Finite Group Databasebeta

← D15×D255 #29506038

Subgroups — D15×D255 #29506038

Order 15300.

224 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 46 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⋊(C3⋊(C5⋊D85))C211yesmaximal, characteristic, complemented
2C3×C5×D255C211yesmaximal, characteristic, complemented
3C3×C5×C17×D15C211yesmaximal, characteristic, complemented
4D15×D85—31nomaximal
5D5×D255—31nomaximal
6C32×C52×C17C2211yescharacteristic, complemented, Hall
7D15×D51—51nomaximal
8D3×D255—51nomaximal
9C3⋊(C5⋊D85)—31no—
10C3⋊(C5⋊D85)—31no—
11C3⋊(C5⋊D85)—61no—
12C5×D255D311yescharacteristic, complemented
13C5×C17×D15D311yescharacteristic, complemented
14C3×C5×D85—31no—
15C3×C5×D5×C17—31no—
16D5×D85—91noHall
17C3⋊D255—51no—
18C3⋊D255—51no—
19C3⋊D255—102no—
20C3×D255D511yescharacteristic, complemented
21C3×C17×D15D511yescharacteristic, 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×D255—151no—
28D3×D85—151no—
29D5×D51—151no—
30D15×D17—151no—
31D152—171nomaximal, Hall
32C5⋊D85—91no—
33C5×D85—31no—
34C5×D5×C17—31no—
35C32×C5×C17—22no—
36C32×C5×C17C2×D511yescharacteristic, complemented
37C32×C5×C17C2×D511yescharacteristic, complemented
38D3×D51—251noHall
39C2×C3×C5×C17—151no—
40D255—151no—
41D255—151no—
42D255—151no—
43D255—151no—
44D255—302no—
45D255—302no—
46D255—301no—
47D255—301no—
48D255—304no—
49D255D1511yescharacteristic, direct product factor
50C17×D15D1511yescharacteristic, complemented
51C5×D51—51no—
52C5×D3×C17—51no—
53C3×D85—31no—
54C3×D5×C17—31no—
55C3×C5×D17—151no—
56C3⋊(C3⋊(C5⋊D5))—171no—
57C3×C5×D15—171no—
58C3×C5×D15D1711yescharacteristic, complemented
59C52×C17D3211yescharacteristic, complemented, Hall
60C2×D85—451no—
61D5×D17—451no—
62C3⋊D51—251no—
63C3×D51—51no—
64C3×D3×C17—51no—
65D5×D15—511no—
66D5×D15—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×D1511yescharacteristic, complemented
75C3×C5×C17C2×D1511yescharacteristic, complemented
76C32×C52C2×D1711yescharacteristic, complemented, Hall
77C2×D51—751no—
78D3×D17—751no—
79D3×D15—851no—
80D3×D15—851no—
81C2×C5×C17—151no—
82D85—31no—
83D85—451no—
84D85—451no—
85D85—902no—
86C5×D17—151no—
87D5×C17—31no—
88C32×C17D5211yescharacteristic, complemented, Hall
89C3⋊(C5⋊D5)—511no—
90C3⋊(C5⋊D5)—511no—
91C3⋊(C5⋊D5)—1021no—
92C5×D15—171no—
93C5×D15D5111yescharacteristic, complemented
94C3×C5×D5—31no—
95C3×C5×D5—511no—
96C2×C3×C17—151no—
97D51—51no—
98D51—751no—
99D51—751no—
100D51—1501no—
101C3×D17—151no—
102D3×C17—51no—
103D52—1531noHall
104C3⋊D15—851no—
105C3⋊D15—851no—
106C3⋊D15—1702no—
107C3×D15—171no—
108C3×D15D8511yescharacteristic, complemented
109C3×C5×D3—51no—
110C3×C5×D3—851no—
111C5×C17—22no—
112C5×C17D3×D1511yescharacteristic, complemented
113C5×C17D3×D1511yescharacteristic, complemented
114C3×C52—21no—
115C3×C52D3×D1711yescharacteristic, complemented
116C3×C52C2×D5111yescharacteristic, complemented
117C2×D17—2251noHall
118C2×D15—2551no—
119C2×D15—2551no—
120D3×D5—2551no—
121D3×D5—2551no—
122C3×C17—21no—
123C3×C17D5×D1511yescharacteristic, complemented
124C3×C17D5×D1511yescharacteristic, complemented
125C5⋊D5—1531no—
126C5×D5—31no—
127C5×D5—511no—
128C32×C5—22no—
129C32×C5D5×D1711yescharacteristic, complemented
130C32×C5C2×D8511yescharacteristic, complemented
131D32—4251noHall
132C2×C17—151no—
133D17—151no—
134D17—2251no—
135C2×C3×C5—151no—
136C2×C3×C5—2551no—
137D15—171no—
138D15—5104no—
139D15—5101no—
140D15—5101no—
141D15—5102no—
142D15—5102no—
143D15—2551no—
144D15—2551no—
145D15—2551no—
146D15—2551no—
147D15D25511yescharacteristic, direct product factor
148C3×D5—31no—
149C3×D5—511no—
150C5×D3—51no—
151C5×D3—851no—
152C52D3×D5111yescharacteristic, complemented, Sylow
153C2×D5—7651no—
154C2×D5—7651no—
155C3⋊D3—4251no—
156C3×D3—51no—
157C3×D3—851no—
158C17D15211yescharacteristic, complemented, Sylow
159C3×C5—24no—
160C3×C5—21no—
161C3×C5—21no—
162C3×C5—22no—
163C3×C5—22no—
164C3×C5D15×D1711yescharacteristic, complemented
165C3×C5D5×D5111yescharacteristic, complemented
166C3×C5D3×D8511yescharacteristic, complemented
167C3×C5C2×D25511yescharacteristic, complemented
168C2×D3—12751no—
169C2×D3—12751no—
170C2×C5—151no—
171C2×C5—2551no—
172D5—31no—
173D5—511no—
174D5—15302no—
175D5—7651no—
176D5—7651no—
177C32D5×D8511yescharacteristic, complemented, Sylow
178C2×C3—151no—
179C2×C3—2551no—
180D3—51no—
181D3—851no—
182D3—25501no—
183D3—12751no—
184D3—12751no—
185C5—22no—
186C5D3×D25511yescharacteristic, complemented
187C5D15×D5111yescharacteristic, complemented
188C22—38251noSylow
189C3—21no—
190C3D5×D25511yescharacteristic, complemented
191C3D15×D8511yescharacteristic, complemented
192C2—151no—
193C2—38251no—
194C2—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. C3⋊(C3⋊(C5⋊D85))C2semidirect
2. C3×C5×D255C2semidirect
3. C3×C5×C17×D15C2semidirect
6. C32×C52×C17C22semidirect
12. C5×D255D3semidirect
13. C5×C17×D15D3semidirect
20. C3×D255D5semidirect
21. C3×C17×D15D5semidirect
25. C3×C52×C17C2×D3semidirect
26. C3×C52×C17C2×D3semidirect
36. C32×C5×C17C2×D5semidirect
37. C32×C5×C17C2×D5semidirect
49. D255D15direct (N × H)
50. C17×D15D15semidirect
58. C3×C5×D15D17semidirect
59. C52×C17D32semidirect
72. C3×C5×C17D3×D5semidirect
73. C3×C5×C17D3×D5semidirect
74. C3×C5×C17C2×D15semidirect
75. C3×C5×C17C2×D15semidirect
76. C32×C52C2×D17semidirect
88. C32×C17D52semidirect
93. C5×D15D51semidirect
108. C3×D15D85semidirect
112. C5×C17D3×D15semidirect
113. C5×C17D3×D15semidirect
115. C3×C52D3×D17semidirect
116. C3×C52C2×D51semidirect
123. C3×C17D5×D15semidirect
124. C3×C17D5×D15semidirect
129. C32×C5D5×D17semidirect
130. C32×C5C2×D85semidirect
147. D15D255direct (N × H)
152. C52D3×D51semidirect
158. C17D152semidirect
164. C3×C5D15×D17semidirect
165. C3×C5D5×D51semidirect
166. C3×C5D3×D85semidirect
167. C3×C5C2×D255semidirect
177. C32D5×D85semidirect
186. C5D3×D255semidirect
187. C5D15×D51semidirect
190. C3D5×D255semidirect
191. C3D15×D85semidirect

Maximal subgroups

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

subgroupindex
C3⋊(C3⋊(C5⋊D85))2
C3×C5×D2552
C3×C5×C17×D152
D15×D853
D5×D2553
D15×D515
D3×D2555
D15217