Finite Group Databasebeta

← #13089274

Subgroups — #13089274

Order 1440.

996 conjugacy classes of subgroups; only the 200 normal subgroups are shown.

normal subgroups only

This group has 996 conjugacy classes of subgroups — too many to draw. Only its 200 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
1#10624283C211yesmaximal, characteristic, complemented
2C5×#3828C211yesmaximal, characteristic, complemented
3C2×C32×D20C211yesmaximal, characteristic, complemented
4D5×#638C214yesmaximal, complemented
5#10624160C212yesmaximal, complemented
6C3⋊D3×D20C212yesmaximal, complemented
7#10624149C212yesmaximal, complemented
8#10624148C212yesmaximal, complemented
9#92017—34nomaximal
10C22×C32×D5C2212yescomplemented
11C2×D5×C3⋊D3C2214yescomplemented
12C2×C32×C4×C5C2211yescharacteristic, complemented
13#67184C2212yescomplemented
14C4⋊(C3⋊D15)C2211yescharacteristic, complemented
15C4×C3⋊D15C2212yescomplemented
16#67180C2211yescharacteristic, complemented
17C5×#638C2212yescomplemented
18C5×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
19C4×C5×C3⋊D3C2212yescomplemented
20C5×#634C2211yescharacteristic, complemented
21C32×D20C2212yescomplemented
22C32×D20C2212yescomplemented
23#67139C2214yescomplemented
24#67138C2214yescomplemented
25D5×C3⋊Dic3C2214yescomplemented
26#64361—51nomaximal, Hall
27#6817—34no—
28C5×#235—34no—
29C2×C3×D20D314yescomplemented
30D5×#67—316no—
31#6777—38no—
32D3×D20—38no—
33#6766—38no—
34#6765—38no—
35C22×C32×C5C2311yescharacteristic
36C2×C3⋊D15C2312yes—
37C2×C5×C3⋊D3C2312yes—
38C2×C32×D5—42no—
39C2×C32×D5C2314yes—
40D5×C3⋊D3—44no—
41C32×C4×C5C2311yescharacteristic
42C32×C4×C5C2311yescharacteristic
43C3⋊Dic15C2312yes—
44C5×C3⋊Dic3C2312yes—
45#4149—91noHall
46C2×C32×D4—51no—
47C2×#638—54no—
48#3830—52no—
49#3830—52no—
50D4×C3⋊D3—52no—
51D4×C3⋊D3—52no—
52#3828—51no—
53#3828D511yescharacteristic, complemented
54C22×C3×D5C2×D318yescomplemented
55C2×D3×D5—316no—
56C2×C3×C4×C5C2×D314yescomplemented
57#1220—38no—
58D60—34no—
59C4×D15—38no—
60Dic30—34no—
61C5×#67—38no—
62C5×D12—34no—
63C4×C5×D3—38no—
64C5×Dic6—34no—
65C3×D20C2×D318yescomplemented
66C3×D20C2×D318yescomplemented
67#1202—316no—
68#1201—316no—
69D5×Dic3—316no—
70#1004—154no—
71C2×C32×C5—21no—
72C2×C32×C5C2411yescharacteristic
73C3⋊D15—22no—
74C5×C3⋊D3—22no—
75C32×D5—24no—
76C5×#41—91no—
77#713—92no—
78D4×D5—94no—
79D4×D5—92no—
80#709—91no—
81#709—92no—
82C2×D20—92no—
83C2×D20C3⋊D311yescharacteristic, complemented
84C23×C32—52no—
85C22×C3⋊D3—54no—
86C32×D4—52no—
87C32×D4—52no—
88C2×C32×C4C2×D511yescharacteristic, complemented
89#638—52no—
90#638—54no—
91#638—54no—
92#638C2×D512yescomplemented
93C2×C3⋊Dic3—54no—
94C4⋊(C3⋊D3)—51no—
95C4⋊(C3⋊D3)C2×D511yescharacteristic, complemented
96C4×C3⋊D3—52no—
97C4×C3⋊D3C2×D512yescomplemented
98#634—51no—
99#634C2×D511yescharacteristic, complemented
100C22×C3×C5C22×D314yes—
101C2×D15—38no—
102C2×C5×D3—38no—
103C2×C3×D5—48no—
104C2×C3×D5C22×D3116yes—
105D3×D5—1216no—
106C3×C4×C5C22×D314yes—
107C3×C4×C5C22×D314yes—
108Dic15—38no—
109C5×Dic3—38no—
110C2×C3×D4—54no—
111C2×#67—1516no—
112#237—158no—
113#237—158no—
114D3×D4—158no—
115D3×D4—158no—
116#235—34no—
117#235—154no—
118C32×C5H(5,𝔽2)11yescharacteristic, complemented, Hall
119C22×D5—94no—
120C22×D5C2×C3⋊D312yescomplemented
121C5×Q8—91no—
122C5×D4—92no—
123C5×D4—91no—
124C2×C4×C5—92no—
125C2×C4×C5C2×C3⋊D311yescharacteristic, complemented
126C22⋊D5—92no—
127C22⋊D5—94no—
128D20—94no—
129D20—91no—
130D20C2×C3⋊D312yescomplemented
131D20C2×C3⋊D312yescomplemented
132C4×D5—94no—
133C4×D5—92no—
134Dic10—91no—
135C22×C32—54no—
136C22×C32—202no—
137C22×C32C22×D511yescharacteristic
138C2×C3⋊D3—52no—
139C2×C3⋊D3—204no—
140C2×C3⋊D3C22×D512yes—
141C32×C4C22×D511yescharacteristic
142C32×C4C22×D511yescharacteristic
143C3⋊Dic3—52no—
144C3⋊Dic3C22×D512yes—
145H(5,𝔽2)—451noSylow
146C2×C3×C5—24no—
147C2×C3×C5C23×D314yes—
148D15—68no—
149C3×D5—216no—
150C5×D3—68no—
151C23×C3—58no—
152C22×D3—1516no—
153C3×D4—58no—
154C3×D4—58no—
155C2×C3×C4D3×D514yescomplemented
156#67—38no—
157#67—1516no—
158#67—1516no—
159#67—158no—
160C2×Dic3—1516no—
161D12—34no—
162D12—154no—
163C4×D3—38no—
164C4×D3—158no—
165Dic6—34no—
166Dic6—154no—
167C22×C5—92no—
168C22×C5C22×C3⋊D311yescharacteristic
169C2×D5—42no—
170C2×D5—92no—
171C2×D5—364no—
172C2×D5C22×C3⋊D314yes—
173C4×C5—92no—
174C4×C5C22×C3⋊D311yescharacteristic
175C4×C5C22×C3⋊D311yescharacteristic
176Dic5—92no—
177C2×C32—21no—
178C2×C32—104no—
179C2×C32C23×D511yescharacteristic
180C3⋊D3—22no—
181C3⋊D3—102no—
182#41—91no—
183#41—452no—
184#41—452no—
185#41—451no—
186C2×D4—51no—
187C2×D4—452no—
188C2×D4—452no—
189C2×D4—454no—
190C3×C5#100414yescomplemented
191C22×C3—516no—
192C22×C3—208no—
193C22×C3C2×D3×D514yes—
194C2×D3—38no—
195C2×D3—158no—
196C2×D3—6016no—
197C3×C4C2×D3×D514yes—
198C3×C4C2×D3×D514yes—
199Dic3—38no—
200Dic3—158no—
201C2×C5—21no—
202C2×C5—182no—
203C2×C5C23×C3⋊D311yescharacteristic
204D5—24no—
205D5—182no—
206C32#414911yescharacteristic, complemented, Sylow
207C23—52no—
208C23—454no—
209Q8—91no—
210Q8—451no—
211D4—52no—
212D4—52no—
213D4—92no—
214D4—91no—
215D4—454no—
216D4—454no—
217D4—452no—
218D4—451no—
219C2×C4—92no—
220C2×C4—454no—
221C2×C4—452no—
222C2×C4D5×C3⋊D311yescharacteristic, complemented
223C2×C3—24no—
224C2×C3—1016no—
225C2×C3C22×D3×D514yes—
226D3—68no—
227D3—308no—
228C5#6436111yescharacteristic, complemented, Sylow
229C22—54no—
230C22—92no—
231C22—202no—
232C22—452no—
233C22—1804no—
234C22C2×D5×C3⋊D311yescharacteristic
235C4—92no—
236C4—452no—
237C4C2×D5×C3⋊D311yescharacteristic
238C4C2×D5×C3⋊D311yescharacteristic
239C3#9201714yescomplemented
240C2—21no—
241C2—104no—
242C2—182no—
243C2—902no—
244C2C22×D5×C3⋊D311yescharacteristic
subgroupG/H
center, FrattiniC2C22×D5×C3⋊D3
commutator, socle, cosocleC2×C32×C5C24
FittingC2×C32×C4×C5C22
hypercenterC2×C4D5×C3⋊D3
hypocenterC32×C5H(5,𝔽2)
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C2 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. #10624283C2semidirect
2. C5×#3828C2semidirect
3. C2×C32×D20C2semidirect
4. D5×#638C2semidirect
5. #10624160C2semidirect
6. C3⋊D3×D20C2semidirect
7. #10624149C2semidirect
8. #10624148C2semidirect
10. C22×C32×D5C22semidirect
11. C2×D5×C3⋊D3C22semidirect
12. C2×C32×C4×C5C22semidirect
13. #67184C22semidirect
14. C4⋊(C3⋊D15)C22semidirect
15. C4×C3⋊D15C22semidirect
16. #67180C22semidirect
17. C5×#638C22semidirect
18. C5×C4⋊(C3⋊D3)C22semidirect
19. C4×C5×C3⋊D3C22semidirect
20. C5×#634C22semidirect
21. C32×D20C22semidirect
22. C32×D20C22semidirect
23. #67139C22semidirect
24. #67138C22semidirect
25. D5×C3⋊Dic3C22semidirect
29. C2×C3×D20D3semidirect
53. #3828D5semidirect
54. C22×C3×D5C2×D3semidirect
56. C2×C3×C4×C5C2×D3semidirect
65. C3×D20C2×D3semidirect
66. C3×D20C2×D3semidirect
83. C2×D20C3⋊D3semidirect
88. C2×C32×C4C2×D5semidirect
92. #638C2×D5semidirect
95. C4⋊(C3⋊D3)C2×D5semidirect
97. C4×C3⋊D3C2×D5semidirect
99. #634C2×D5semidirect
118. C32×C5H(5,𝔽2)semidirect
120. C22×D5C2×C3⋊D3semidirect
125. C2×C4×C5C2×C3⋊D3semidirect
130. D20C2×C3⋊D3semidirect
131. D20C2×C3⋊D3semidirect
155. C2×C3×C4D3×D5semidirect
190. C3×C5#1004semidirect
206. C32#4149semidirect
222. C2×C4D5×C3⋊D3semidirect
228. C5#64361semidirect
239. C3#92017semidirect

Maximal subgroups

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

subgroupindex
#106242832
C5×#38282
C2×C32×D202
D5×#6382
#106241602
C3⋊D3×D202
#106241492
#106241482
#920173
#643615