Finite Group Databasebeta

← #12002389

Subgroups — #12002389

Order 1280.

454 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 97 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#10605039C211yesmaximal, characteristic, complemented
2#10601583C212yesmaximal
3#10600188C211yesmaximal, characteristic
4C5×#1276C211yesmaximal, characteristic, complemented
5#10598229C212yesmaximal, complemented
6#65811C2211yescharacteristic
7C2×#4015—21no—
8C5×#431C2212yes—
9C43×C5C2211yescharacteristic
10#65225—21no—
11#65225C2212yes—
12#65218—24no—
13C2×#3937—21no—
14C2×#3937—21no—
15#65213C2211yescharacteristic
16#64690—24no—
17#10362—51nomaximal, Sylow
18C2×#709—21no—
19C22×Dic10—22no—
20C2×C42×C5—22no—
21C2×C42×C5D411yescharacteristic
22C2×C42×C5D411yescharacteristic
23C2×C42×C5C2311yescharacteristic
24#4076—22no—
25C2×C4⋊Dic5—22no—
26C2×C4⋊Dic5—22no—
27C2×#681—21no—
28#4021—21no—
29#4020Q811yescharacteristic, complemented
30C4×D20—22no—
31#4015—42no—
32#4015—42no—
33#4015Q811yescharacteristic, complemented
34C5×C4⋊C8—22no—
35C5×C22⋊C8—22no—
36C4×C5×C8—22no—
37#3963—24no—
38#3963—22no—
39#3963D414yes—
40#3937—42no—
41#3937—42no—
42C4⋊#168—22no—
43#2862—51no—
44#1962—51no—
45#1517—52no—
46#1286—52no—
47#1276D511yescharacteristic, complemented
48C22×C4×C5—21no—
49C22×C4×C5—21no—
50C22×C4×C5C2×D411yescharacteristic
51C22×C4×C5C2×D412yes—
52C2×C22⋊D5—41no—
53C22×Dic5—24no—
54#709—41no—
55#709—41no—
56#709—41no—
57#709—41no—
58C2×D20—21no—
59C2×D20—22no—
60C2×C4×D5—41no—
61C2×Dic10—21no—
62C2×Dic10—48no—
63C2×Dic10—44no—
64C2×C5×C8—42no—
65C42×C5—21no—
66C42×C5—21no—
67C42×C5—44no—
68C42×C5D812yes—
69C42×C5SD1612yes—
70C42×C5C2×Q811yescharacteristic
71C42×C5#4112yes—
72C42×C5#4111yescharacteristic
73#685—42no—
74C4⋊Dic5—22no—
75C4⋊Dic5—44no—
76C4⋊Dic5—42no—
77C4⋊Dic5—42no—
78#681—41no—
79#681—41no—
80C2×#168—41no—
81#532—51no—
82C2×C4⋊Q8—101no—
83#431C2×D512yes—
84#423—51no—
85C2×#104—101no—
86C2×#104—101no—
87#391—104no—
88#382—52no—
89#382—101no—
90C43C2×D511yescharacteristic
91#327—104no—
92C23×C5#12011yescharacteristic
93C22×D5—41no—
94C2×C4×C5—24no—
95C2×C4×C5—22no—
96C2×C4×C5—22no—
97C2×C4×C5—42no—
98C2×C4×C5—42no—
99C2×C4×C5C22⋊Q812yes—
100C2×C4×C5C22⋊Q811yescharacteristic
101C2×C4×C5#12411yescharacteristic
102C2×C4×C5#12412yes—
103C2×C4×C5C2×D811yescharacteristic
104C2×C4×C5C2×SD1611yescharacteristic
105C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
106C2×C4×C5#13711yescharacteristic
107C22⋊D5—81no—
108C22⋊D5—81no—
109C2×Dic5—48no—
110C2×Dic5—41no—
111C2×Dic5—44no—
112D20—41no—
113D20—41no—
114D20—82no—
115C4×D5—81no—
116C4×D5—81no—
117Dic10—41no—
118Dic10—41no—
119Dic10—88no—
120C5×C8—82no—
121#168—81no—
122C2×#41—101no—
123C22×Q8—102no—
124C2×M16—101no—
125C4⋊Q8—51no—
126C4⋊Q8—202no—
127C4⋊Q8—202no—
128#127—51no—
129#124—101no—
130#121—102no—
131C4×D4—102no—
132C2×C4⋊C4—102no—
133C2×C4⋊C4—102no—
134C2×C42—22no—
135C2×C42D2011yescharacteristic
136C2×C42D2011yescharacteristic
137C2×C42C22×D511yescharacteristic
138C4⋊C8—22no—
139C4⋊C8—102no—
140#104—202no—
141#104—202no—
142C22⋊C8—22no—
143C4×C8—22no—
144#95—54no—
145#95—104no—
146#95—102no—
147C22×C5—22no—
148C22×C5#39311yescharacteristic
149C22×C5#44711yescharacteristic
150C22×C5#44811yescharacteristic
151C2×D5—81no—
152C2×D5—82no—
153C4×C5—24no—
154C4×C5—22no—
155C4×C5—22no—
156C4×C5—42no—
157C4×C5#47411yescharacteristic
158C4×C5#47611yescharacteristic
159C4×C5#48611yescharacteristic
160C4×C5#48911yescharacteristic
161Dic5—84no—
162Dic5—81no—
163#41—201no—
164#41—201no—
165#41—201no—
166#41—201no—
167C2×Q8—101no—
168C2×Q8—204no—
169C2×Q8—208no—
170C2×D4—102no—
171C2×D4—101no—
172C2×D4—201no—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—104no—
176C22×C4—201no—
177C22×C4C2×D2011yescharacteristic
178C22×C4D4×D512yes—
179M16—201no—
180M16—201no—
181C2×C8—42no—
182C2×C8—201no—
183C4⋊C4—102no—
184C4⋊C4—204no—
185C4⋊C4—202no—
186C4⋊C4—202no—
187C22⋊C4—202no—
188C42—21no—
189C42—21no—
190C42—44no—
191C42#67712yes—
192C42D4012yes—
193C42#70912yes—
194C42#71111yescharacteristic
195C42Q8×D511yescharacteristic
196C2×C5—21no—
197C2×C5—21no—
198C2×C5#202311yescharacteristic
199C2×C5#203112yes—
200D5—161no—
201C23—201no—
202C23#402811yescharacteristic
203Q8—201no—
204Q8—201no—
205Q8—408no—
206D4—201no—
207D4—201no—
208D4—402no—
209D4—401no—
210D4—401no—
211C2×C4—24no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—208no—
217C2×C4—201no—
218C2×C4—204no—
219C2×C4—401no—
220C2×C4—401no—
221C2×C4#402111yescharacteristic
222C2×C4#403112yes—
223C2×C4#404212yes—
224C2×C4#404311yescharacteristic
225C2×C4C2×#67711yescharacteristic
226C2×C4C2×D4011yescharacteristic
227C2×C4#405411yescharacteristic
228C2×C4#405511yescharacteristic
229C8—82no—
230C8—401no—
231C5#1036211yescharacteristic, complemented, Sylow
232C22—22no—
233C22—401no—
234C22—402no—
235C22#6496211yescharacteristic
236C22#6502111yescharacteristic
237C22#6502711yescharacteristic
238C4—24no—
239C4—22no—
240C4—22no—
241C4—42no—
242C4—404no—
243C4—401no—
244C4#6498311yescharacteristic
245C4#6500311yescharacteristic
246C4#6513111yescharacteristic
247C4#6513511yescharacteristic
248C2—21no—
249C2—21no—
250C2—801no—
251C2#1059947111yescharacteristic
252C2#1059957212yes—
subgroupG/H
centerC22#64962
commutator, cosocleC2×C42×C5C23
FrattiniC2×C42C22×D5
FittingC5×#1276C2
socleC22×C5#393
prime radical#65811C22
hypercenter#1276D5
hypocenterC5#10362
LCSG ▷ C2×C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1276

Complements

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

NH ≅ G/Ntype
1. #10605039C2semidirect
4. C5×#1276C2semidirect
5. #10598229C2semidirect
29. #4020Q8semidirect
33. #4015Q8semidirect
47. #1276D5semidirect
231. C5#10362semidirect

Maximal subgroups

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

subgroupindex
#106050392
#106015832
#106001882
C5×#12762
#105982292
#103625