Finite Group Databasebeta

← C3×C5×D5×D51 #29505957

Subgroups — C3×C5×D5×D51 #29505957

Order 15300.

212 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 64 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×D255C211yesmaximal, characteristic, complemented
2C3×C52×D51C211yesmaximal, characteristic, complemented
3C32×C5×D5×C17C211yesmaximal, characteristic, complemented
4C5×D5×D51C311yesmaximal, characteristic, direct product factor
5C3×C5×D5×D17—31nomaximal
6C32×C52×C17C2211yescharacteristic, complemented, Hall
7C2×C3×C5×D51—51nomaximal
8C3×D5×D51C511yesmaximal, characteristic, direct product factor
9C5×D255C2×C311yescharacteristic, complemented
10C52×D51C2×C311yescharacteristic, complemented
11C3×C5×D85—31no—
12C3×C5×D5×C17—21no—
13C3×C5×D5×C17D311yescharacteristic, complemented
14C3×C5×D5×C17C2×C311yescharacteristic, complemented
15C3×C52×D17—31no—
16C5×D5×D17—31noHall
17C2×C32×C5×C17—51no—
18C3×D255C2×C511yescharacteristic, complemented
19C3×C5×D51—22no—
20C3×C5×D51—51no—
21C3×C5×D51D511yescharacteristic, direct product factor
22C3×C5×D51C2×C511yescharacteristic, complemented
23C32×D5×C17C2×C511yescharacteristic, complemented
24C3×C52×C17—21no—
25C3×C52×C17C2×D311yescharacteristic, complemented
26C3×C52×C17C22×C311yescharacteristic, complemented
27C2×C5×D51—51no—
28C2×C3×C5×D17—151no—
29D5×D51C3×C511yescharacteristic, direct product factor
30C3×D5×D17—31no—
31C3×C5×D3×D5—171nomaximal, Hall
32C5×D85—31no—
33C5×D5×C17C3×D311yescharacteristic, complemented
34C52×D17—31no—
35C32×C5×C17—22no—
36C32×C5×C17C2×D511yescharacteristic, complemented
37C32×C5×C17C22×C511yescharacteristic, complemented
38C2×C3×D51—51noHall
39C2×C3×C5×C17—51no—
40C2×C3×C5×C17—51no—
41C2×C3×C5×C17—101no—
42D255C2×C3×C511yescharacteristic, complemented
43C5×D51—22no—
44C5×D51—51no—
45C5×D51C3×D511yescharacteristic, direct product factor
46C5×D51C2×C3×C511yescharacteristic, complemented
47C3×D85—31no—
48C3×D5×C17—21no—
49C3×D5×C17C5×D311yescharacteristic, complemented
50C3×D5×C17C2×C3×C511yescharacteristic, complemented
51C3×C5×D17—31no—
52C3×C5×D17—31no—
53C3×C5×D17—62no—
54C3×C5×D17—151no—
55C3×C5×D15—171no—
56C3×C52×D3—171no—
57C32×C5×D5D1711yescharacteristic, complemented
58C52×C17C2×C3×D311yescharacteristic, complemented, Hall
59C2×C5×D17—151no—
60D5×D17—31no—
61C2×C32×C17—51no—
62C3×D51—51no—
63C3×D51C5×D511yescharacteristic, direct product factor
64C2×C3×C5×D5—511no—
65C5×D3×D5—171no—
66C3×C5×C17—21no—
67C3×C5×C17—21no—
68C3×C5×C17—22no—
69C3×C5×C17—22no—
70C3×C5×C17—42no—
71C3×C5×C17D3×D511yescharacteristic, complemented
72C3×C5×C17C2×C3×D511yescharacteristic, complemented
73C3×C5×C17C2×C5×D311yescharacteristic, complemented
74C3×C5×C17C22×C3×C511yescharacteristic, complemented
75C32×C52C2×D1711yescharacteristic, complemented, Hall
76C2×D51—51no—
77C2×C3×D17—151no—
78C2×C3×C5×D3—851no—
79C3×D3×D5—171no—
80C2×C5×C17—51no—
81D85—31no—
82C5×D17—31no—
83C5×D17—31no—
84C5×D17—62no—
85C5×D17—151no—
86D5×C17C3×C5×D311yescharacteristic, complemented
87C32×C17C2×C5×D511yescharacteristic, complemented, Hall
88C2×C3×C52—511no—
89C5×D15—171no—
90C52×D3—171no—
91C3×C5×D5—21no—
92C3×C5×D5—511no—
93C3×C5×D5C3×D1711yescharacteristic, complemented
94C3×C5×D5D5111yescharacteristic, direct product factor
95C2×C3×C17—51no—
96C2×C3×C17—51no—
97C2×C3×C17—101no—
98D51—51no—
99D51C3×C5×D511yescharacteristic, direct product factor
100C3×D17—31no—
101C3×D17—151no—
102C2×C5×D5—511noHall
103C2×C32×C5—51no—
104C3×D15—171no—
105C3×C5×D3—171no—
106C3×C5×D3—171no—
107C3×C5×D3—342no—
108C3×C5×D3—851no—
109C32×D5C5×D1711yescharacteristic, complemented
110C5×C17—22no—
111C5×C17C3×D3×D511yescharacteristic, complemented
112C5×C17C2×C3×C5×D311yescharacteristic, complemented
113C3×C52—21no—
114C3×C52C2×C3×D1711yescharacteristic, complemented
115C3×C52C2×D5111yescharacteristic, complemented
116C2×D17—151noHall
117C22×C3×C5—2551no—
118C2×C5×D3—851no—
119C2×C3×D5—511no—
120D3×D5—171no—
121C3×C17—21no—
122C3×C17C5×D3×D511yescharacteristic, complemented
123C3×C17C2×C3×C5×D511yescharacteristic, complemented
124C2×C52—511no—
125C5×D5—511no—
126C5×D5C3×D5111yescharacteristic, direct product factor
127C32×C5—22no—
128C32×C5D5×D1711yescharacteristic, complemented
129C32×C5C2×C5×D1711yescharacteristic, complemented
130C2×C3×D3—851noHall
131C2×C17—51no—
132D17—31no—
133D17—151no—
134C2×C3×C5—51no—
135C2×C3×C5—51no—
136C2×C3×C5—101no—
137C2×C3×C5—511no—
138C2×C3×C5—511no—
139C2×C3×C5—1022no—
140C2×C3×C5—2551no—
141D15—171no—
142C3×D5—21no—
143C3×D5—511no—
144C3×D5C3×C5×D1711yescharacteristic, complemented
145C3×D5C5×D5111yescharacteristic, direct product factor
146C5×D3—171no—
147C5×D3—171no—
148C5×D3—342no—
149C5×D3—851no—
150C52C2×C3×D5111yescharacteristic, complemented, Sylow
151C22×C5—2551no—
152C2×D5—511no—
153C2×C32—51no—
154C3×D3—171no—
155C3×D3—851no—
156C17C3×C5×D3×D511yescharacteristic, complemented, Sylow
157C3×C5—21no—
158C3×C5—21no—
159C3×C5—22no—
160C3×C5—22no—
161C3×C5—42no—
162C3×C5C3×D5×D1711yescharacteristic, complemented
163C3×C5D5×D5111yescharacteristic, direct product factor
164C3×C5C2×C3×C5×D1711yescharacteristic, complemented
165C3×C5C2×C5×D5111yescharacteristic, complemented
166C22×C3—2551no—
167C2×D3—851no—
168C2×C5—51no—
169C2×C5—511no—
170C2×C5—511no—
171C2×C5—1022no—
172C2×C5—2551no—
173D5—511no—
174D5C3×C5×D5111yescharacteristic, direct product factor
175C32C5×D5×D1711yescharacteristic, complemented, Sylow
176C2×C3—51no—
177C2×C3—51no—
178C2×C3—101no—
179C2×C3—511no—
180C2×C3—2551no—
181D3—171no—
182D3—851no—
183C5—22no—
184C5C3×D5×D5111yescharacteristic, direct product factor
185C5C2×C3×C5×D5111yescharacteristic, complemented
186C22—2551noSylow
187C3—21no—
188C3C3×C5×D5×D1711yescharacteristic, complemented
189C3C5×D5×D5111yescharacteristic, direct product factor
190C2—51no—
191C2—511no—
192C2—2551no—
subgroupG/H
center, hypercenterC3×C5D5×D51
commutator, cosocle, hypocenterC3×C5×C17C22×C3×C5
FrattiniC1G
Fitting, socleC32×C52×C17C22
LCSG ▷ C3×C5×C17
UCSC1 ◁ C3×C5

Complements

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

NH ≅ G/Ntype
1. C3×C5×D255C2semidirect
2. C3×C52×D51C2semidirect
3. C32×C5×D5×C17C2semidirect
4. C5×D5×D51C3direct (N × H)
6. C32×C52×C17C22semidirect
8. C3×D5×D51C5direct (N × H)
9. C5×D255C2×C3semidirect
10. C52×D51C2×C3semidirect
13. C3×C5×D5×C17D3semidirect
14. C3×C5×D5×C17C2×C3semidirect
18. C3×D255C2×C5semidirect
21. C3×C5×D51D5direct (N × H)
22. C3×C5×D51C2×C5semidirect
23. C32×D5×C17C2×C5semidirect
25. C3×C52×C17C2×D3semidirect
26. C3×C52×C17C22×C3semidirect
29. D5×D51C3×C5direct (N × H)
33. C5×D5×C17C3×D3semidirect
36. C32×C5×C17C2×D5semidirect
37. C32×C5×C17C22×C5semidirect
42. D255C2×C3×C5semidirect
45. C5×D51C3×D5direct (N × H)
46. C5×D51C2×C3×C5semidirect
49. C3×D5×C17C5×D3semidirect
50. C3×D5×C17C2×C3×C5semidirect
57. C32×C5×D5D17semidirect
58. C52×C17C2×C3×D3semidirect
63. C3×D51C5×D5direct (N × H)
71. C3×C5×C17D3×D5semidirect
72. C3×C5×C17C2×C3×D5semidirect
73. C3×C5×C17C2×C5×D3semidirect
74. C3×C5×C17C22×C3×C5semidirect
75. C32×C52C2×D17semidirect
86. D5×C17C3×C5×D3semidirect
87. C32×C17C2×C5×D5semidirect
93. C3×C5×D5C3×D17semidirect
94. C3×C5×D5D51direct (N × H)
99. D51C3×C5×D5direct (N × H)
109. C32×D5C5×D17semidirect
111. C5×C17C3×D3×D5semidirect
112. C5×C17C2×C3×C5×D3semidirect
114. C3×C52C2×C3×D17semidirect
115. C3×C52C2×D51semidirect
122. C3×C17C5×D3×D5semidirect
123. C3×C17C2×C3×C5×D5semidirect
126. C5×D5C3×D51direct (N × H)
128. C32×C5D5×D17semidirect
129. C32×C5C2×C5×D17semidirect
144. C3×D5C3×C5×D17semidirect
145. C3×D5C5×D51direct (N × H)
150. C52C2×C3×D51semidirect
156. C17C3×C5×D3×D5semidirect
162. C3×C5C3×D5×D17semidirect
163. C3×C5D5×D51direct (N × H)
164. C3×C5C2×C3×C5×D17semidirect
165. C3×C5C2×C5×D51semidirect
174. D5C3×C5×D51direct (N × H)
175. C32C5×D5×D17semidirect
184. C5C3×D5×D51direct (N × H)
185. C5C2×C3×C5×D51semidirect
188. C3C3×C5×D5×D17semidirect
189. C3C5×D5×D51direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×D2552
C3×C52×D512
C32×C5×D5×C172
C5×D5×D513
C3×C5×D5×D173
C2×C3×C5×D515
C3×D5×D515
C3×C5×D3×D517