Finite Group Databasebeta

← #13183379

Subgroups — #13183379

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
1C2×D220C211yesmaximal, characteristic, complemented
2C11×#709C211yesmaximal, characteristic, complemented
3C5×#4339C211yesmaximal, characteristic, complemented
4#11725007C214yesmaximal, complemented
5D5×D44C212yesmaximal, complemented
6D11×D20C212yesmaximal, complemented
7#11724990C212yesmaximal, complemented
8#11724986C212yesmaximal, complemented
9C22×D55C2212yescomplemented
10C2×D5×D11C2214yescomplemented
11C2×C4×C5×C11C2211yescharacteristic, complemented
12D220C2212yescomplemented
13D220C2212yescomplemented
14C11×C22⋊D5C2212yescomplemented
15C11×D20C2211yescharacteristic, complemented
16C4×D5×C11C2212yescomplemented
17C11×Dic10C2211yescharacteristic, complemented
18C5×C22⋊D11C2212yescomplemented
19C5×D44C2211yescharacteristic, complemented
20C4×C5×D11C2212yescomplemented
21C5×Dic22C2211yescharacteristic, complemented
22#89169C2214yescomplemented
23#89168C2214yescomplemented
24#89166C2214yescomplemented
25#67042—51nomaximal, Hall
26C22×C5×C11C2311yescharacteristic
27C2×D55—42no—
28C2×D55C2314yes—
29C2×D5×C11C2312yes—
30C2×C5×D11C2312yes—
31D5×D11—44no—
32C4×C5×C11C2311yescharacteristic
33C4×C5×C11C2311yescharacteristic
34C5×Dic11C2312yes—
35C11×Dic5C2312yes—
36C11×#41—51no—
37#4343—52no—
38D4×D11—54no—
39D4×D11—52no—
40#4339—52no—
41#4339D511yescharacteristic, complemented
42C2×D44—52no—
43C2×D44—51no—
44#4149—111nomaximal, Hall
45C2×C5×C11—21no—
46C2×C5×C11C2411yescharacteristic
47D55—24no—
48C5×D11—22no—
49D5×C11—22no—
50C22×D11—52no—
51C22×D11—54no—
52Q8×C11—51no—
53D4×C11—52no—
54D4×C11—51no—
55C2×C4×C11—52no—
56C2×C4×C11C2×D511yescharacteristic, complemented
57C22⋊D11—54no—
58C22⋊D11C2×D512yescomplemented
59D44—54no—
60D44—52no—
61D44—52no—
62D44C2×D511yescharacteristic, complemented
63C4×D11—54no—
64C4×D11C2×D512yescomplemented
65Dic22C2×D511yescharacteristic, complemented
66C5×#41—111no—
67#713—112no—
68D4×D5—114no—
69D4×D5—112no—
70#709—112no—
71#709D1111yescharacteristic, complemented
72C2×D20—111no—
73C2×D20—112no—
74C5×C11H(5,𝔽2)11yescharacteristic, complemented, Hall
75C22×C11—52no—
76C22×C11C22×D511yescharacteristic
77C2×D11—54no—
78C2×D11—204no—
79C2×D11—202no—
80C2×D11C22×D512yes—
81C4×C11—52no—
82C4×C11C22×D511yescharacteristic
83C4×C11C22×D511yescharacteristic
84Dic11C22×D512yes—
85C22×D5—112no—
86C22×D5—114no—
87C5×Q8—111no—
88C5×D4—112no—
89C5×D4—111no—
90C2×C4×C5—112no—
91C2×C4×C5C2×D1111yescharacteristic, complemented
92C22⋊D5—114no—
93C22⋊D5C2×D1112yescomplemented
94D20—114no—
95D20—112no—
96D20—112no—
97D20C2×D1111yescharacteristic, complemented
98C4×D5—114no—
99C4×D5C2×D1112yescomplemented
100Dic10C2×D1111yescharacteristic, complemented
101H(5,𝔽2)—551noSylow
102C2×C11—21no—
103C2×C11—102no—
104C2×C11C23×D511yescharacteristic
105D11—22no—
106D11—104no—
107C22×C5—112no—
108C22×C5C22×D1111yescharacteristic
109C2×D5—114no—
110C2×D5—444no—
111C2×D5—442no—
112C2×D5C22×D1112yes—
113C4×C5—112no—
114C4×C5C22×D1111yescharacteristic
115C4×C5C22×D1111yescharacteristic
116Dic5C22×D1112yes—
117#41—51no—
118#41—111no—
119#41—552no—
120#41—552no—
121C2×D4—552no—
122C2×D4—552no—
123C2×D4—554no—
124C2×D4—551no—
125C11#414911yescharacteristic, complemented, Sylow
126C2×C5—21no—
127C2×C5—222no—
128C2×C5C23×D1111yescharacteristic
129D5—22no—
130D5—224no—
131C23—554no—
132C23—552no—
133Q8—51no—
134Q8—111no—
135D4—52no—
136D4—51no—
137D4—112no—
138D4—111no—
139D4—554no—
140D4—554no—
141D4—552no—
142D4—552no—
143C2×C4—52no—
144C2×C4—112no—
145C2×C4—554no—
146C2×C4D5×D1111yescharacteristic, complemented
147C5#6704211yescharacteristic, complemented, Sylow
148C22—52no—
149C22—112no—
150C22—554no—
151C22—2202no—
152C22—2204no—
153C22C2×D5×D1111yescharacteristic
154C4—52no—
155C4—112no—
156C4C2×D5×D1111yescharacteristic
157C4C2×D5×D1111yescharacteristic
158C2—21no—
159C2—102no—
160C2—222no—
161C2—1104no—
162C2C22×D5×D1111yescharacteristic
subgroupG/H
center, FrattiniC2C22×D5×D11
commutator, socle, cosocleC2×C5×C11C24
FittingC2×C4×C5×C11C22
hypercenterC2×C4D5×D11
hypocenterC5×C11H(5,𝔽2)
LCSG ▷ C2×C5×C11 ▷ C5×C11
UCSC1 ◁ C2 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C2×D220C2semidirect
2. C11×#709C2semidirect
3. C5×#4339C2semidirect
4. #11725007C2semidirect
5. D5×D44C2semidirect
6. D11×D20C2semidirect
7. #11724990C2semidirect
8. #11724986C2semidirect
9. C22×D55C22semidirect
10. C2×D5×D11C22semidirect
11. C2×C4×C5×C11C22semidirect
12. D220C22semidirect
13. D220C22semidirect
14. C11×C22⋊D5C22semidirect
15. C11×D20C22semidirect
16. C4×D5×C11C22semidirect
17. C11×Dic10C22semidirect
18. C5×C22⋊D11C22semidirect
19. C5×D44C22semidirect
20. C4×C5×D11C22semidirect
21. C5×Dic22C22semidirect
22. #89169C22semidirect
23. #89168C22semidirect
24. #89166C22semidirect
41. #4339D5semidirect
56. C2×C4×C11C2×D5semidirect
58. C22⋊D11C2×D5semidirect
62. D44C2×D5semidirect
64. C4×D11C2×D5semidirect
65. Dic22C2×D5semidirect
71. #709D11semidirect
74. C5×C11H(5,𝔽2)semidirect
91. C2×C4×C5C2×D11semidirect
93. C22⋊D5C2×D11semidirect
97. D20C2×D11semidirect
99. C4×D5C2×D11semidirect
100. Dic10C2×D11semidirect
125. C11#4149semidirect
146. C2×C4D5×D11semidirect
147. C5#67042semidirect

Maximal subgroups

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

subgroupindex
C2×D2202
C11×#7092
C5×#43392
#117250072
D5×D442
D11×D202
#117249902
#117249862
#670425
#414911