Finite Group Databasebeta

← #29506043

Subgroups — #29506043

Order 15300.

212 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 43 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
1C5×C3⋊D255C211yesmaximal, characteristic, complemented
2C3×C17×C3⋊(C5⋊D5)C211yesmaximal, characteristic, complemented
3C3×C5×D255C211yesmaximal, characteristic, complemented
4#19099830—31nomaximal
5D85⋊D15—31nomaximal
6C32×C52×C17C2211yescharacteristic, complemented, Hall
7D15⋊D51—51nomaximal
8D15×D51—51nomaximal
9C17×C3⋊(C5⋊D5)D311yescharacteristic, complemented
10C5×D255—31no—
11C5×D255—31no—
12C5×D255—61no—
13C5×D255D311yescharacteristic, complemented
14C3×C17×C5⋊D5—31no—
15C3×C5×D85—31no—
16(C5⋊D5)⋊D17—91noHall
17C3⋊D255D511yescharacteristic, complemented
18C5×C3⋊D51—51no—
19C3×D255D511yescharacteristic, complemented
20C3×C17×D15—51no—
21C3×C17×D15—51no—
22C3×C17×D15—102no—
23C3×C5×D51—51no—
24C3×C52×C17—21no—
25C3×C52×C17C2×D311yescharacteristic, complemented
26C3×C52×C17C2×D311yescharacteristic, complemented
27D15⋊D17—151no—
28D5×D51—151no—
29D5×D51—151no—
30D15×D17—151no—
31D15⋊D15—171nomaximal, Hall
32C17×C5⋊D5—31no—
33C5×D85—31no—
34C5×D85—91no—
35C32×C5×C17—22no—
36C32×C5×C17C2×D511yescharacteristic, complemented
37C32×C5×C17C2×D511yescharacteristic, complemented
38D3×D51—251noHall
39D255—31no—
40D255—31no—
41D255—61no—
42D255D1511yescharacteristic, complemented
43C17×D15—51no—
44C17×D15—51no—
45C17×D15—102no—
46C5×D51—51no—
47C5×D51—151no—
48C5×D51—151no—
49C5×D51—301no—
50C3×D85—31no—
51C3×D5×C17—151no—
52C3×D5×C17—151no—
53C3×D5×C17—302no—
54C3×C5×D17—151no—
55C5×C3⋊D15—171no—
56C3×C3⋊(C5⋊D5)D1711yescharacteristic, complemented
57C3×C5×D15—171no—
58C52×C17D3211yescharacteristic, complemented, Hall
59D5×D17—451no—
60D5×D17—451no—
61C3⋊D51—51no—
62C3×D51—51no—
63C3×D3×C17—251no—
64D15⋊D5—511no—
65D5×D15—511no—
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×C17D3×D511yescharacteristic, complemented
73C3×C5×C17D3×D511yescharacteristic, complemented
74C3×C5×C17C2×D1511yescharacteristic, complemented
75C32×C52C2×D1711yescharacteristic, complemented, Hall
76C2×D51—751no—
77D3×D17—751no—
78(C3⋊D3)⋊D5—851no—
79D3×D15—851no—
80D85—31no—
81D85—91no—
82C5×D17—151no—
83C5×D17—451no—
84D5×C17—151no—
85D5×C17—151no—
86D5×C17—302no—
87C32×C17D5211yescharacteristic, complemented, Hall
88C3⋊(C5⋊D5)D5111yescharacteristic, complemented
89C5×D15—171no—
90C5×D15—511no—
91C5×D15—511no—
92C5×D15—1021no—
93C3×C5⋊D5—31no—
94C3×C5×D5—511no—
95C2×C3×C17—751no—
96D51—51no—
97D51—151no—
98D51—151no—
99D51—301no—
100C3×D17—151no—
101D3×C17—251no—
102D52—1531noHall
103C3⋊D15—171no—
104C5×C3⋊D3—851no—
105C3×D15—51no—
106C3×D15—51no—
107C3×D15—102no—
108C3×D15—171no—
109C3×C5×D3—851no—
110C5×C17—22no—
111C5×C17D3×D1511yescharacteristic, complemented
112C5×C17(C3⋊D3)⋊D511yescharacteristic, complemented
113C3×C52—21no—
114C3×C52D3×D1711yescharacteristic, complemented
115C3×C52C2×D5111yescharacteristic, complemented
116C2×D17—2251noHall
117C2×D15—2551no—
118D3×D5—2551no—
119D3×D5—2551no—
120D3×D5—2551no—
121C3×C17—21no—
122C3×C17D5×D1511yescharacteristic, complemented
123C3×C17D15⋊D511yescharacteristic, complemented
124C5⋊D5—31no—
125C5×D5—511no—
126C5×D5—1531no—
127C32×C5—22no—
128C32×C5D5×D1711yescharacteristic, complemented
129C32×C5D5×D1711yescharacteristic, complemented
130D32—4251noHall
131C2×C17—751no—
132D17—151no—
133D17—451no—
134C2×C3×C5—2551no—
135D15—51no—
136D15—51no—
137D15—102no—
138D15—171no—
139D15—511no—
140D15—511no—
141D15—1021no—
142C3×D5—151no—
143C3×D5—151no—
144C3×D5—302no—
145C3×D5—511no—
146C5×D3—851no—
147C5×D3—5101no—
148C5×D3—2551no—
149C5×D3—2551no—
150C52D3×D5111yescharacteristic, complemented, Sylow
151C2×D5—7651no—
152C2×D5—7651no—
153C3⋊D3—851no—
154C3×D3—251no—
155C3×D3—851no—
156C17D15⋊D1511yescharacteristic, complemented, Sylow
157C3×C5—21no—
158C3×C5—21no—
159C3×C5—22no—
160C3×C5—22no—
161C3×C5—42no—
162C3×C5D15×D1711yescharacteristic, complemented
163C3×C5D5×D5111yescharacteristic, complemented
164C3×C5D5×D5111yescharacteristic, complemented
165C3×C5D15⋊D1711yescharacteristic, complemented
166C2×D3—12751no—
167C2×D3—12751no—
168C2×C5—7651no—
169C2×C5—2551no—
170D5—151no—
171D5—151no—
172D5—302no—
173D5—511no—
174D5—1531no—
175C32(C5⋊D5)⋊D1711yescharacteristic, complemented, Sylow
176C2×C3—751no—
177C2×C3—2551no—
178D3—251no—
179D3—851no—
180D3—5101no—
181D3—2551no—
182D3—2551no—
183C5—22no—
184C5D15×D5111yescharacteristic, complemented
185C5D15⋊D5111yescharacteristic, complemented
186C22—38251noSylow
187C3—21no—
188C3D85⋊D1511yescharacteristic, complemented
189C3#1909983011yescharacteristic, complemented
190C2—751no—
191C2—7651no—
192C2—2551no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C52×C17C22
LCSG ▷ C32×C52×C17
UCSC1

Complements

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

NH ≅ G/Ntype
1. C5×C3⋊D255C2semidirect
2. C3×C17×C3⋊(C5⋊D5)C2semidirect
3. C3×C5×D255C2semidirect
6. C32×C52×C17C22semidirect
9. C17×C3⋊(C5⋊D5)D3semidirect
13. C5×D255D3semidirect
17. C3⋊D255D5semidirect
19. C3×D255D5semidirect
25. C3×C52×C17C2×D3semidirect
26. C3×C52×C17C2×D3semidirect
36. C32×C5×C17C2×D5semidirect
37. C32×C5×C17C2×D5semidirect
42. D255D15semidirect
56. C3×C3⋊(C5⋊D5)D17semidirect
58. C52×C17D32semidirect
71. C3×C5×C17D3×D5semidirect
72. C3×C5×C17D3×D5semidirect
73. C3×C5×C17D3×D5semidirect
74. C3×C5×C17C2×D15semidirect
75. C32×C52C2×D17semidirect
87. C32×C17D52semidirect
88. C3⋊(C5⋊D5)D51semidirect
111. C5×C17D3×D15semidirect
112. C5×C17(C3⋊D3)⋊D5semidirect
114. C3×C52D3×D17semidirect
115. C3×C52C2×D51semidirect
122. C3×C17D5×D15semidirect
123. C3×C17D15⋊D5semidirect
128. C32×C5D5×D17semidirect
129. C32×C5D5×D17semidirect
150. C52D3×D51semidirect
156. C17D15⋊D15semidirect
162. C3×C5D15×D17semidirect
163. C3×C5D5×D51semidirect
164. C3×C5D5×D51semidirect
165. C3×C5D15⋊D17semidirect
175. C32(C5⋊D5)⋊D17semidirect
184. C5D15×D51semidirect
185. C5D15⋊D51semidirect
188. C3D85⋊D15semidirect
189. C3#19099830semidirect

Maximal subgroups

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

subgroupindex
C5×C3⋊D2552
C3×C17×C3⋊(C5⋊D5)2
C3×C5×D2552
#190998303
D85⋊D153
D15⋊D515
D15×D515
D15⋊D1517