Finite Group Databasebeta

← #13183386

Subgroups — #13183386

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
1D4×D55C211yesmaximal, characteristic, complemented
2C11×#711C211yesmaximal, characteristic, complemented
3C5×D4×D11C211yesmaximal, characteristic, complemented
4#11725007C212yesmaximal, complemented
5D11×C22⋊D5C212yesmaximal, complemented
6C2×#89168C212yesmaximal, complemented
7#11724996C212yesmaximal, complemented
8D5×D44C211yesmaximal, characteristic, complemented
9#11724990C211yesmaximal, characteristic, complemented
10#11724988C211yesmaximal, characteristic, complemented
11#11724983C211yesmaximal, characteristic, complemented
12C22×D55C2212yescomplemented
13C22×C5×D11C2212yescomplemented
14C2×D5×D11C2212yescomplemented
15C5×D4×C11C2211yescharacteristic, complemented
16C22⋊D55C2212yescomplemented
17D220C2211yescharacteristic, complemented
18C4×D55C2211yescharacteristic, complemented
19C11×C22⋊D5C2212yescomplemented
20C2×C11×Dic5C2212yescomplemented
21C4×D5×C11C2211yescharacteristic, complemented
22C11×Dic10C2211yescharacteristic, complemented
23C5×C22⋊D11C2212yescomplemented
24C5×D44C2211yescharacteristic, complemented
25C4×C5×D11C2211yescharacteristic, complemented
26#89170C2211yescharacteristic, complemented
27#89169C2211yescharacteristic, complemented
28#89168C2212yescomplemented
29#89168C2211yescharacteristic, complemented
30#89168C2212yescomplemented
31#89168C2212yescomplemented
32#89167C2211yescharacteristic, complemented
33#89166C2212yescomplemented
34Dic5×D11C2212yescomplemented
35#67042—51nomaximal, Hall
36C22×C5×C11C2312yes—
37C2×D55—42no—
38C2×D55C2312yes—
39C2×D55C2311yescharacteristic
40C2×D5×C11C2311yescharacteristic
41C2×C5×D11—42no—
42C2×C5×D11C2312yes—
43C2×C5×D11C2311yescharacteristic
44D5×D11—42no—
45C4×C5×C11C2311yescharacteristic
46Dic55C2311yescharacteristic
47C5×Dic11C2311yescharacteristic
48C11×Dic5C2312yes—
49C11×Dic5C2311yescharacteristic
50C11×#41—51no—
51#4343—51no—
52#4343—51no—
53D4×D11—52no—
54D4×D11—52no—
55D4×D11—51no—
56D4×D11D511yescharacteristic, complemented
57#4339—52no—
58#4339—51no—
59C2×D44—51no—
60C2×D44—52no—
61#4144—111nomaximal, Hall
62C2×C5×C11—22no—
63C2×C5×C11C2411yescharacteristic
64D55—22no—
65D55—21no—
66C5×D11—22no—
67C5×D11—21no—
68D5×C11—21no—
69C22×D11—52no—
70C22×D11—52no—
71C22×D11C2×D512yescomplemented
72Q8×C11—51no—
73D4×C11—52no—
74D4×C11C2×D511yescharacteristic, complemented
75C2×C4×C11—52no—
76C2×C4×C11—51no—
77C22⋊D11—52no—
78C22⋊D11—51no—
79C22⋊D11—51no—
80C22⋊D11C2×D512yescomplemented
81D44—52no—
82D44—51no—
83D44—52no—
84D44—52no—
85D44—51no—
86D44C2×D511yescharacteristic, complemented
87C4×D11—52no—
88C4×D11—51no—
89C4×D11—52no—
90C4×D11C2×D511yescharacteristic, complemented
91Dic22—51no—
92C2×C5×D4—111no—
93C2×C22⋊D5—112no—
94C2×C22⋊D5—112no—
95#711—112no—
96#711—111no—
97#711D1111yescharacteristic, complemented
98D4×D5—111no—
99D4×D5—112no—
100D4×D5—111no—
101#709—111no—
102#709—111no—
103C5×C11H(5,𝔽2)11yescharacteristic, complemented, Hall
104C22×C11—51no—
105C22×C11C22×D512yes—
106C2×D11—42no—
107C2×D11—51no—
108C2×D11—52no—
109C2×D11—202no—
110C2×D11—202no—
111C2×D11C22×D512yes—
112C2×D11C22×D511yescharacteristic
113C4×C11—51no—
114C4×C11—52no—
115C4×C11C22×D511yescharacteristic
116Dic11—51no—
117Dic11C22×D511yescharacteristic
118C23×C5—112no—
119C22×D5—112no—
120C22×D5—112no—
121C5×D4—112no—
122C5×D4—111no—
123C5×D4C2×D1111yescharacteristic, complemented
124C2×C4×C5—111no—
125C22⋊D5—112no—
126C22⋊D5—111no—
127C22⋊D5—111no—
128C22⋊D5—112no—
129C22⋊D5—112no—
130C22⋊D5—112no—
131C22⋊D5C2×D1112yescomplemented
132C2×Dic5—112no—
133C2×Dic5C2×D1112yescomplemented
134D20—111no—
135D20—111no—
136C4×D5—111no—
137C4×D5—112no—
138C4×D5C2×D1111yescharacteristic, complemented
139Dic10—111no—
140Dic10C2×D1111yescharacteristic, complemented
141H(5,𝔽2)—551noSylow
142C2×C11—22no—
143C2×C11—101no—
144C2×C11C23×D511yescharacteristic
145D11—21no—
146D11—22no—
147D11—102no—
148D11—101no—
149C22×C5—112no—
150C22×C5—111no—
151C22×C5—442no—
152C22×C5C22×D1112yes—
153C2×D5—111no—
154C2×D5—112no—
155C2×D5—442no—
156C2×D5—442no—
157C2×D5C22×D1111yescharacteristic
158C4×C5—111no—
159C4×C5C22×D1111yescharacteristic
160Dic5—111no—
161Dic5C22×D1111yescharacteristic
162Dic5C22×D1112yes—
163#41—51no—
164#41—551no—
165#41—552no—
166#41—551no—
167#41—551no—
168C2×D4—111no—
169C2×D4—551no—
170C2×D4—552no—
171C2×D4—552no—
172C2×D4—552no—
173C2×D4—551no—
174C11#414411yescharacteristic, complemented, Sylow
175C2×C5—22no—
176C2×C5—222no—
177C2×C5—221no—
178C2×C5C23×D1111yescharacteristic
179D5—21no—
180D5—222no—
181D5—221no—
182C23—112no—
183C23—552no—
184C23—552no—
185Q8—51no—
186Q8—551no—
187D4—52no—
188D4—112no—
189D4—111no—
190D4—551no—
191D4—552no—
192D4—552no—
193D4—552no—
194D4—551no—
195D4—551no—
196D4—552no—
197D4—551no—
198D4D5×D1111yescharacteristic, complemented
199C2×C4—52no—
200C2×C4—51no—
201C2×C4—111no—
202C2×C4—552no—
203C2×C4—552no—
204C2×C4—551no—
205C5#6704211yescharacteristic, complemented, Sylow
206C22—51no—
207C22—111no—
208C22—112no—
209C22—442no—
210C22—552no—
211C22—551no—
212C22—2202no—
213C22—2202no—
214C22C2×D5×D1112yes—
215C4—51no—
216C4—52no—
217C4—111no—
218C4—551no—
219C4C2×D5×D1111yescharacteristic
220C2—22no—
221C2—101no—
222C2—221no—
223C2—222no—
224C2—1101no—
225C2—1102no—
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. D4×D55C2semidirect
2. C11×#711C2semidirect
3. C5×D4×D11C2semidirect
4. #11725007C2semidirect
5. D11×C22⋊D5C2semidirect
6. C2×#89168C2semidirect
7. #11724996C2semidirect
8. D5×D44C2semidirect
9. #11724990C2semidirect
10. #11724988C2semidirect
11. #11724983C2semidirect
12. C22×D55C22semidirect
13. C22×C5×D11C22semidirect
14. C2×D5×D11C22semidirect
15. C5×D4×C11C22semidirect
16. C22⋊D55C22semidirect
17. D220C22semidirect
18. C4×D55C22semidirect
19. C11×C22⋊D5C22semidirect
20. C2×C11×Dic5C22semidirect
21. C4×D5×C11C22semidirect
22. C11×Dic10C22semidirect
23. C5×C22⋊D11C22semidirect
24. C5×D44C22semidirect
25. C4×C5×D11C22semidirect
26. #89170C22semidirect
27. #89169C22semidirect
28. #89168C22semidirect
29. #89168C22semidirect
30. #89168C22semidirect
31. #89168C22semidirect
32. #89167C22semidirect
33. #89166C22semidirect
34. Dic5×D11C22semidirect
56. D4×D11D5semidirect
71. C22×D11C2×D5semidirect
74. D4×C11C2×D5semidirect
80. C22⋊D11C2×D5semidirect
86. D44C2×D5semidirect
90. C4×D11C2×D5semidirect
97. #711D11semidirect
103. C5×C11H(5,𝔽2)semidirect
123. C5×D4C2×D11semidirect
131. C22⋊D5C2×D11semidirect
133. C2×Dic5C2×D11semidirect
138. C4×D5C2×D11semidirect
140. Dic10C2×D11semidirect
174. C11#4144semidirect
198. D4D5×D11semidirect
205. C5#67042semidirect

Maximal subgroups

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

subgroupindex
D4×D552
C11×#7112
C5×D4×D112
#117250072
D11×C22⋊D52
C2×#891682
#117249962
D5×D442
#117249902
#117249882
#117249832
#670425
#414411