Finite Group Databasebeta

← C5×D93⋊D15 #42124928

Subgroups — C5×D93⋊D15 #42124928

Order 27900.

212 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 50 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×C52×D93C211yesmaximal, characteristic, complemented
2C3×C5×D465C211yesmaximal, characteristic, complemented
3C5×C31×C3⋊D15C211yesmaximal, characteristic, complemented
4C5×D15⋊D31—31nomaximal
5C5×D15×D31—31nomaximal
6C32×C52×C31C2211yescharacteristic, complemented, Hall
7D93⋊D15C511yesmaximal, characteristic, direct product factor
8C5×(C3⋊D3)⋊D31—51nomaximal
9C5×D465D311yescharacteristic, complemented
10C5×D15×C31—31no—
11C5×D15×C31—31no—
12C5×D15×C31—61no—
13C52×D93D311yescharacteristic, complemented
14C3×C5×D155—31no—
15C3×C52×D31—31no—
16C5×D5×D31—91noHall
17C31×C3⋊D15C2×C511yescharacteristic, complemented
18C5×C3⋊D3×C31—51no—
19C3×D465C2×C511yescharacteristic, complemented
20C3×C5×D93—22no—
21C3×C5×D93—51no—
22C3×C5×D93D511yescharacteristic, complemented
23C3×C5×D93C2×C511yescharacteristic, complemented
24C3×C52×C31—21no—
25C3×C52×C31C2×D311yescharacteristic, complemented
26C3×C52×C31C2×D311yescharacteristic, complemented
27D15⋊D31—31no—
28D15×D31—31no—
29C5×D3×D31—151no—
30C5×D3×D31—151no—
31C5×D155—31no—
32C5×D5×C31—91no—
33C52×D31—31no—
34C32×C5×C31—22no—
35C32×C5×C31C2×D511yescharacteristic, complemented
36C32×C5×C31C22×C511yescharacteristic, complemented
37(C3⋊D3)⋊D31—51noHall
38D465C5×D311yescharacteristic, complemented
39D15×C31—31no—
40D15×C31—31no—
41D15×C31—61no—
42C5×D93—22no—
43C5×D93—51no—
44C5×D93C5×D311yescharacteristic, complemented
45C5×D93D1511yescharacteristic, complemented
46C5×D3×C31—151no—
47C5×D3×C31—151no—
48C5×D3×C31—301no—
49C3×D155—31no—
50C3×C5×D31—31no—
51C3×C5×D31—31no—
52C3×C5×D31—62no—
53C3×C5×D31—151no—
54C5×D3×D15—311nomaximal, Hall
55C52×C31D3211yescharacteristic, complemented, Hall
56C2×C5×D31—451no—
57D5×D31—91no—
58C3⋊D3×C31—51no—
59C3×D93—51no—
60C3×D93C5×D511yescharacteristic, complemented
61C3×C5×C31—21no—
62C3×C5×C31—21no—
63C3×C5×C31—22no—
64C3×C5×C31—22no—
65C3×C5×C31—42no—
66C3×C5×C31D3×D511yescharacteristic, complemented
67C3×C5×C31C2×C5×D311yescharacteristic, complemented
68C3×C5×C31C2×C5×D311yescharacteristic, complemented
69C3×C5×C31C2×D1511yescharacteristic, complemented
70C5×C3⋊D15D3111yescharacteristic, complemented
71C3×C5×D15—311no—
72C3×C52×D3—311no—
73D3×D31—151no—
74D3×D31—151no—
75C2×C5×C31—451no—
76D155—31no—
77C5×D31—31no—
78C5×D31—31no—
79C5×D31—62no—
80C5×D31—151no—
81D5×C31—91no—
82C2×C5×D15—931no—
83C5×D3×D5—931no—
84C32×C31C2×C5×D511yescharacteristic, complemented, Hall
85C32×C52C2×D3111yescharacteristic, complemented, Hall
86D93—51no—
87D93C5×D1511yescharacteristic, complemented
88C3×D31—31no—
89C3×D31—151no—
90D3×C31—151no—
91D3×C31—151no—
92D3×C31—301no—
93D3×D15—311no—
94C5×D32—1551no—
95C5×C31—22no—
96C5×C31C5×D3211yescharacteristic, complemented
97C5×C31D3×D1511yescharacteristic, complemented
98C2×C3×C52—931no—
99C5×D15—31no—
100C5×D15—31no—
101C5×D15—61no—
102C5×D15—311no—
103C52×D3—311no—
104C3×C5×D5—931no—
105C2×D31—451noHall
106C2×C5×D5—2791noHall
107C3×C31—21no—
108C3×C31C5×D3×D511yescharacteristic, complemented
109C3×C31C2×C5×D1511yescharacteristic, complemented
110C3⋊D15C5×D3111yescharacteristic, complemented
111C5×C3⋊D3—51no—
112C3×D15—311no—
113C3×C5×D3—311no—
114C3×C5×D3—311no—
115C3×C5×D3—622no—
116C3×C5×D3—1551no—
117C3×C52—21no—
118C3×C52D3×D3111yescharacteristic, complemented
119C3×C52D3×D3111yescharacteristic, complemented
120C2×C31—451no—
121D31—31no—
122D31—151no—
123C2×D15—931no—
124C2×C5×D3—4651no—
125C2×C5×D3—4651no—
126D3×D5—931no—
127C2×C52—931no—
128C5×D5—91no—
129C5×D5—931no—
130C32×C5—22no—
131C32×C5D5×D3111yescharacteristic, complemented
132C32×C5C2×C5×D3111yescharacteristic, complemented
133D32—1551noHall
134C31C5×D3×D1511yescharacteristic, complemented, Sylow
135C2×C3×C5—931no—
136C2×C3×C5—931no—
137C2×C3×C5—1862no—
138C2×C3×C5—4651no—
139D15—31no—
140D15—31no—
141D15—61no—
142D15—311no—
143C3×D5—931no—
144C5×D3—151no—
145C5×D3—151no—
146C5×D3—301no—
147C5×D3—311no—
148C5×D3—311no—
149C5×D3—622no—
150C5×D3—1551no—
151C52(C3⋊D3)⋊D3111yescharacteristic, complemented, Sylow
152C22×C5—13951no—
153C2×D5—2791no—
154C3⋊D3—51no—
155C3×D3—311no—
156C3×D3—1551no—
157C3×C5—21no—
158C3×C5—21no—
159C3×C5—22no—
160C3×C5—22no—
161C3×C5—42no—
162C3×C5C5×D3×D3111yescharacteristic, complemented
163C3×C5C5×D3×D3111yescharacteristic, complemented
164C3×C5D15×D3111yescharacteristic, complemented
165C3×C5D15⋊D3111yescharacteristic, complemented
166C2×D3—4651no—
167C2×D3—4651no—
168C2×C5—451no—
169C2×C5—931no—
170C2×C5—931no—
171C2×C5—1862no—
172C2×C5—4651no—
173D5—91no—
174D5—931no—
175C32C5×D5×D3111yescharacteristic, complemented, Sylow
176C2×C3—931no—
177C2×C3—4651no—
178D3—151no—
179D3—151no—
180D3—301no—
181D3—311no—
182D3—1551no—
183C5—22no—
184C5C5×(C3⋊D3)⋊D3111yescharacteristic, complemented
185C5D93⋊D1511yescharacteristic, direct product factor
186C22—13951noSylow
187C3—21no—
188C3C5×D15×D3111yescharacteristic, complemented
189C3C5×D15⋊D3111yescharacteristic, complemented
190C2—451no—
191C2—931no—
192C2—4651no—
subgroupG/H
center, hypercenterC5D93⋊D15
commutator, cosocle, hypocenterC32×C5×C31C22×C5
FrattiniC1G
Fitting, socleC32×C52×C31C22
LCSG ▷ C32×C5×C31
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
1. C3×C52×D93C2semidirect
2. C3×C5×D465C2semidirect
3. C5×C31×C3⋊D15C2semidirect
6. C32×C52×C31C22semidirect
7. D93⋊D15C5direct (N × H)
9. C5×D465D3semidirect
13. C52×D93D3semidirect
17. C31×C3⋊D15C2×C5semidirect
19. C3×D465C2×C5semidirect
22. C3×C5×D93D5semidirect
23. C3×C5×D93C2×C5semidirect
25. C3×C52×C31C2×D3semidirect
26. C3×C52×C31C2×D3semidirect
35. C32×C5×C31C2×D5semidirect
36. C32×C5×C31C22×C5semidirect
38. D465C5×D3semidirect
44. C5×D93C5×D3semidirect
45. C5×D93D15semidirect
55. C52×C31D32semidirect
60. C3×D93C5×D5semidirect
66. C3×C5×C31D3×D5semidirect
67. C3×C5×C31C2×C5×D3semidirect
68. C3×C5×C31C2×C5×D3semidirect
69. C3×C5×C31C2×D15semidirect
70. C5×C3⋊D15D31semidirect
84. C32×C31C2×C5×D5semidirect
85. C32×C52C2×D31semidirect
87. D93C5×D15semidirect
96. C5×C31C5×D32semidirect
97. C5×C31D3×D15semidirect
108. C3×C31C5×D3×D5semidirect
109. C3×C31C2×C5×D15semidirect
110. C3⋊D15C5×D31semidirect
118. C3×C52D3×D31semidirect
119. C3×C52D3×D31semidirect
131. C32×C5D5×D31semidirect
132. C32×C5C2×C5×D31semidirect
134. C31C5×D3×D15semidirect
151. C52(C3⋊D3)⋊D31semidirect
162. C3×C5C5×D3×D31semidirect
163. C3×C5C5×D3×D31semidirect
164. C3×C5D15×D31semidirect
165. C3×C5D15⋊D31semidirect
175. C32C5×D5×D31semidirect
184. C5C5×(C3⋊D3)⋊D31semidirect
185. C5D93⋊D15direct (N × H)
188. C3C5×D15×D31semidirect
189. C3C5×D15⋊D31semidirect

Maximal subgroups

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

subgroupindex
C3×C52×D932
C3×C5×D4652
C5×C31×C3⋊D152
C5×D15⋊D313
C5×D15×D313
D93⋊D155
C5×(C3⋊D3)⋊D315
C5×D3×D1531