Finite Group Databasebeta

← #13183385

Subgroups — #13183385

Order 1760.

332 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 108 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#11725033C211yesmaximal, characteristic, complemented
2D4×D5×C11C211yesmaximal, characteristic, complemented
3C5×D4×D11C211yesmaximal, characteristic, complemented
4D5×C22⋊D11C212yesmaximal, complemented
5D11×C22⋊D5C212yesmaximal, complemented
6C2×#89167C212yesmaximal, complemented
7#11724997C212yesmaximal, complemented
8#11724994C211yesmaximal, characteristic, complemented
9#11724989C211yesmaximal, characteristic, complemented
10#11724988C211yesmaximal, characteristic, complemented
11#11724982C211yesmaximal, characteristic, complemented
12C22×D5×C11C2212yescomplemented
13C22×C5×D11C2212yescomplemented
14C2×D5×D11C2212yescomplemented
15C5×D4×C11C2211yescharacteristic, complemented
16C22⋊D55C2212yescomplemented
17C2×Dic55C2212yescomplemented
18C4×D55C2211yescharacteristic, complemented
19Dic110C2211yescharacteristic, complemented
20C11×C22⋊D5C2212yescomplemented
21C11×D20C2211yescharacteristic, complemented
22C4×D5×C11C2211yescharacteristic, complemented
23C5×C22⋊D11C2212yescomplemented
24C5×D44C2211yescharacteristic, complemented
25C4×C5×D11C2211yescharacteristic, complemented
26#89170C2211yescharacteristic, complemented
27#89169C2211yescharacteristic, complemented
28#89168C2211yescharacteristic, complemented
29#89167C2212yescomplemented
30#89167C2211yescharacteristic, complemented
31#89167C2212yescomplemented
32#89167C2212yescomplemented
33D5×Dic11C2212yescomplemented
34Dic5×D11C2212yescomplemented
35#67037—51nomaximal, Hall
36C22×C5×C11C2312yes—
37C2×D55C2311yescharacteristic
38C2×D5×C11—42no—
39C2×D5×C11C2312yes—
40C2×D5×C11C2311yescharacteristic
41C2×C5×D11—42no—
42C2×C5×D11C2312yes—
43C2×C5×D11C2311yescharacteristic
44D5×D11—42no—
45C4×C5×C11C2311yescharacteristic
46Dic55C2312yes—
47Dic55C2311yescharacteristic
48C5×Dic11C2311yescharacteristic
49C11×Dic5C2311yescharacteristic
50C2×D4×C11—51no—
51C2×C22⋊D11—52no—
52C2×C22⋊D11—52no—
53#4341—52no—
54#4341—51no—
55#4341—51no—
56D4×D11—51no—
57D4×D11—52no—
58D4×D11D511yescharacteristic, complemented
59#4339—51no—
60#4339—51no—
61#4144—111nomaximal, Hall
62C2×C5×C11—22no—
63C2×C5×C11C2411yescharacteristic
64D55—21no—
65C5×D11—22no—
66C5×D11—21no—
67D5×C11—22no—
68D5×C11—21no—
69C23×C11—52no—
70C22×D11—52no—
71C22×D11C2×D512yescomplemented
72D4×C11—52no—
73D4×C11—51no—
74D4×C11C2×D511yescharacteristic, complemented
75C2×C4×C11—51no—
76C22⋊D11—52no—
77C22⋊D11—52no—
78C22⋊D11—51no—
79C22⋊D11—52no—
80C22⋊D11—52no—
81C22⋊D11—51no—
82C22⋊D11C2×D512yescomplemented
83C2×Dic11—52no—
84C2×Dic11—52no—
85D44—51no—
86D44C2×D511yescharacteristic, complemented
87C4×D11—52no—
88C4×D11—51no—
89C4×D11C2×D511yescharacteristic, complemented
90Dic22—51no—
91Dic22—51no—
92C2×C5×D4—111no—
93C2×C22⋊D5—112no—
94C2×C22⋊D5—112no—
95#711—111no—
96#711—112no—
97#711—111no—
98D4×D5—112no—
99D4×D5—111no—
100D4×D5D1111yescharacteristic, complemented
101#709—111no—
102#709—111no—
103C5×C11H(5,𝔽2)11yescharacteristic, complemented, Hall
104C22×C11—51no—
105C22×C11—52no—
106C22×C11—202no—
107C22×C11C22×D512yes—
108C2×D11—42no—
109C2×D11—51no—
110C2×D11—202no—
111C2×D11C22×D512yes—
112C2×D11C22×D511yescharacteristic
113C4×C11—51no—
114C4×C11C22×D511yescharacteristic
115Dic11—52no—
116Dic11—51no—
117Dic11C22×D511yescharacteristic
118C23×C5—112no—
119C22×D5—112no—
120C22×D5C2×D1112yescomplemented
121C5×D4—112no—
122C5×D4—111no—
123C5×D4C2×D1111yescharacteristic, complemented
124C2×C4×C5—111no—
125C22⋊D5—112no—
126C22⋊D5—112no—
127C22⋊D5—111no—
128C22⋊D5—112no—
129C22⋊D5—112no—
130C22⋊D5—111no—
131C22⋊D5C2×D1112yescomplemented
132C2×Dic5—112no—
133C2×Dic5—112no—
134D20—111no—
135D20C2×D1111yescharacteristic, complemented
136C4×D5—112no—
137C4×D5—111no—
138C4×D5C2×D1111yescharacteristic, complemented
139Dic10—111no—
140Dic10—111no—
141H(5,𝔽2)—551noSylow
142C2×C11—22no—
143C2×C11—102no—
144C2×C11—101no—
145C2×C11C23×D511yescharacteristic
146D11—21no—
147D11—22no—
148D11—101no—
149C22×C5—112no—
150C22×C5—111no—
151C22×C5—442no—
152C22×C5C22×D1112yes—
153C2×D5—42no—
154C2×D5—111no—
155C2×D5—442no—
156C2×D5C22×D1112yes—
157C2×D5C22×D1111yescharacteristic
158C4×C5—111no—
159C4×C5C22×D1111yescharacteristic
160Dic5—112no—
161Dic5—111no—
162Dic5C22×D1111yescharacteristic
163#41—551no—
164#41—551no—
165#41—551no—
166#41—552no—
167#41—551no—
168C2×D4—51no—
169C2×D4—111no—
170C2×D4—551no—
171C2×D4—552no—
172C2×D4—552no—
173C2×D4—552no—
174C11#414411yescharacteristic, complemented, Sylow
175C2×C5—22no—
176C2×C5—222no—
177C2×C5—221no—
178C2×C5C23×D1111yescharacteristic
179D5—21no—
180D5—22no—
181D5—221no—
182C23—52no—
183C23—112no—
184C23—552no—
185Q8—551no—
186Q8—551no—
187D4—52no—
188D4—51no—
189D4—112no—
190D4—111no—
191D4—551no—
192D4—551no—
193D4—551no—
194D4—552no—
195D4—552no—
196D4—552no—
197D4—552no—
198D4D5×D1111yescharacteristic, complemented
199C2×C4—51no—
200C2×C4—111no—
201C2×C4—552no—
202C2×C4—552no—
203C2×C4—552no—
204C2×C4—551no—
205C5#6703711yescharacteristic, complemented, Sylow
206C22—51no—
207C22—52no—
208C22—111no—
209C22—112no—
210C22—202no—
211C22—442no—
212C22—551no—
213C22—2202no—
214C22C2×D5×D1112yes—
215C4—51no—
216C4—111no—
217C4—552no—
218C4—551no—
219C4C2×D5×D1111yescharacteristic
220C2—22no—
221C2—101no—
222C2—102no—
223C2—221no—
224C2—222no—
225C2—1101no—
226C2C22×D5×D1111yescharacteristic
subgroupG/H
center, FrattiniC2C22×D5×D11
commutator, socle, cosocleC2×C5×C11C24
FittingC5×D4×C11C22
hypercenterD4D5×D11
hypocenterC5×C11H(5,𝔽2)
LCSG ▷ C2×C5×C11 ▷ C5×C11
UCSC1 ◁ C2 ◁ D4

Complements

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

NH ≅ G/Ntype
1. #11725033C2semidirect
2. D4×D5×C11C2semidirect
3. C5×D4×D11C2semidirect
4. D5×C22⋊D11C2semidirect
5. D11×C22⋊D5C2semidirect
6. C2×#89167C2semidirect
7. #11724997C2semidirect
8. #11724994C2semidirect
9. #11724989C2semidirect
10. #11724988C2semidirect
11. #11724982C2semidirect
12. C22×D5×C11C22semidirect
13. C22×C5×D11C22semidirect
14. C2×D5×D11C22semidirect
15. C5×D4×C11C22semidirect
16. C22⋊D55C22semidirect
17. C2×Dic55C22semidirect
18. C4×D55C22semidirect
19. Dic110C22semidirect
20. C11×C22⋊D5C22semidirect
21. C11×D20C22semidirect
22. C4×D5×C11C22semidirect
23. C5×C22⋊D11C22semidirect
24. C5×D44C22semidirect
25. C4×C5×D11C22semidirect
26. #89170C22semidirect
27. #89169C22semidirect
28. #89168C22semidirect
29. #89167C22semidirect
30. #89167C22semidirect
31. #89167C22semidirect
32. #89167C22semidirect
33. D5×Dic11C22semidirect
34. Dic5×D11C22semidirect
58. D4×D11D5semidirect
71. C22×D11C2×D5semidirect
74. D4×C11C2×D5semidirect
82. C22⋊D11C2×D5semidirect
86. D44C2×D5semidirect
89. C4×D11C2×D5semidirect
100. D4×D5D11semidirect
103. C5×C11H(5,𝔽2)semidirect
120. C22×D5C2×D11semidirect
123. C5×D4C2×D11semidirect
131. C22⋊D5C2×D11semidirect
135. D20C2×D11semidirect
138. C4×D5C2×D11semidirect
174. C11#4144semidirect
198. D4D5×D11semidirect
205. C5#67037semidirect

Maximal subgroups

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

subgroupindex
#117250332
D4×D5×C112
C5×D4×D112
D5×C22⋊D112
D11×C22⋊D52
C2×#891672
#117249972
#117249942
#117249892
#117249882
#117249822
#670375
#414411