Finite Group Databasebeta

← #13183380

Subgroups — #13183380

Order 1760.

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

normal subgroups only

This group has 292 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
2C11×#711C211yesmaximal, characteristic, complemented
3C5×#4341C211yesmaximal, characteristic, complemented
4C2×#89170C212yesmaximal, complemented
5#11724999C212yesmaximal, complemented
6#11724997C212yesmaximal, complemented
7#11724996C212yesmaximal, complemented
8#11724988C211yesmaximal, characteristic, complemented
9D55⋊Q8C211yesmaximal, characteristic, complemented
10D5×Dic22C211yesmaximal, characteristic, complemented
11D11×Dic10C211yesmaximal, characteristic, complemented
12C5×D4×C11C2211yescharacteristic
13C22⋊D55C2212yes—
14C2×Dic55C2212yes—
15C4×D55C2211yescharacteristic
16Dic110C2211yescharacteristic
17C11×C22⋊D5C2212yes—
18C2×C11×Dic5C2212yes—
19C4×D5×C11C2211yescharacteristic
20C11×Dic10C2211yescharacteristic
21C5×C22⋊D11C2212yes—
22C2×C5×Dic11C2212yes—
23C4×C5×D11C2211yescharacteristic
24C5×Dic22C2211yescharacteristic
25#89170C2212yes—
26#89170C2212yes—
27#89170C2212yes—
28#89170C2211yescharacteristic
29#89169C2211yescharacteristic
30#89168C2211yescharacteristic
31#89167C2211yescharacteristic
32#89166C2212yes—
33D5×Dic11C2212yes—
34Dic5×D11C2212yes—
35#67043—51nomaximal, Hall
36C22×C5×C11C2312yes—
37C2×D55C2311yescharacteristic
38C2×D5×C11C2311yescharacteristic
39C2×C5×D11C2311yescharacteristic
40C4×C5×C11C2311yescharacteristic
41Dic55C2312yes—
42Dic55C2311yescharacteristic
43C5×Dic11C2312yes—
44C5×Dic11C2311yescharacteristic
45C11×Dic5C2312yes—
46C11×Dic5C2311yescharacteristic
47C11×#41—51no—
48Q8×D11—51no—
49Q8×D11—51no—
50#4341—52no—
51#4341—52no—
52#4341—51no—
53#4341D511yescharacteristic, complemented
54#4339—52no—
55#4339—51no—
56C2×Dic22—52no—
57C2×Dic22—51no—
58#4150—111nomaximal, Hall
59C2×C5×C11—22no—
60C2×C5×C11C2411yescharacteristic
61D55—21no—
62C5×D11—21no—
63D5×C11—21no—
64Q8×C11—51no—
65D4×C11—52no—
66D4×C11C2×D511yescharacteristic
67C2×C4×C11—52no—
68C2×C4×C11—51no—
69C22⋊D11—52no—
70C22⋊D11—51no—
71C22⋊D11—51no—
72C22⋊D11C2×D512yes—
73C2×Dic11—52no—
74C2×Dic11—52no—
75C2×Dic11C2×D512yes—
76D44—51no—
77C4×D11—52no—
78C4×D11—51no—
79C4×D11—52no—
80C4×D11C2×D511yescharacteristic
81Dic22—51no—
82Dic22—51no—
83Dic22—52no—
84Dic22—52no—
85Dic22—52no—
86Dic22C2×D511yescharacteristic
87C5×#41—111no—
88Q8×D5—111no—
89Q8×D5—111no—
90#711—111no—
91#711—112no—
92#711—112no—
93#711D1111yescharacteristic, complemented
94#709—112no—
95#709—111no—
96C2×Dic10—112no—
97C2×Dic10—111no—
98C5×C112−1+411yescharacteristic, complemented, Hall
99C22×C11—51no—
100C22×C11C22×D512yes—
101C2×D11—51no—
102C2×D11C22×D511yescharacteristic
103C4×C11—51no—
104C4×C11—52no—
105C4×C11C22×D511yescharacteristic
106Dic11—52no—
107Dic11—51no—
108Dic11C22×D511yescharacteristic
109Dic11C22×D512yes—
110C5×Q8—111no—
111C5×D4—112no—
112C5×D4C2×D1111yescharacteristic
113C2×C4×C5—112no—
114C2×C4×C5—111no—
115C22⋊D5—112no—
116C22⋊D5—111no—
117C22⋊D5—111no—
118C22⋊D5C2×D1112yes—
119C2×Dic5—112no—
120C2×Dic5—112no—
121C2×Dic5C2×D1112yes—
122D20—111no—
123C4×D5—112no—
124C4×D5—111no—
125C4×D5—112no—
126C4×D5C2×D1111yescharacteristic
127Dic10—111no—
128Dic10—111no—
129Dic10—112no—
130Dic10—112no—
131Dic10—112no—
132Dic10C2×D1111yescharacteristic
1332−1+4—551noSylow
134C2×C11—22no—
135C2×C11—101no—
136C2×C11C23×D511yescharacteristic
137D11—21no—
138D11—101no—
139C22×C5—111no—
140C22×C5C22×D1112yes—
141C2×D5—111no—
142C2×D5C22×D1111yescharacteristic
143C4×C5—111no—
144C4×C5—112no—
145C4×C5C22×D1111yescharacteristic
146Dic5—112no—
147Dic5—111no—
148Dic5C22×D1111yescharacteristic
149Dic5C22×D1112yes—
150#41—51no—
151#41—111no—
152#41—551no—
153#41—552no—
154#41—552no—
155#41—552no—
156#41—551no—
157C2×Q8—552no—
158C2×Q8—551no—
159C2×Q8—551no—
160C2×Q8—551no—
161C11#415011yescharacteristic, complemented, Sylow
162C2×C5—22no—
163C2×C5—221no—
164C2×C5C23×D1111yescharacteristic
165D5—21no—
166D5—221no—
167Q8—51no—
168Q8—111no—
169Q8—551no—
170Q8—552no—
171Q8—552no—
172Q8—552no—
173Q8—551no—
174D4—52no—
175D4—112no—
176D4—551no—
177D4—551no—
178D4—551no—
179D4—552no—
180D4D5×D1111yescharacteristic
181C2×C4—52no—
182C2×C4—51no—
183C2×C4—112no—
184C2×C4—111no—
185C2×C4—552no—
186C2×C4—552no—
187C2×C4—552no—
188C2×C4—552no—
189C2×C4—551no—
190C5#6704311yescharacteristic, complemented, Sylow
191C22—51no—
192C22—111no—
193C22—551no—
194C22C2×D5×D1112yes—
195C4—51no—
196C4—52no—
197C4—111no—
198C4—112no—
199C4—552no—
200C4—551no—
201C4C2×D5×D1111yescharacteristic
202C2—22no—
203C2—101no—
204C2—221no—
205C2—1101no—
206C2C22×D5×D1111yescharacteristic
subgroupG/H
center, FrattiniC2C22×D5×D11
commutator, socle, cosocleC2×C5×C11C24
FittingC5×D4×C11C22
hypercenterD4D5×D11
hypocenterC5×C112−1+4
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. C11×#711C2semidirect
3. C5×#4341C2semidirect
4. C2×#89170C2semidirect
5. #11724999C2semidirect
6. #11724997C2semidirect
7. #11724996C2semidirect
8. #11724988C2semidirect
9. D55⋊Q8C2semidirect
10. D5×Dic22C2semidirect
11. D11×Dic10C2semidirect
53. #4341D5semidirect
93. #711D11semidirect
98. C5×C112−1+4semidirect
161. C11#4150semidirect
190. C5#67043semidirect

Maximal subgroups

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

subgroupindex
#117250332
C11×#7112
C5×#43412
C2×#891702
#117249992
#117249972
#117249962
#117249882
D55⋊Q82
D5×Dic222
D11×Dic102
#670435
#415011