Finite Group Databasebeta

← #13183378

Subgroups — #13183378

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#11725031C211yesmaximal, characteristic, complemented
2C2×C11×D20C211yesmaximal, characteristic, complemented
3C5×#4339C211yesmaximal, characteristic, complemented
4D5×C22⋊D11C214yesmaximal, complemented
5#11724994C212yesmaximal, complemented
6D11×D20C212yesmaximal, complemented
7#11724989C212yesmaximal, complemented
8#11724985C212yesmaximal, complemented
9C22×D5×C11C2212yescomplemented
10C2×D5×D11C2214yescomplemented
11C2×C4×C5×C11C2211yescharacteristic, complemented
12C22⋊D55C2212yescomplemented
13D220C2211yescharacteristic, complemented
14C4×D55C2212yescomplemented
15Dic110C2211yescharacteristic, complemented
16C11×D20C2212yescomplemented
17C11×D20C2212yescomplemented
18C5×C22⋊D11C2212yescomplemented
19C5×D44C2211yescharacteristic, complemented
20C4×C5×D11C2212yescomplemented
21C5×Dic22C2211yescharacteristic, complemented
22#89169C2214yescomplemented
23#89167C2214yescomplemented
24D5×Dic11C2214yescomplemented
25#67037—51nomaximal, Hall
26C22×C5×C11C2311yescharacteristic
27C2×D55C2312yes—
28C2×D5×C11—42no—
29C2×D5×C11C2314yes—
30C2×C5×D11C2312yes—
31D5×D11—44no—
32C4×C5×C11C2311yescharacteristic
33C4×C5×C11C2311yescharacteristic
34Dic55C2312yes—
35C5×Dic11C2312yes—
36C2×D4×C11—51no—
37C2×C22⋊D11—54no—
38#4341—52no—
39#4341—52no—
40D4×D11—52no—
41D4×D11—52no—
42#4339—51no—
43#4339D511yescharacteristic, complemented
44#4149—111nomaximal, Hall
45C2×C5×C11—21no—
46C2×C5×C11C2411yescharacteristic
47D55—22no—
48C5×D11—22no—
49D5×C11—24no—
50C23×C11—52no—
51C22×D11—54no—
52D4×C11—52no—
53D4×C11—52no—
54C2×C4×C11C2×D511yescharacteristic, complemented
55C22⋊D11—52no—
56C22⋊D11—54no—
57C22⋊D11—54no—
58C22⋊D11C2×D512yescomplemented
59C2×Dic11—54no—
60D44—51no—
61D44C2×D511yescharacteristic, complemented
62C4×D11—52no—
63C4×D11C2×D512yescomplemented
64Dic22—51no—
65Dic22C2×D511yescharacteristic, complemented
66C5×#41—111no—
67#713—112no—
68D4×D5—114no—
69D4×D5—112no—
70#709—111no—
71#709—112no—
72C2×D20—112no—
73C2×D20D1111yescharacteristic, complemented
74C5×C11H(5,𝔽2)11yescharacteristic, complemented, Hall
75C22×C11—54no—
76C22×C11—202no—
77C22×C11C22×D511yescharacteristic
78C2×D11—52no—
79C2×D11—204no—
80C2×D11C22×D512yes—
81C4×C11C22×D511yescharacteristic
82C4×C11C22×D511yescharacteristic
83Dic11—52no—
84Dic11C22×D512yes—
85C22×D5—114no—
86C22×D5C2×D1112yescomplemented
87C5×Q8—111no—
88C5×D4—112no—
89C5×D4—111no—
90C2×C4×C5—112no—
91C2×C4×C5C2×D1111yescharacteristic, complemented
92C22⋊D5—112no—
93C22⋊D5—114no—
94D20—114no—
95D20—111no—
96D20C2×D1112yescomplemented
97D20C2×D1112yescomplemented
98C4×D5—114no—
99C4×D5—112no—
100Dic10—111no—
101H(5,𝔽2)—551noSylow
102C2×C11—21no—
103C2×C11—104no—
104C2×C11C23×D511yescharacteristic
105D11—22no—
106D11—102no—
107C22×C5—112no—
108C22×C5C22×D1111yescharacteristic
109C2×D5—42no—
110C2×D5—112no—
111C2×D5—444no—
112C2×D5C22×D1114yes—
113C4×C5—112no—
114C4×C5C22×D1111yescharacteristic
115C4×C5C22×D1111yescharacteristic
116Dic5—112no—
117#41—111no—
118#41—552no—
119#41—552no—
120#41—551no—
121C2×D4—51no—
122C2×D4—552no—
123C2×D4—552no—
124C2×D4—554no—
125C11#414911yescharacteristic, complemented, Sylow
126C2×C5—21no—
127C2×C5—222no—
128C2×C5C23×D1111yescharacteristic
129D5—24no—
130D5—222no—
131C23—52no—
132C23—554no—
133Q8—111no—
134Q8—551no—
135D4—52no—
136D4—52no—
137D4—112no—
138D4—111no—
139D4—554no—
140D4—554no—
141D4—552no—
142D4—551no—
143C2×C4—112no—
144C2×C4—554no—
145C2×C4—552no—
146C2×C4D5×D1111yescharacteristic, complemented
147C5#6703711yescharacteristic, complemented, Sylow
148C22—54no—
149C22—112no—
150C22—202no—
151C22—552no—
152C22—2204no—
153C22C2×D5×D1111yescharacteristic
154C4—112no—
155C4—552no—
156C4C2×D5×D1111yescharacteristic
157C4C2×D5×D1111yescharacteristic
158C2—21no—
159C2—104no—
160C2—222no—
161C2—1102no—
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. #11725031C2semidirect
2. C2×C11×D20C2semidirect
3. C5×#4339C2semidirect
4. D5×C22⋊D11C2semidirect
5. #11724994C2semidirect
6. D11×D20C2semidirect
7. #11724989C2semidirect
8. #11724985C2semidirect
9. C22×D5×C11C22semidirect
10. C2×D5×D11C22semidirect
11. C2×C4×C5×C11C22semidirect
12. C22⋊D55C22semidirect
13. D220C22semidirect
14. C4×D55C22semidirect
15. Dic110C22semidirect
16. C11×D20C22semidirect
17. C11×D20C22semidirect
18. C5×C22⋊D11C22semidirect
19. C5×D44C22semidirect
20. C4×C5×D11C22semidirect
21. C5×Dic22C22semidirect
22. #89169C22semidirect
23. #89167C22semidirect
24. D5×Dic11C22semidirect
43. #4339D5semidirect
54. C2×C4×C11C2×D5semidirect
58. C22⋊D11C2×D5semidirect
61. D44C2×D5semidirect
63. C4×D11C2×D5semidirect
65. Dic22C2×D5semidirect
73. C2×D20D11semidirect
74. C5×C11H(5,𝔽2)semidirect
86. C22×D5C2×D11semidirect
91. C2×C4×C5C2×D11semidirect
96. D20C2×D11semidirect
97. D20C2×D11semidirect
125. C11#4149semidirect
146. C2×C4D5×D11semidirect
147. C5#67037semidirect

Maximal subgroups

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

subgroupindex
#117250312
C2×C11×D202
C5×#43392
D5×C22⋊D112
#117249942
D11×D202
#117249892
#117249852
#670375
#414911