊C311yescharacteristic, complemented
165C13C3×D5×D1511yescharacteristic, complemented, Sylow
166C22×C3—9751no—
167C2×D3—251no—
168C2×C5—51no—
169C2×C5—151no—
170D5—31no—
171D5—151no—
172D5—151no—
173D5—302no—
174D5D15×C13⋊C311yescharacteristic, direct product factor
175C32—131noSylow
176C2×C3—51no—
177C2×C3—651no—
178C2×C3—1301no—
179C2×C3—1951no—
180C2×C3—9751no—
181D3—51no—
182D3—251no—
183C5—22no—
184C5D3×D5×C13⋊C311yescharacteristic, complemented
185C5C2×D15×C13⋊C311yescharacteristic, complemented
186C22—751noSylow
187C3—131no—
188C3—261no—
189C3D52×C13⋊C311yescharacteristic, complemented
190C2—51no—
191C2—151no—
192C2—751no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C52×C13C22×C3
LCSG ▷ C3×C52×C13
UCSC1

Complements

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

NH ≅ G/Ntype
1. C13⋊C3×C3⋊(C5⋊D5)C2semidirect
2. C5×D15×C13⋊C3C2semidirect
3. C3×C5×D5×C13⋊C3C2semidirect
4. D5×C13×D15C3semidirect
6. C3×C52×C13⋊C3C22semidirect
9. C13×C3⋊(C5⋊D5)C2×C3semidirect
10. C5×C13×D15C2×C3semidirect
11. C3×C5×D5×C13C2×C3semidirect
15. C5×D5×C13⋊C3D3semidirect
21. D15×C13⋊C3D5direct (N × H)
23. C3×D5×C13⋊C3D5semidirect
24. C3×C52×C13C22×C3semidirect
26. C52×C13⋊C3C2×D3semidirect
34. C5×D5×C13C3×D3semidirect
36. C3×C5×C13⋊C3C2×D5semidirect
37. C3×C5×C13⋊C3C2×D5semidirect
46. C13×D15C3×D5semidirect
48. C3×D5×C13C3×D5semidirect
57. D5×C13⋊C3D15direct (N × H)
58. C52×C13C2×C3×D3semidirect
59. D5×D15C13⋊C3direct (N × H)
68. C3×C5×C13C2×C3×D5semidirect
69. C3×C5×C13C2×C3×D5semidirect
74. C5×C13⋊C3D3×D5semidirect
75. C5×C13⋊C3C2×D15semidirect
80. C3⋊(C5⋊D5)C2×C13⋊C3semidirect
81. C5×D15C2×C13⋊C3semidirect
86. C3×C5×D5C2×C13⋊C3semidirect
93. D5×C13C3×D15semidirect
94. C3×C13⋊C3D52semidirect
112. C3×C52C22×C13⋊C3semidirect
114. C5×C13C3×D3×D5semidirect
115. C5×C13C2×C3×D15semidirect
123. C5×D5D3×C13⋊C3semidirect
127. C3×C13C3×D52semidirect
129. C13⋊C3D5×D15direct (N × H)
138. D15D5×C13⋊C3direct (N × H)
145. C3×D5D5×C13⋊C3semidirect
150. C52C2×D3×C13⋊C3semidirect
163. C3×C5C2×D5×C13⋊C3semidirect
164. C3×C5C2×D5×C13⋊C3semidirect
165. C13C3×D5×D15semidirect
174. D5D15×C13⋊C3direct (N × H)
184. C5D3×D5×C13⋊C3semidirect
185. C5C2×D15×C13⋊C3semidirect
189. C3D52×C13⋊C3semidirect

Maximal subgroups

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

subgroupindex
C13⋊C3×C3⋊(C5⋊D5)2
C5×D15×C13⋊C32
C3×C5×D5×C13⋊C32
D5×C13×D153
D52×C13⋊C33
C2×D15×C13⋊C35
D3×D5×C13⋊C35
C3×D5×D1513