Finite Group Databasebeta

← C5×D15⋊D51 #29506028

Subgroups — C5×D15⋊D51 #29506028

Order 15300.

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

normal subgroups only

This group has 224 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
1C52×C3⋊D51C211yesmaximal, characteristic, complemented
2C3×C5×D255C211yesmaximal, characteristic, complemented
3C3×C5×C17×D15C211yesmaximal, characteristic, complemented
4C5×D15⋊D17—31nomaximal
5C5×D5×D51—31nomaximal
6C32×C52×C17C2211yescharacteristic, complemented, Hall
7D15⋊D51C511yesmaximal, characteristic, direct product factor
8C5×D3×D51—51nomaximal
9C5×D255D311yescharacteristic, complemented
10C5×C17×D15D311yescharacteristic, complemented
11C52×D51—31no—
12C52×D51—31no—
13C52×D51—61no—
14C3×C5×D85—31no—
15C3×C5×D5×C17—31no—
16C5×D5×D17—91noHall
17C5×C3⋊D51—22no—
18C5×C3⋊D51D511yescharacteristic, complemented
19C5×C3⋊D51C2×C511yescharacteristic, complemented
20C3×D255C2×C511yescharacteristic, complemented
21C3×C17×D15C2×C511yescharacteristic, complemented
22C3×C5×D51—51no—
23C3×C5×D3×C17—51no—
24C3×C52×C17—21no—
25C3×C52×C17C2×D311yescharacteristic, complemented
26C3×C52×C17C2×D311yescharacteristic, complemented
27C2×C5×D51—151no—
28D15⋊D17—31no—
29D5×D51—31no—
30C5×D3×D17—151no—
31C5×(C3⋊D3)⋊D5—171nomaximal, Hall
32C5×D85—31no—
33C5×D5×C17—31no—
34C52×D17—91no—
35C32×C5×C17—22no—
36C32×C5×C17C2×D511yescharacteristic, complemented
37C32×C5×C17C22×C511yescharacteristic, complemented
38D3×D51—51noHall
39C2×C3×C5×C17—151no—
40D255C5×D311yescharacteristic, complemented
41C17×D15C5×D311yescharacteristic, complemented
42C5×D51—31no—
43C5×D51—31no—
44C5×D51—31no—
45C5×D51—31no—
46C5×D51—51no—
47C5×D51—62no—
48C5×D51—62no—
49C5×D51—61no—
50C5×D51—61no—
51C5×D51—64no—
52C5×D3×C17—51no—
53C3×D85—31no—
54C3×D5×C17—31no—
55C3×C5×D17—151no—
56C52×C3⋊D3—171no—
57C3×C5×D15—171no—
58C3×C5×D15D1711yescharacteristic, complemented
59C52×C17D3211yescharacteristic, complemented, Hall
60C2×C5×D17—451no—
61D5×D17—91no—
62C3⋊D51C5×D511yescharacteristic, complemented
63C3×D51—51no—
64C3×D3×C17—51no—
65C5×D3×D5—511no—
66C5×D3×D5—511no—
67C3×C5×C17—24no—
68C3×C5×C17—21no—
69C3×C5×C17—21no—
70C3×C5×C17—22no—
71C3×C5×C17—22no—
72C3×C5×C17D3×D511yescharacteristic, complemented
73C3×C5×C17D3×D511yescharacteristic, complemented
74C3×C5×C17C2×C5×D311yescharacteristic, complemented
75C3×C5×C17C2×C5×D311yescharacteristic, complemented
76C32×C52C2×D1711yescharacteristic, complemented, Hall
77C2×D51—151no—
78D3×D17—151no—
79(C3⋊D3)⋊D5—171no—
80C5×D32—851no—
81C2×C5×C17—151no—
82D85—31no—
83C5×D17—91no—
84C5×D17—91no—
85C5×D17—151no—
86C5×D17—182no—
87D5×C17—31no—
88C32×C17C2×C5×D511yescharacteristic, complemented, Hall
89C5×D15—171no—
90C5×D15D5111yescharacteristic, complemented
91C52×D3—511no—
92C52×D3—511no—
93C52×D3—1021no—
94C3×C5×D5—31no—
95C3×C5×D5—511no—
96C2×C3×C17—151no—
97D51—31no—
98D51—31no—
99D51—51no—
100D51—61no—
101C3×D17—151no—
102D3×C17—51no—
103C2×C5×D5—1531noHall
104C5×C3⋊D3—171no—
105C5×C3⋊D3—171no—
106C5×C3⋊D3—342no—
107C3×D15—171no—
108C3×D15C5×D1711yescharacteristic, complemented
109C3×C5×D3—51no—
110C3×C5×D3—851no—
111C5×C17—22no—
112C5×C17C5×D3211yescharacteristic, complemented
113C5×C17(C3⋊D3)⋊D511yescharacteristic, complemented
114C3×C52—21no—
115C3×C52D3×D1711yescharacteristic, complemented
116C3×C52C2×D5111yescharacteristic, complemented
117C2×D17—451noHall
118C2×C5×D3—2551no—
119C2×C5×D3—2551no—
120D3×D5—511no—
121D3×D5—511no—
122C3×C17—21no—
123C3×C17C5×D3×D511yescharacteristic, complemented
124C3×C17C5×D3×D511yescharacteristic, complemented
125C2×C52—1531no—
126C5×D5—31no—
127C5×D5—511no—
128C32×C5—22no—
129C32×C5D5×D1711yescharacteristic, complemented
130C32×C5C2×C5×D1711yescharacteristic, complemented
131D32—851noHall
132C2×C17—151no—
133D17—91no—
134D17—151no—
135C2×C3×C5—151no—
136C2×C3×C5—2551no—
137D15—171no—
138D15C5×D5111yescharacteristic, complemented
139C3×D5—31no—
140C3×D5—511no—
141C5×D3—51no—
142C5×D3—511no—
143C5×D3—511no—
144C5×D3—511no—
145C5×D3—511no—
146C5×D3—851no—
147C5×D3—1022no—
148C5×D3—1022no—
149C5×D3—1024no—
150C5×D3—1021no—
151C5×D3—1021no—
152C52D3×D5111yescharacteristic, complemented, Sylow
153C22×C5—7651no—
154C2×D5—1531no—
155C3⋊D3—171no—
156C3×D3—51no—
157C3×D3—851no—
158C17C5×(C3⋊D3)⋊D511yescharacteristic, complemented, Sylow
159C3×C5—24no—
160C3×C5—21no—
161C3×C5—21no—
162C3×C5—22no—
163C3×C5—22no—
164C3×C5C5×D3×D1711yescharacteristic, complemented
165C3×C5D5×D5111yescharacteristic, complemented
166C3×C5D15⋊D1711yescharacteristic, complemented
167C3×C5C2×C5×D5111yescharacteristic, complemented
168C2×D3—2551no—
169C2×D3—2551no—
170C2×C5—151no—
171C2×C5—3062no—
172C2×C5—1531no—
173C2×C5—1531no—
174C2×C5—2551no—
175D5—31no—
176D5—511no—
177C32C5×D5×D1711yescharacteristic, complemented, Sylow
178C2×C3—151no—
179C2×C3—2551no—
180D3—51no—
181D3—511no—
182D3—511no—
183D3—851no—
184D3—1021no—
185C5—22no—
186C5C5×D3×D5111yescharacteristic, complemented
187C5D15⋊D5111yescharacteristic, direct product factor
188C22—7651noSylow
189C3—21no—
190C3C5×D5×D5111yescharacteristic, complemented
191C3C5×D15⋊D1711yescharacteristic, complemented
192C2—151no—
193C2—1531no—
194C2—2551no—
subgroupG/H
center, hypercenterC5D15⋊D51
commutator, cosocle, hypocenterC32×C5×C17C22×C5
FrattiniC1G
Fitting, socleC32×C52×C17C22
LCSG ▷ C32×C5×C17
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
1. C52×C3⋊D51C2semidirect
2. C3×C5×D255C2semidirect
3. C3×C5×C17×D15C2semidirect
6. C32×C52×C17C22semidirect
7. D15⋊D51C5direct (N × H)
9. C5×D255D3semidirect
10. C5×C17×D15D3semidirect
18. C5×C3⋊D51D5semidirect
19. C5×C3⋊D51C2×C5semidirect
20. C3×D255C2×C5semidirect
21. C3×C17×D15C2×C5semidirect
25. C3×C52×C17C2×D3semidirect
26. C3×C52×C17C2×D3semidirect
36. C32×C5×C17C2×D5semidirect
37. C32×C5×C17C22×C5semidirect
40. D255C5×D3semidirect
41. C17×D15C5×D3semidirect
58. C3×C5×D15D17semidirect
59. C52×C17D32semidirect
62. C3⋊D51C5×D5semidirect
72. C3×C5×C17D3×D5semidirect
73. C3×C5×C17D3×D5semidirect
74. C3×C5×C17C2×C5×D3semidirect
75. C3×C5×C17C2×C5×D3semidirect
76. C32×C52C2×D17semidirect
88. C32×C17C2×C5×D5semidirect
90. C5×D15D51semidirect
108. C3×D15C5×D17semidirect
112. C5×C17C5×D32semidirect
113. C5×C17(C3⋊D3)⋊D5semidirect
115. C3×C52D3×D17semidirect
116. C3×C52C2×D51semidirect
123. C3×C17C5×D3×D5semidirect
124. C3×C17C5×D3×D5semidirect
129. C32×C5D5×D17semidirect
130. C32×C5C2×C5×D17semidirect
138. D15C5×D51semidirect
152. C52D3×D51semidirect
158. C17C5×(C3⋊D3)⋊D5semidirect
164. C3×C5C5×D3×D17semidirect
165. C3×C5D5×D51semidirect
166. C3×C5D15⋊D17semidirect
167. C3×C5C2×C5×D51semidirect
177. C32C5×D5×D17semidirect
186. C5C5×D3×D51semidirect
187. C5D15⋊D51direct (N × H)
190. C3C5×D5×D51semidirect
191. C3C5×D15⋊D17semidirect

Maximal subgroups

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

subgroupindex
C52×C3⋊D512
C3×C5×D2552
C3×C5×C17×D152
C5×D15⋊D173
C5×D5×D513
D15⋊D515
C5×D3×D515
C5×(C3⋊D3)⋊D517