Finite Group Databasebeta

← C2×#11725007 #13183408

Subgroups — C2×#11725007 #13183408

Order 1760.

472 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 124 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
1C23×D55C211yesmaximal, characteristic, complemented
2C22×D5×D11C211yesmaximal, characteristic, complemented
3C2×C11×C22⋊D5C211yesmaximal, characteristic, complemented
4C2×C5×C22⋊D11C211yesmaximal, characteristic, complemented
5#11725007C218yesmaximal, direct product factor
6C2×#89169C211yesmaximal, characteristic, complemented
7C2×#89168C211yesmaximal, characteristic, complemented
8C2×#89166C211yesmaximal, characteristic, complemented
9C23×C5×C11C2211yescharacteristic, complemented
10C22×D55—24no—
11C22×D55C2211yescharacteristic
12C22×D55C2214yescomplemented
13C22×D55C2211yescharacteristic, complemented
14C22×D5×C11C2211yescharacteristic, complemented
15C22×C5×D11C2211yescharacteristic, complemented
16C2×D5×D11—24no—
17C2×D5×D11C2214yescomplemented
18C11×C22⋊D5C2214yescomplemented
19C2×C11×Dic5C2211yescharacteristic, complemented
20C5×C22⋊D11C2214yescomplemented
21C2×C5×Dic11C2211yescharacteristic, complemented
22#89169C2214yescomplemented
23#89168C2214yescomplemented
24#89166C2214yescomplemented
25C2×D4×D11—51nomaximal, Hall
26C22×C5×C11—22no—
27C22×C5×C11C2311yescharacteristic
28C22×C5×C11C2312yescomplemented
29C2×D55—22no—
30C2×D55—28no—
31C2×D55D414yescomplemented
32C2×D55C2312yes—
33C2×D55C2312yescomplemented
34C2×D5×C11—22no—
35C2×D5×C11C2312yescomplemented
36C2×C5×D11—22no—
37C2×C5×D11C2312yescomplemented
38D5×D11—28no—
39C5×Dic11C2312yescomplemented
40C11×Dic5C2312yescomplemented
41C23×D11—51no—
42C23×D11—51no—
43C2×D4×C11—51no—
44C2×C22⋊D11—51no—
45C2×C22⋊D11D511yescharacteristic, complemented
46D4×D11—58no—
47C2×D44—51no—
48C2×C4×D11—51no—
49C2×D4×D5—111nomaximal, Hall
50C2×C5×C11—22no—
51C2×C5×C11C2×D412yescomplemented
52C2×C5×C11C2411yescharacteristic
53D55—22no—
54D55C2×D414yescomplemented
55C5×D11—22no—
56D5×C11—22no—
57C23×C11—51no—
58C23×C11C2×D511yescharacteristic, complemented
59C22×D11—51no—
60C22×D11—51no—
61C22×D11—54no—
62C22×D11—54no—
63C22×D11—104no—
64C22×D11—104no—
65C22×D11C2×D511yescharacteristic, complemented
66D4×C11—54no—
67C2×C4×C11—51no—
68C22⋊D11—54no—
69C22⋊D11C2×D514yescomplemented
70C2×Dic11C2×D511yescharacteristic, complemented
71D44—54no—
72C4×D11—54no—
73C23×D5—111no—
74C23×D5—111no—
75C2×C5×D4—111no—
76C2×C22⋊D5—111no—
77C2×C22⋊D5D1111yescharacteristic, complemented
78D4×D5—118no—
79C2×D20—111no—
80C2×C4×D5—111no—
81C5×C11C22×D411yescharacteristic, complemented, Hall
82C22×C11—22no—
83C22×C11—52no—
84C22×C11—102no—
85C22×C11C22×D511yescharacteristic
86C22×C11C22×D512yescomplemented
87C2×D11—22no—
88C2×D11—54no—
89C2×D11—52no—
90C2×D11—52no—
91C2×D11—108no—
92C2×D11—108no—
93C2×D11—102no—
94C2×D11C22×D512yescomplemented
95C4×C11—52no—
96Dic11C22×D512yescomplemented
97C23×C5—111no—
98C23×C5C2×D1111yescharacteristic, complemented
99C22×D5—111no—
100C22×D5—111no—
101C22×D5—114no—
102C22×D5—114no—
103C22×D5—224no—
104C22×D5—224no—
105C22×D5C2×D1111yescharacteristic, complemented
106C5×D4—114no—
107C2×C4×C5—111no—
108C22⋊D5—114no—
109C22⋊D5C2×D1114yescomplemented
110C2×Dic5C2×D1111yescharacteristic, complemented
111D20—114no—
112C4×D5—114no—
113C22×D4—551noSylow
114C2×C11—22no—
115C2×C11—102no—
116C2×C11D4×D512yescomplemented
117C2×C11C23×D511yescharacteristic
118D11—22no—
119D11—54no—
120D11—102no—
121C22×C5—22no—
122C22×C5—112no—
123C22×C5—222no—
124C22×C5C22×D1111yescharacteristic
125C22×C5C22×D1112yescomplemented
126C2×D5—22no—
127C2×D5—114no—
128C2×D5—112no—
129C2×D5—112no—
130C2×D5—228no—
131C2×D5—228no—
132C2×D5—222no—
133C2×D5C22×D1112yescomplemented
134C4×C5—112no—
135Dic5C22×D1112yescomplemented
136C24—551no—
137C24—551no—
138C2×D4—51no—
139C2×D4—111no—
140C2×D4—551no—
141C2×D4—551no—
142C2×D4—558no—
143C22×C4—551no—
144C11C2×D4×D511yescharacteristic, complemented, Sylow
145C2×C5—22no—
146C2×C5—222no—
147C2×C5D4×D1112yescomplemented
148C2×C5C23×D1111yescharacteristic
149D5—22no—
150D5—114no—
151D5—222no—
152C23—51no—
153C23—111no—
154C23—554no—
155C23—551no—
156C23—551no—
157C23—554no—
158C23—1104no—
159C23—1104no—
160C23D5×D1111yescharacteristic, complemented
161D4—54no—
162D4—114no—
163D4—554no—
164D4—554no—
165C2×C4—51no—
166C2×C4—111no—
167C2×C4—554no—
168C5C2×D4×D1111yescharacteristic, complemented, Sylow
169C22—22no—
170C22—52no—
171C22—102no—
172C22—112no—
173C22—222no—
174C22—554no—
175C22—552no—
176C22—552no—
177C22—1108no—
178C22—1108no—
179C22—1102no—
180C22C2×D5×D1111yescharacteristic
181C22C2×D5×D1112yescomplemented
182C4—52no—
183C4—112no—
184C2—22no—
185C2—102no—
186C2—222no—
187C2—554no—
188C2—1102no—
189C2#1172500712yesdirect product factor
190C2C22×D5×D1111yescharacteristic
subgroupG/H
centerC22C2×D5×D11
commutator, cosocleC2×C5×C11C24
FrattiniC2C22×D5×D11
FittingC23×C5×C11C22
socleC22×C5×C11C23
hypercenterC23D5×D11
hypocenterC5×C11C22×D4
LCSG ▷ C2×C5×C11 ▷ C5×C11
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C23×D55C2semidirect
2. C22×D5×D11C2semidirect
3. C2×C11×C22⋊D5C2semidirect
4. C2×C5×C22⋊D11C2semidirect
5. #11725007C2direct (N × H)
6. C2×#89169C2semidirect
7. C2×#89168C2semidirect
8. C2×#89166C2semidirect
9. C23×C5×C11C22semidirect
12. C22×D55C22semidirect
13. C22×D55C22semidirect
14. C22×D5×C11C22semidirect
15. C22×C5×D11C22semidirect
17. C2×D5×D11C22semidirect
18. C11×C22⋊D5C22semidirect
19. C2×C11×Dic5C22semidirect
20. C5×C22⋊D11C22semidirect
21. C2×C5×Dic11C22semidirect
22. #89169C22semidirect
23. #89168C22semidirect
24. #89166C22semidirect
28. C22×C5×C11C23semidirect
31. C2×D55D4semidirect
33. C2×D55C23semidirect
35. C2×D5×C11C23semidirect
37. C2×C5×D11C23semidirect
39. C5×Dic11C23semidirect
40. C11×Dic5C23semidirect
45. C2×C22⋊D11D5semidirect
51. C2×C5×C11C2×D4semidirect
54. D55C2×D4semidirect
58. C23×C11C2×D5semidirect
65. C22×D11C2×D5semidirect
69. C22⋊D11C2×D5semidirect
70. C2×Dic11C2×D5semidirect
77. C2×C22⋊D5D11semidirect
81. C5×C11C22×D4semidirect
86. C22×C11C22×D5semidirect
94. C2×D11C22×D5semidirect
96. Dic11C22×D5semidirect
98. C23×C5C2×D11semidirect
105. C22×D5C2×D11semidirect
109. C22⋊D5C2×D11semidirect
110. C2×Dic5C2×D11semidirect
116. C2×C11D4×D5semidirect
125. C22×C5C22×D11semidirect
133. C2×D5C22×D11semidirect
135. Dic5C22×D11semidirect
144. C11C2×D4×D5semidirect
147. C2×C5D4×D11semidirect
160. C23D5×D11semidirect
168. C5C2×D4×D11semidirect
181. C22C2×D5×D11semidirect
189. C2#11725007direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D552
C22×D5×D112
C2×C11×C22⋊D52
C2×C5×C22⋊D112
#117250072
C2×#891692
C2×#891682
C2×#891662
C2×D4×D115
C2×D4×D511