Finite Group Databasebeta

← D15×D465 #42124934

Subgroups — D15×D465 #42124934

Order 27900.

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×C31C211yesmaximal, characteristic, complemented
2C3×C5×D465C211yesmaximal, characteristic, complemented
3C3⋊(C3⋊(C5⋊D155))C211yesmaximal, characteristic, complemented
4D15×D155—31nomaximal
5D5×D465—31nomaximal
6C32×C52×C31C2211yescharacteristic, complemented, Hall
7D15×D93—51nomaximal
8D3×D465—51nomaximal
9C3⋊(C5⋊D155)—31no—
10C3⋊(C5⋊D155)—31no—
11C3⋊(C5⋊D155)—61no—
12C5×D465D311yescharacteristic, complemented
13C5×D15×C31D311yescharacteristic, complemented
14C3×C5×D155—31no—
15C3×C5×D5×C31—31no—
16D5×D155—91noHall
17C3⋊D465—51no—
18C3⋊D465—51no—
19C3⋊D465—102no—
20C3×D465D511yescharacteristic, complemented
21C3×D15×C31D511yescharacteristic, complemented
22C3×C5×D93—51no—
23C3×C5×D3×C31—51no—
24C3×C52×C31—21no—
25C3×C52×C31C2×D311yescharacteristic, complemented
26C3×C52×C31C2×D311yescharacteristic, complemented
27C2×D465—151no—
28D3×D155—151no—
29D5×D93—151no—
30D15×D31—151no—
31C5⋊D155—91no—
32C5×D155—31no—
33C5×D5×C31—31no—
34C32×C5×C31—22no—
35C32×C5×C31C2×D511yescharacteristic, complemented
36C32×C5×C31C2×D511yescharacteristic, complemented
37D3×D93—251noHall
38C2×C3×C5×C31—151no—
39D465—151no—
40D465—151no—
41D465—151no—
42D465—151no—
43D465—302no—
44D465—302no—
45D465—301no—
46D465—301no—
47D465—304no—
48D465D1511yescharacteristic, direct product factor
49D15×C31D1511yescharacteristic, complemented
50C5×D93—51no—
51C5×D3×C31—51no—
52C3×D155—31no—
53C3×D5×C31—31no—
54C3×C5×D31—151no—
55D152—311nomaximal, Hall
56C52×C31D3211yescharacteristic, complemented, Hall
57C2×D155—451no—
58D5×D31—451no—
59C3⋊D93—251no—
60C3×D93—51no—
61C3×D3×C31—51no—
62C3×C5×C31—24no—
63C3×C5×C31—21no—
64C3×C5×C31—21no—
65C3×C5×C31—22no—
66C3×C5×C31—22no—
67C3×C5×C31D3×D511yescharacteristic, complemented
68C3×C5×C31D3×D511yescharacteristic, complemented
69C3×C5×C31C2×D1511yescharacteristic, complemented
70C3×C5×C31C2×D1511yescharacteristic, complemented
71C3⋊(C3⋊(C5⋊D5))—311no—
72C3×C5×D15—311no—
73C3×C5×D15D3111yescharacteristic, complemented
74C2×D93—751no—
75D3×D31—751no—
76C2×C5×C31—151no—
77D155—31no—
78D155—451no—
79D155—451no—
80D155—902no—
81C5×D31—151no—
82D5×C31—31no—
83D5×D15—931no—
84D5×D15—931no—
85C32×C31D5211yescharacteristic, complemented, Hall
86C32×C52C2×D3111yescharacteristic, complemented, Hall
87C2×C3×C31—151no—
88D93—51no—
89D93—751no—
90D93—751no—
91D93—1501no—
92C3×D31—151no—
93D3×C31—51no—
94D3×D15—1551no—
95D3×D15—1551no—
96C5×C31—22no—
97C5×C31D3×D1511yescharacteristic, complemented
98C5×C31D3×D1511yescharacteristic, complemented
99C3⋊(C5⋊D5)—931no—
100C3⋊(C5⋊D5)—931no—
101C3⋊(C5⋊D5)—1861no—
102C5×D15—311no—
103C5×D15D9311yescharacteristic, complemented
104C3×C5×D5—31no—
105C3×C5×D5—931no—
106C2×D31—2251noHall
107D52—2791noHall
108C3×C31—21no—
109C3×C31D5×D1511yescharacteristic, complemented
110C3×C31D5×D1511yescharacteristic, complemented
111C3⋊D15—3102no—
112C3⋊D15—1551no—
113C3⋊D15—1551no—
114C3×D15—311no—
115C3×D15D15511yescharacteristic, complemented
116C3×C5×D3—51no—
117C3×C5×D3—1551no—
118C3×C52—21no—
119C3×C52D3×D3111yescharacteristic, complemented
120C3×C52C2×D9311yescharacteristic, complemented
121C2×C31—151no—
122D31—151no—
123D31—2251no—
124C2×D15—4651no—
125C2×D15—4651no—
126D3×D5—4651no—
127D3×D5—4651no—
128C5⋊D5—2791no—
129C5×D5—31no—
130C5×D5—931no—
131C32×C5—22no—
132C32×C5D5×D3111yescharacteristic, complemented
133C32×C5C2×D15511yescharacteristic, complemented
134D32—7751noHall
135C31D15211yescharacteristic, complemented, Sylow
136C2×C3×C5—151no—
137C2×C3×C5—4651no—
138D15—311no—
139D15—9302no—
140D15—9302no—
141D15—9301no—
142D15—9301no—
143D15—9304no—
144D15—4651no—
145D15—4651no—
146D15—4651no—
147D15—4651no—
148D15D46511yescharacteristic, direct product factor
149C3×D5—31no—
150C3×D5—931no—
151C5×D3—51no—
152C5×D3—1551no—
153C52D3×D9311yescharacteristic, complemented, Sylow
154C2×D5—13951no—
155C2×D5—13951no—
156C3⋊D3—7751no—
157C3×D3—51no—
158C3×D3—1551no—
159C3×C5—24no—
160C3×C5—21no—
161C3×C5—21no—
162C3×C5—22no—
163C3×C5—22no—
164C3×C5D15×D3111yescharacteristic, complemented
165C3×C5D5×D9311yescharacteristic, complemented
166C3×C5D3×D15511yescharacteristic, complemented
167C3×C5C2×D46511yescharacteristic, complemented
168C2×D3—23251no—
169C2×D3—23251no—
170C2×C5—151no—
171C2×C5—4651no—
172D5—31no—
173D5—931no—
174D5—13951no—
175D5—13951no—
176D5—27902no—
177C32D5×D15511yescharacteristic, complemented, Sylow
178C2×C3—151no—
179C2×C3—4651no—
180D3—51no—
181D3—23251no—
182D3—23251no—
183D3—46501no—
184D3—1551no—
185C5—22no—
186C5D3×D46511yescharacteristic, complemented
187C5D15×D9311yescharacteristic, complemented
188C22—69751noSylow
189C3—21no—
190C3D5×D46511yescharacteristic, complemented
191C3D15×D15511yescharacteristic, complemented
192C2—151no—
193C2—69751no—
194C2—4651no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C52×C31C22
LCSG ▷ C32×C52×C31
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C5×D15×C31C2semidirect
2. C3×C5×D465C2semidirect
3. C3⋊(C3⋊(C5⋊D155))C2semidirect
6. C32×C52×C31C22semidirect
12. C5×D465D3semidirect
13. C5×D15×C31D3semidirect
20. C3×D465D5semidirect
21. C3×D15×C31D5semidirect
25. C3×C52×C31C2×D3semidirect
26. C3×C52×C31C2×D3semidirect
35. C32×C5×C31C2×D5semidirect
36. C32×C5×C31C2×D5semidirect
48. D465D15direct (N × H)
49. D15×C31D15semidirect
56. C52×C31D32semidirect
67. C3×C5×C31D3×D5semidirect
68. C3×C5×C31D3×D5semidirect
69. C3×C5×C31C2×D15semidirect
70. C3×C5×C31C2×D15semidirect
73. C3×C5×D15D31semidirect
85. C32×C31D52semidirect
86. C32×C52C2×D31semidirect
97. C5×C31D3×D15semidirect
98. C5×C31D3×D15semidirect
103. C5×D15D93semidirect
109. C3×C31D5×D15semidirect
110. C3×C31D5×D15semidirect
115. C3×D15D155semidirect
119. C3×C52D3×D31semidirect
120. C3×C52C2×D93semidirect
132. C32×C5D5×D31semidirect
133. C32×C5C2×D155semidirect
135. C31D152semidirect
148. D15D465direct (N × H)
153. C52D3×D93semidirect
164. C3×C5D15×D31semidirect
165. C3×C5D5×D93semidirect
166. C3×C5D3×D155semidirect
167. C3×C5C2×D465semidirect
177. C32D5×D155semidirect
186. C5D3×D465semidirect
187. C5D15×D93semidirect
190. C3D5×D465semidirect
191. C3D15×D155semidirect

Maximal subgroups

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

subgroupindex
C3×C5×D15×C312
C3×C5×D4652
C3⋊(C3⋊(C5⋊D155))2
D15×D1553
D5×D4653
D15×D935
D3×D4655
D15231