Finite Group Databasebeta

← #11998681

Subgroups — #11998681

Order 1280.

400 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 111 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#10610194C211yesmaximal, characteristic
2C5×#1835C211yesmaximal, characteristic, complemented
3#10600517C211yesmaximal, characteristic, complemented
4#10600339C212yesmaximal, complemented
5#10600338C212yesmaximal
6#65811C2211yescharacteristic
7#65804C2211yescharacteristic
8C2×C4×C5×C8C2211yescharacteristic
9C5×#382C2212yes—
10#65402—22no—
11#65214C2212yes—
12#64986—21no—
13#64986—21no—
14#64983C412yescomplemented
15#64970C412yescomplemented
16C5×#340—22no—
17#64675—21no—
18C8×#168—21no—
19#64672—24no—
20#64671—24no—
21#9757—51nomaximal, Sylow
22C2×#709—21no—
23C22×C5×C8D412yes—
24C2×C5×C4⋊C4—22no—
25C2×C42×C5C2311yescharacteristic
26#4076—22no—
27#4072—21no—
28#4070—22no—
29#4021—21no—
30#4020C2×C411yescharacteristic
31C4×D20—22no—
32#4016—21no—
33#4015C2×C412yes—
34#4015C2×C411yescharacteristic
35C4×Dic10—22no—
36C4×C5×C8C2×C412yes—
37C4×C5×C8D411yescharacteristic
38C4×C5×C8D411yescharacteristic
39C5×#95—22no—
40C5×#95—22no—
41C22⋊#168D414yes—
42#3953—22no—
43#3953—22no—
44#3948—22no—
45#3948—22no—
46C4⋊#168—22no—
47C4×#168—22no—
48#3131—51no—
49#1835D511yescharacteristic, complemented
50#1518—52no—
51#1517—52no—
52#1450—51no—
53C22×C4×C5—42no—
54C22×C4×C5C2×D412yes—
55C22×C4×C5C2×D411yescharacteristic
56C2×C22⋊D5—41no—
57#709—44no—
58C2×D20—21no—
59C2×D20—22no—
60C2×C4×D5—41no—
61C2×Dic10—21no—
62C2×Dic10—22no—
63C2×C5×C8—24no—
64C2×C5×C8C22⋊C412yes—
65C2×C5×C8C22⋊C412yes—
66C5×C4⋊C4—44no—
67C42×C5C22×C411yescharacteristic
68C42×C5C2×D411yescharacteristic
69C42×C5#4112yes—
70C22⋊Dic5—41no—
71#685—42no—
72C4⋊Dic5—22no—
73C4⋊Dic5—22no—
74C4⋊Dic5—22no—
75#683—42no—
76C4×Dic5—41no—
77C2×#168—24no—
78#533—51no—
79#532—51no—
80#488—101no—
81#488—101no—
82#487—52no—
83#486—52no—
84#431—52no—
85#416—102no—
86C2×C4×C8C2×D511yescharacteristic
87#382C2×D512yes—
88#340—22no—
89#328—104no—
90#327—104no—
91#322—101no—
92C82—101no—
93C23×C5#12711yescharacteristic
94C22×D5—41no—
95C2×C4×C5—42no—
96C2×C4×C5—84no—
97C2×C4×C5—82no—
98C2×C4×C5C2×C22⋊C411yescharacteristic
99C2×C4×C5C4×D412yes—
100C2×C4×C5#12112yes—
101C2×C4×C5#12411yescharacteristic
102C2×C4×C5#13514yes—
103C22⋊D5—82no—
104C2×Dic5—42no—
105C2×Dic5—41no—
106D20—42no—
107D20—82no—
108C4×D5—82no—
109Dic10—42no—
110Dic10—82no—
111C5×C8—22no—
112C5×C8—22no—
113#168—44no—
114C2×#41—101no—
115C22×C8C22⋊D512yes—
116C4⋊Q8—51no—
117C4⋊Q8—52no—
118#127—51no—
119#125—101no—
120#124—101no—
121C22⋊Q8—102no—
122#121—102no—
123C4×Q8—102no—
124C4×D4—102no—
125#117—101no—
126C2×C4⋊C4—22no—
127C2×C42C22×D511yescharacteristic
128C4⋊C8—102no—
129#103—102no—
130#103—102no—
131#102—102no—
132#102—102no—
133C22⋊C8—54no—
134C4×C8—102no—
135C4×C8C4×D512yes—
136C4×C8D2011yescharacteristic
137C4×C8D2011yescharacteristic
138#95—22no—
139#95—22no—
140C22×C5—22no—
141C22×C5#39011yescharacteristic
142C22×C5#49512yes—
143C2×D5—81no—
144C2×D5—82no—
145C4×C5—22no—
146C4×C5—22no—
147C4×C5—162no—
148C4×C5#41612yes—
149C4×C5#48812yes—
150Dic5—81no—
151Dic5—82no—
152#41—204no—
153C2×Q8—102no—
154C2×Q8—101no—
155C2×D4—102no—
156C2×D4—101no—
157C2×D4—201no—
158C22×C4—42no—
159C22×C4—201no—
160C22×C4D4×D512yes—
161C22×C4C2×C22⋊D511yescharacteristic
162C2×C8—24no—
163C2×C8—104no—
164C2×C8#68512yes—
165C2×C8#68512yes—
166C4⋊C4—44no—
167C4⋊C4—102no—
168C4⋊C4—102no—
169C4⋊C4—102no—
170C4⋊C4—202no—
171C22⋊C4—201no—
172C22⋊C4—202no—
173C42—201no—
174C42C2×C4×D511yescharacteristic
175C42C2×D2011yescharacteristic
176C42#71312yes—
177C2×C5—22no—
178C2×C5#195811yescharacteristic
179C2×C5#197612yes—
180D5—161no—
181C23—201no—
182C23#408611yescharacteristic
183Q8—202no—
184Q8—402no—
185D4—202no—
186D4—402no—
187D4—402no—
188C2×C4—42no—
189C2×C4—84no—
190C2×C4—82no—
191C2×C4—202no—
192C2×C4—201no—
193C2×C4—402no—
194C2×C4#403912yes—
195C2×C4#404112yes—
196C2×C4C2×#68511yescharacteristic
197C2×C4#409311yescharacteristic
198C2×C4#409614yes—
199C8—22no—
200C8—22no—
201C8—204no—
202C5#975711yescharacteristic, complemented, Sylow
203C22—22no—
204C22—401no—
205C22—402no—
206C22#6527711yescharacteristic
207C22#6534812yes—
208C4—22no—
209C4—22no—
210C4—162no—
211C4—401no—
212C4—402no—
213C4#6529112yes—
214C4#6535712yes—
215C2—22no—
216C2—801no—
217C2#1060034411yescharacteristic
218C2#1060145112yes—
subgroupG/H
centerC22#65277
commutatorC42×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#1835C2
socleC22×C5#390
prime radical#65811C22
cosocleC2×C42×C5C23
hypercenter#1835D5
hypocenterC5#9757
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1835

Complements

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

NH ≅ G/Ntype
2. C5×#1835C2semidirect
3. #10600517C2semidirect
4. #10600339C2semidirect
14. #64983C4semidirect
15. #64970C4semidirect
49. #1835D5semidirect
202. C5#9757semidirect

Maximal subgroups

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

subgroupindex
#106101942
C5×#18352
#106005172
#106003392
#106003382
#97575