Finite Group Databasebeta

← D15×D555 #45686453

Subgroups — D15×D555 #45686453

Order 33300.

224 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 46 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×D15×C37C211yesmaximal, characteristic, complemented
2C3×C5×D555C211yesmaximal, characteristic, complemented
3C3⋊(C3⋊(C5⋊D185))C211yesmaximal, characteristic, complemented
4D15×D185—31nomaximal
5D5×D555—31nomaximal
6C32×C52×C37C2211yescharacteristic, complemented, Hall
7D15×D111—51nomaximal
8D3×D555—51nomaximal
9C3⋊(C5⋊D185)—31no—
10C3⋊(C5⋊D185)—31no—
11C3⋊(C5⋊D185)—61no—
12C5×D555D311yescharacteristic, complemented
13C5×D15×C37D311yescharacteristic, complemented
14C3×C5×D185—31no—
15C3×C5×D5×C37—31no—
16D5×D185—91noHall
17C3⋊D555—51no—
18C3⋊D555—51no—
19C3⋊D555—102no—
20C3×D555D511yescharacteristic, complemented
21C3×D15×C37D511yescharacteristic, complemented
22C3×C5×D111—51no—
23C3×C5×D3×C37—51no—
24C3×C52×C37—21no—
25C3×C52×C37C2×D311yescharacteristic, complemented
26C3×C52×C37C2×D311yescharacteristic, complemented
27C2×D555—151no—
28D3×D185—151no—
29D5×D111—151no—
30D15×D37—151no—
31C5⋊D185—91no—
32C5×D185—31no—
33C5×D5×C37—31no—
34C32×C5×C37—22no—
35C32×C5×C37C2×D511yescharacteristic, complemented
36C32×C5×C37C2×D511yescharacteristic, complemented
37D3×D111—251noHall
38C2×C3×C5×C37—151no—
39D555—151no—
40D555—151no—
41D555—151no—
42D555—151no—
43D555—302no—
44D555—302no—
45D555—301no—
46D555—301no—
47D555—304no—
48D555D1511yescharacteristic, direct product factor
49D15×C37D1511yescharacteristic, complemented
50C5×D111—51no—
51C5×D3×C37—51no—
52C3×D185—31no—
53C3×D5×C37—31no—
54C3×C5×D37—151no—
55C52×C37D3211yescharacteristic, complemented, Hall
56D152—371nomaximal, Hall
57C2×D185—451no—
58D5×D37—451no—
59C3⋊D111—251no—
60C3×D111—51no—
61C3×D3×C37—51no—
62C3×C5×C37—24no—
63C3×C5×C37—22no—
64C3×C5×C37—22no—
65C3×C5×C37—21no—
66C3×C5×C37—21no—
67C3×C5×C37D3×D511yescharacteristic, complemented
68C3×C5×C37D3×D511yescharacteristic, complemented
69C3×C5×C37C2×D1511yescharacteristic, complemented
70C3×C5×C37C2×D1511yescharacteristic, complemented
71C3⋊(C3⋊(C5⋊D5))—371no—
72C3×C5×D15—371no—
73C3×C5×D15D3711yescharacteristic, complemented
74C2×D111—751no—
75D3×D37—751no—
76C2×C5×C37—151no—
77D185—31no—
78D185—451no—
79D185—451no—
80D185—902no—
81C5×D37—151no—
82D5×C37—31no—
83C32×C37D5211yescharacteristic, complemented, Hall
84D5×D15—1111no—
85D5×D15—1111no—
86C32×C52C2×D3711yescharacteristic, complemented, Hall
87C2×C3×C37—151no—
88D111—51no—
89D111—751no—
90D111—751no—
91D111—1501no—
92C3×D37—151no—
93D3×C37—51no—
94C5×C37—22no—
95C5×C37D3×D1511yescharacteristic, complemented
96C5×C37D3×D1511yescharacteristic, complemented
97D3×D15—1851no—
98D3×D15—1851no—
99C3⋊(C5⋊D5)—1111no—
100C3⋊(C5⋊D5)—1111no—
101C3⋊(C5⋊D5)—2221no—
102C5×D15—371no—
103C5×D15D11111yescharacteristic, complemented
104C3×C5×D5—31no—
105C3×C5×D5—1111no—
106C2×D37—2251noHall
107C3×C37—21no—
108C3×C37D5×D1511yescharacteristic, complemented
109C3×C37D5×D1511yescharacteristic, complemented
110D52—3331noHall
111C3⋊D15—3702no—
112C3⋊D15—1851no—
113C3⋊D15—1851no—
114C3×D15—371no—
115C3×D15D18511yescharacteristic, complemented
116C3×C5×D3—51no—
117C3×C5×D3—1851no—
118C3×C52—21no—
119C3×C52D3×D3711yescharacteristic, complemented
120C3×C52C2×D11111yescharacteristic, complemented
121C2×C37—151no—
122D37—151no—
123D37—2251no—
124C2×D15—5551no—
125C2×D15—5551no—
126D3×D5—5551no—
127D3×D5—5551no—
128C5⋊D5—3331no—
129C5×D5—31no—
130C5×D5—1111no—
131C32×C5—22no—
132C32×C5D5×D3711yescharacteristic, complemented
133C32×C5C2×D18511yescharacteristic, complemented
134C37D15211yescharacteristic, complemented, Sylow
135D32—9251noHall
136C2×C3×C5—151no—
137C2×C3×C5—5551no—
138D15—371no—
139D15—5551no—
140D15—5551no—
141D15—5551no—
142D15—5551no—
143D15—11104no—
144D15—11101no—
145D15—11101no—
146D15—11102no—
147D15—11102no—
148D15D55511yescharacteristic, direct product factor
149C3×D5—31no—
150C3×D5—1111no—
151C5×D3—51no—
152C5×D3—1851no—
153C52D3×D11111yescharacteristic, complemented, Sylow
154C2×D5—16651no—
155C2×D5—16651no—
156C3⋊D3—9251no—
157C3×D3—51no—
158C3×D3—1851no—
159C3×C5—24no—
160C3×C5—21no—
161C3×C5—21no—
162C3×C5—22no—
163C3×C5—22no—
164C3×C5D15×D3711yescharacteristic, complemented
165C3×C5D5×D11111yescharacteristic, complemented
166C3×C5D3×D18511yescharacteristic, complemented
167C3×C5C2×D55511yescharacteristic, complemented
168C2×D3—27751no—
169C2×D3—27751no—
170C2×C5—151no—
171C2×C5—5551no—
172D5—33302no—
173D5—31no—
174D5—1111no—
175D5—16651no—
176D5—16651no—
177C32D5×D18511yescharacteristic, complemented, Sylow
178C2×C3—151no—
179C2×C3—5551no—
180D3—51no—
181D3—55501no—
182D3—1851no—
183D3—27751no—
184D3—27751no—
185C5—22no—
186C5D3×D55511yescharacteristic, complemented
187C5D15×D11111yescharacteristic, complemented
188C22—83251noSylow
189C3—21no—
190C3D5×D55511yescharacteristic, complemented
191C3D15×D18511yescharacteristic, complemented
192C2—151no—
193C2—5551no—
194C2—83251no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C52×C37C22
LCSG ▷ C32×C52×C37
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C5×D15×C37C2semidirect
2. C3×C5×D555C2semidirect
3. C3⋊(C3⋊(C5⋊D185))C2semidirect
6. C32×C52×C37C22semidirect
12. C5×D555D3semidirect
13. C5×D15×C37D3semidirect
20. C3×D555D5semidirect
21. C3×D15×C37D5semidirect
25. C3×C52×C37C2×D3semidirect
26. C3×C52×C37C2×D3semidirect
35. C32×C5×C37C2×D5semidirect
36. C32×C5×C37C2×D5semidirect
48. D555D15direct (N × H)
49. D15×C37D15semidirect
55. C52×C37D32semidirect
67. C3×C5×C37D3×D5semidirect
68. C3×C5×C37D3×D5semidirect
69. C3×C5×C37C2×D15semidirect
70. C3×C5×C37C2×D15semidirect
73. C3×C5×D15D37semidirect
83. C32×C37D52semidirect
86. C32×C52C2×D37semidirect
95. C5×C37D3×D15semidirect
96. C5×C37D3×D15semidirect
103. C5×D15D111semidirect
108. C3×C37D5×D15semidirect
109. C3×C37D5×D15semidirect
115. C3×D15D185semidirect
119. C3×C52D3×D37semidirect
120. C3×C52C2×D111semidirect
132. C32×C5D5×D37semidirect
133. C32×C5C2×D185semidirect
134. C37D152semidirect
148. D15D555direct (N × H)
153. C52D3×D111semidirect
164. C3×C5D15×D37semidirect
165. C3×C5D5×D111semidirect
166. C3×C5D3×D185semidirect
167. C3×C5C2×D555semidirect
177. C32D5×D185semidirect
186. C5D3×D555semidirect
187. C5D15×D111semidirect
190. C3D5×D555semidirect
191. C3D15×D185semidirect

Maximal subgroups

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

subgroupindex
C3×C5×D15×C372
C3×C5×D5552
C3⋊(C3⋊(C5⋊D185))2
D15×D1853
D5×D5553
D15×D1115
D3×D5555
D15237