Finite Group Databasebeta

← D5×D15×C31⋊C3 #42124809

Subgroups — D5×D15×C31⋊C3 #42124809

Order 27900.

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
1C31⋊C3×C3⋊(C5⋊D5)C211yesmaximal, characteristic, complemented
2C5×D15×C31⋊C3C211yesmaximal, characteristic, complemented
3C3×C5×D5×C31⋊C3C211yesmaximal, characteristic, complemented
4D5×D15×C31C311yesmaximal, characteristic, complemented
5D52×C31⋊C3—31nomaximal
6C3×C52×C31⋊C3C2211yescharacteristic, complemented, Hall
7C2×D15×C31⋊C3—51nomaximal
8D3×D5×C31⋊C3—51nomaximal
9C31×C3⋊(C5⋊D5)C2×C311yescharacteristic, complemented
10C5×D15×C31C2×C311yescharacteristic, complemented
11C3×C5×D5×C31C2×C311yescharacteristic, complemented
12C5⋊D5×C31⋊C3—31no—
13C5×D5×C31⋊C3—21no—
14C5×D5×C31⋊C3—31no—
15C5×D5×C31⋊C3D311yescharacteristic, complemented
16D52×C31—31noHall
17C2×C3×C5×C31⋊C3—51no—
18D15×C31⋊C3—51no—
19D15×C31⋊C3—51no—
20D15×C31⋊C3—102no—
21D15×C31⋊C3D511yescharacteristic, direct product factor
22C5×D3×C31⋊C3—51no—
23C3×D5×C31⋊C3D511yescharacteristic, complemented
24C52×C31⋊C3—21no—
25C52×C31⋊C3C2×D311yescharacteristic, complemented
26C3×C52×C31C22×C311yescharacteristic, complemented
27C2×D15×C31—51no—
28D3×D5×C31—51no—
29C2×D5×C31⋊C3—151no—
30C2×D5×C31⋊C3—151no—
31C31×C5⋊D5—31no—
32C5×D5×C31—31no—
33C5×D5×C31C3×D311yescharacteristic, complemented
34C3×C5×C31⋊C3—22no—
35C3×C5×C31⋊C3C2×D511yescharacteristic, complemented
36C3×C5×C31⋊C3C2×D511yescharacteristic, complemented
37C2×D3×C31⋊C3—251noHall
38C2×C3×C5×C31—51no—
39D15×C31—51no—
40D15×C31—51no—
41D15×C31—102no—
42D15×C31C3×D511yescharacteristic, complemented
43C5×D3×C31—51no—
44C3×D5×C31C3×D511yescharacteristic, complemented
45C2×C5×C31⋊C3—51no—
46C2×C5×C31⋊C3—101no—
47C2×C5×C31⋊C3—151no—
48D5×C31⋊C3—21no—
49D5×C31⋊C3—31no—
50D5×C31⋊C3—151no—
51D5×C31⋊C3—151no—
52D5×C31⋊C3—302no—
53D5×C31⋊C3D1511yescharacteristic, direct product factor
54C3×D5×D15—311nomaximal, Hall
55C52×C31C2×C3×D311yescharacteristic, complemented, Hall
56C2×D5×C31—151no—
57C2×D5×C31—151no—
58C2×C3×C31⋊C3—51no—
59D3×C31⋊C3—51no—
60D3×C31⋊C3—251no—
61C3×C5×C31—22no—
62C3×C5×C31C2×C3×D511yescharacteristic, complemented
63C3×C5×C31C2×C3×D511yescharacteristic, complemented
64C5×C31⋊C3—21no—
65C5×C31⋊C3—21no—
66C5×C31⋊C3—22no—
67C5×C31⋊C3—42no—
68C5×C31⋊C3D3×D511yescharacteristic, complemented
69C5×C31⋊C3C2×D1511yescharacteristic, complemented
70C3×C3⋊(C5⋊D5)—311no—
71C3×C5×D15—311no—
72C32×C5×D5—311no—
73C2×D3×C31—251no—
74C22×C31⋊C3—751no—
75C2×C5×C31—51no—
76C2×C5×C31—151no—
77D5×C31—31no—
78D5×C31—151no—
79D5×C31—151no—
80D5×C31—302no—
81D5×C31C3×D1511yescharacteristic, complemented
82D5×D15C31⋊C311yescharacteristic, direct product factor
83C3×D52—931no—
84C3×C31⋊C3D5211yescharacteristic, complemented, Hall
85C32×C52—311noHall
86C2×C3×C31—51no—
87D3×C31—51no—
88D3×C31—251no—
89C2×C31⋊C3—51no—
90C2×C31⋊C3—101no—
91C2×C31⋊C3—151no—
92C2×C31⋊C3—751no—
93C2×C3×D15—1551no—
94C3×D3×D5—1551no—
95C5×C31—22no—
96C5×C31C3×D3×D511yescharacteristic, complemented
97C5×C31C2×C3×D1511yescharacteristic, complemented
98C3⋊(C5⋊D5)C2×C31⋊C311yescharacteristic, complemented
99C5×D15C2×C31⋊C311yescharacteristic, complemented
100C3×C5⋊D5—931no—
101C3×C5×D5—311no—
102C3×C5×D5—621no—
103C3×C5×D5—931no—
104C3×C5×D5C2×C31⋊C311yescharacteristic, complemented
105C22×C31—751noHall
106D52—31noHall
107C3×C31C3×D5211yescharacteristic, complemented
108C31⋊C3—21no—
109C31⋊C3D5×D1511yescharacteristic, direct product factor
110C2×C32×C5—1551no—
111C3×D15—311no—
112C3×D15—3102no—
113C3×D15—1551no—
114C3×D15—1551no—
115C3×C5×D3—1551no—
116C32×D5—311no—
117C3×C52—311no—
118C3×C52—621no—
119C3×C52C22×C31⋊C311yescharacteristic, complemented
120C2×C31—51no—
121C2×C31—151no—
122C2×C31—751no—
123C2×D15—51no—
124C2×C3×D5—4651no—
125C2×C3×D5—4651no—
126D3×D5—51no—
127C5⋊D5—31no—
128C5×D5—31no—
129C5×D5D3×C31⋊C311yescharacteristic, complemented
130C32×C5—311no—
131C32×C5—311no—
132C32×C5—622no—
133C2×C3×D3—7751noHall
134C31C3×D5×D1511yescharacteristic, complemented, Sylow
135C2×C3×C5—51no—
136C2×C3×C5—3101no—
137C2×C3×C5—1551no—
138C2×C3×C5—4651no—
139D15—51no—
140D15—51no—
141D15—102no—
142D15D5×C31⋊C311yescharacteristic, direct product factor
143C3×D5—311no—
144C3×D5—621no—
145C3×D5—931no—
146C3×D5—9302no—
147C3×D5—4651no—
148C3×D5—4651no—
149C3×D5D5×C31⋊C311yescharacteristic, complemented
150C5×D3—51no—
151C52C2×D3×C31⋊C311yescharacteristic, complemented, Sylow
152C2×D5—151no—
153C2×D5—151no—
154C2×C32—1551no—
155C3×D3—7751no—
156C3×D3—1551no—
157C3×C5—22no—
158C3×C5—311no—
159C3×C5—311no—
160C3×C5—622no—
161C3×C5—621no—
162C3×C5—621no—
163C3×C5—1242no—
164C3×C5C2×D5×C31⋊C311yescharacteristic, complemented
165C3×C5C2×D5×C31⋊C311yescharacteristic, complemented
166C22×C3—23251no—
167C2×D3—251no—
168C2×C5—51no—
169C2×C5—151no—
170D5—31no—
171D5—151no—
172D5—151no—
173D5—302no—
174D5D15×C31⋊C311yescharacteristic, direct product factor
175C32—311noSylow
176C2×C3—51no—
177C2×C3—23251no—
178C2×C3—3101no—
179C2×C3—1551no—
180C2×C3—4651no—
181D3—51no—
182D3—251no—
183C5—22no—
184C5D3×D5×C31⋊C311yescharacteristic, complemented
185C5C2×D15×C31⋊C311yescharacteristic, complemented
186C22—751noSylow
187C3—311no—
188C3—621no—
189C3D52×C31⋊C311yescharacteristic, complemented
190C2—51no—
191C2—151no—
192C2—751no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C52×C31C22×C3
LCSG ▷ C3×C52×C31
UCSC1

Complements

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

NH ≅ G/Ntype
1. C31⋊C3×C3⋊(C5⋊D5)C2semidirect
2. C5×D15×C31⋊C3C2semidirect
3. C3×C5×D5×C31⋊C3C2semidirect
4. D5×D15×C31C3semidirect
6. C3×C52×C31⋊C3C22semidirect
9. C31×C3⋊(C5⋊D5)C2×C3semidirect
10. C5×D15×C31C2×C3semidirect
11. C3×C5×D5×C31C2×C3semidirect
15. C5×D5×C31⋊C3D3semidirect
21. D15×C31⋊C3D5direct (N × H)
23. C3×D5×C31⋊C3D5semidirect
25. C52×C31⋊C3C2×D3semidirect
26. C3×C52×C31C22×C3semidirect
33. C5×D5×C31C3×D3semidirect
35. C3×C5×C31⋊C3C2×D5semidirect
36. C3×C5×C31⋊C3C2×D5semidirect
42. D15×C31C3×D5semidirect
44. C3×D5×C31C3×D5semidirect
53. D5×C31⋊C3D15direct (N × H)
55. C52×C31C2×C3×D3semidirect
62. C3×C5×C31C2×C3×D5semidirect
63. C3×C5×C31C2×C3×D5semidirect
68. C5×C31⋊C3D3×D5semidirect
69. C5×C31⋊C3C2×D15semidirect
81. D5×C31C3×D15semidirect
82. D5×D15C31⋊C3direct (N × H)
84. C3×C31⋊C3D52semidirect
96. C5×C31C3×D3×D5semidirect
97. C5×C31C2×C3×D15semidirect
98. C3⋊(C5⋊D5)C2×C31⋊C3semidirect
99. C5×D15C2×C31⋊C3semidirect
104. C3×C5×D5C2×C31⋊C3semidirect
107. C3×C31C3×D52semidirect
109. C31⋊C3D5×D15direct (N × H)
119. C3×C52C22×C31⋊C3semidirect
129. C5×D5D3×C31⋊C3semidirect
134. C31C3×D5×D15semidirect
142. D15D5×C31⋊C3direct (N × H)
149. C3×D5D5×C31⋊C3semidirect
151. C52C2×D3×C31⋊C3semidirect
164. C3×C5C2×D5×C31⋊C3semidirect
165. C3×C5C2×D5×C31⋊C3semidirect
174. D5D15×C31⋊C3direct (N × H)
184. C5D3×D5×C31⋊C3semidirect
185. C5C2×D15×C31⋊C3semidirect
189. C3D52×C31⋊C3semidirect

Maximal subgroups

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

subgroupindex
C31⋊C3×C3⋊(C5⋊D5)2
C5×D15×C31⋊C32
C3×C5×D5×C31⋊C32
D5×D15×C313
D52×C31⋊C33
C2×D15×C31⋊C35
D3×D5×C31⋊C35
C3×D5×D1531