Finite Group Databasebeta

← D5×D15×C37⋊C3 #45686302

Subgroups — D5×D15×C37⋊C3 #45686302

Order 33300.

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
1C37⋊C3×C3⋊(C5⋊D5)C211yesmaximal, characteristic, complemented
2C5×D15×C37⋊C3C211yesmaximal, characteristic, complemented
3C3×C5×D5×C37⋊C3C211yesmaximal, characteristic, complemented
4D5×D15×C37C311yesmaximal, characteristic, complemented
5D52×C37⋊C3—31nomaximal
6C3×C52×C37⋊C3C2211yescharacteristic, complemented, Hall
7C2×D15×C37⋊C3—51nomaximal
8D3×D5×C37⋊C3—51nomaximal
9C37×C3⋊(C5⋊D5)C2×C311yescharacteristic, complemented
10C5×D15×C37C2×C311yescharacteristic, complemented
11C3×C5×D5×C37C2×C311yescharacteristic, complemented
12C5⋊D5×C37⋊C3—31no—
13C5×D5×C37⋊C3—21no—
14C5×D5×C37⋊C3—31no—
15C5×D5×C37⋊C3D311yescharacteristic, complemented
16D52×C37—31noHall
17C2×C3×C5×C37⋊C3—51no—
18D15×C37⋊C3—51no—
19D15×C37⋊C3—51no—
20D15×C37⋊C3—102no—
21D15×C37⋊C3D511yescharacteristic, direct product factor
22C5×D3×C37⋊C3—51no—
23C3×D5×C37⋊C3D511yescharacteristic, complemented
24C52×C37⋊C3—21no—
25C52×C37⋊C3C2×D311yescharacteristic, complemented
26C3×C52×C37C22×C311yescharacteristic, complemented
27C2×D15×C37—51no—
28D3×D5×C37—51no—
29C2×D5×C37⋊C3—151no—
30C2×D5×C37⋊C3—151no—
31C37×C5⋊D5—31no—
32C5×D5×C37—31no—
33C5×D5×C37C3×D311yescharacteristic, complemented
34C3×C5×C37⋊C3—22no—
35C3×C5×C37⋊C3C2×D511yescharacteristic, complemented
36C3×C5×C37⋊C3C2×D511yescharacteristic, complemented
37C2×D3×C37⋊C3—251noHall
38C2×C3×C5×C37—51no—
39D15×C37—51no—
40D15×C37—51no—
41D15×C37—102no—
42D15×C37C3×D511yescharacteristic, complemented
43C5×D3×C37—51no—
44C3×D5×C37C3×D511yescharacteristic, complemented
45C2×C5×C37⋊C3—51no—
46C2×C5×C37⋊C3—101no—
47C2×C5×C37⋊C3—151no—
48D5×C37⋊C3—21no—
49D5×C37⋊C3—31no—
50D5×C37⋊C3—151no—
51D5×C37⋊C3—151no—
52D5×C37⋊C3—302no—
53D5×C37⋊C3D1511yescharacteristic, direct product factor
54C52×C37C2×C3×D311yescharacteristic, complemented, Hall
55C3×D5×D15—371nomaximal, Hall
56C2×D5×C37—151no—
57C2×D5×C37—151no—
58C2×C3×C37⋊C3—51no—
59D3×C37⋊C3—51no—
60D3×C37⋊C3—251no—
61C3×C5×C37—22no—
62C3×C5×C37C2×C3×D511yescharacteristic, complemented
63C3×C5×C37C2×C3×D511yescharacteristic, complemented
64C5×C37⋊C3—22no—
65C5×C37⋊C3—21no—
66C5×C37⋊C3—21no—
67C5×C37⋊C3—42no—
68C5×C37⋊C3D3×D511yescharacteristic, complemented
69C5×C37⋊C3C2×D1511yescharacteristic, complemented
70C3×C3⋊(C5⋊D5)—371no—
71C3×C5×D15—371no—
72C32×C5×D5—371no—
73C2×D3×C37—251no—
74C22×C37⋊C3—751no—
75C2×C5×C37—51no—
76C2×C5×C37—151no—
77D5×C37—31no—
78D5×C37—151no—
79D5×C37—151no—
80D5×C37—302no—
81D5×C37C3×D1511yescharacteristic, complemented
82C3×C37⋊C3D5211yescharacteristic, complemented, Hall
83D5×D15C37⋊C311yescharacteristic, direct product factor
84C3×D52—1111no—
85C32×C52—371noHall
86C2×C3×C37—51no—
87D3×C37—51no—
88D3×C37—251no—
89C2×C37⋊C3—51no—
90C2×C37⋊C3—101no—
91C2×C37⋊C3—151no—
92C2×C37⋊C3—751no—
93C5×C37—22no—
94C5×C37C3×D3×D511yescharacteristic, complemented
95C5×C37C2×C3×D1511yescharacteristic, complemented
96C2×C3×D15—1851no—
97C3×D3×D5—1851no—
98C3⋊(C5⋊D5)C2×C37⋊C311yescharacteristic, complemented
99C5×D15C2×C37⋊C311yescharacteristic, complemented
100C3×C5⋊D5—1111no—
101C3×C5×D5—371no—
102C3×C5×D5—741no—
103C3×C5×D5—1111no—
104C3×C5×D5C2×C37⋊C311yescharacteristic, complemented
105C22×C37—751noHall
106C3×C37C3×D5211yescharacteristic, complemented
107C37⋊C3—21no—
108C37⋊C3D5×D1511yescharacteristic, direct product factor
109D52—31noHall
110C2×C32×C5—1851no—
111C3×D15—371no—
112C3×D15—3702no—
113C3×D15—1851no—
114C3×D15—1851no—
115C3×C5×D3—1851no—
116C32×D5—371no—
117C3×C52—371no—
118C3×C52—741no—
119C3×C52C22×C37⋊C311yescharacteristic, complemented
120C2×C37—51no—
121C2×C37—151no—
122C2×C37—751no—
123C2×D15—51no—
124C2×C3×D5—5551no—
125C2×C3×D5—5551no—
126D3×D5—51no—
127C5⋊D5—31no—
128C5×D5—31no—
129C5×D5D3×C37⋊C311yescharacteristic, complemented
130C32×C5—371no—
131C32×C5—371no—
132C32×C5—742no—
133C37C3×D5×D1511yescharacteristic, complemented, Sylow
134C2×C3×D3—9251noHall
135C2×C3×C5—51no—
136C2×C3×C5—5551no—
137C2×C3×C5—3701no—
138C2×C3×C5—1851no—
139D15—51no—
140D15—51no—
141D15—102no—
142D15D5×C37⋊C311yescharacteristic, direct product factor
143C3×D5—371no—
144C3×D5—5551no—
145C3×D5—5551no—
146C3×D5—741no—
147C3×D5—11102no—
148C3×D5—1111no—
149C3×D5D5×C37⋊C311yescharacteristic, complemented
150C5×D3—51no—
151C52C2×D3×C37⋊C311yescharacteristic, complemented, Sylow
152C2×D5—151no—
153C2×D5—151no—
154C2×C32—1851no—
155C3×D3—9251no—
156C3×D3—1851no—
157C3×C5—22no—
158C3×C5—371no—
159C3×C5—371no—
160C3×C5—742no—
161C3×C5—741no—
162C3×C5—741no—
163C3×C5—1482no—
164C3×C5C2×D5×C37⋊C311yescharacteristic, complemented
165C3×C5C2×D5×C37⋊C311yescharacteristic, complemented
166C22×C3—27751no—
167C2×D3—251no—
168C2×C5—51no—
169C2×C5—151no—
170D5—31no—
171D5—151no—
172D5—151no—
173D5—302no—
174D5D15×C37⋊C311yescharacteristic, direct product factor
175C32—371noSylow
176C2×C3—51no—
177C2×C3—5551no—
178C2×C3—3701no—
179C2×C3—1851no—
180C2×C3—27751no—
181D3—51no—
182D3—251no—
183C5—22no—
184C5D3×D5×C37⋊C311yescharacteristic, complemented
185C5C2×D15×C37⋊C311yescharacteristic, complemented
186C22—751noSylow
187C3—371no—
188C3—741no—
189C3D52×C37⋊C311yescharacteristic, complemented
190C2—51no—
191C2—151no—
192C2—751no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C52×C37C22×C3
LCSG ▷ C3×C52×C37
UCSC1

Complements

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

NH ≅ G/Ntype
1. C37⋊C3×C3⋊(C5⋊D5)C2semidirect
2. C5×D15×C37⋊C3C2semidirect
3. C3×C5×D5×C37⋊C3C2semidirect
4. D5×D15×C37C3semidirect
6. C3×C52×C37⋊C3C22semidirect
9. C37×C3⋊(C5⋊D5)C2×C3semidirect
10. C5×D15×C37C2×C3semidirect
11. C3×C5×D5×C37C2×C3semidirect
15. C5×D5×C37⋊C3D3semidirect
21. D15×C37⋊C3D5direct (N × H)
23. C3×D5×C37⋊C3D5semidirect
25. C52×C37⋊C3C2×D3semidirect
26. C3×C52×C37C22×C3semidirect
33. C5×D5×C37C3×D3semidirect
35. C3×C5×C37⋊C3C2×D5semidirect
36. C3×C5×C37⋊C3C2×D5semidirect
42. D15×C37C3×D5semidirect
44. C3×D5×C37C3×D5semidirect
53. D5×C37⋊C3D15direct (N × H)
54. C52×C37C2×C3×D3semidirect
62. C3×C5×C37C2×C3×D5semidirect
63. C3×C5×C37C2×C3×D5semidirect
68. C5×C37⋊C3D3×D5semidirect
69. C5×C37⋊C3C2×D15semidirect
81. D5×C37C3×D15semidirect
82. C3×C37⋊C3D52semidirect
83. D5×D15C37⋊C3direct (N × H)
94. C5×C37C3×D3×D5semidirect
95. C5×C37C2×C3×D15semidirect
98. C3⋊(C5⋊D5)C2×C37⋊C3semidirect
99. C5×D15C2×C37⋊C3semidirect
104. C3×C5×D5C2×C37⋊C3semidirect
106. C3×C37C3×D52semidirect
108. C37⋊C3D5×D15direct (N × H)
119. C3×C52C22×C37⋊C3semidirect
129. C5×D5D3×C37⋊C3semidirect
133. C37C3×D5×D15semidirect
142. D15D5×C37⋊C3direct (N × H)
149. C3×D5D5×C37⋊C3semidirect
151. C52C2×D3×C37⋊C3semidirect
164. C3×C5C2×D5×C37⋊C3semidirect
165. C3×C5C2×D5×C37⋊C3semidirect
174. D5D15×C37⋊C3direct (N × H)
184. C5D3×D5×C37⋊C3semidirect
185. C5C2×D15×C37⋊C3semidirect
189. C3D52×C37⋊C3semidirect

Maximal subgroups

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

subgroupindex
C37⋊C3×C3⋊(C5⋊D5)2
C5×D15×C37⋊C32
C3×C5×D5×C37⋊C32
D5×D15×C373
D52×C37⋊C33
C2×D15×C37⋊C35
D3×D5×C37⋊C35
C3×D5×D1537