Finite Group Databasebeta

← #12000278

Subgroups — #12000278

Order 1280.

584 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 103 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#10614173C212yesmaximal, complemented
2#10610230C211yesmaximal, characteristic
3C5×#1985C211yesmaximal, characteristic, complemented
4#10601219C212yesmaximal, complemented
5#10598151C211yesmaximal, characteristic, complemented
6C2×C4×C5×Q8C2211yescharacteristic
7C2×#4050—22no—
8#65811C2212yes—
9C2×C5×C4⋊C8C2211yescharacteristic
10C2×C5×#97C2211yescharacteristic
11#65516—22no—
12#65316—22no—
13C4×#688—24no—
14#65309—22no—
15#65257—22no—
16#65214C2212yes—
17#65004—22no—
18#65001—22no—
19C5×#336—22no—
20#64703—24no—
21#10034—51nomaximal, Sylow
22C22×C5×Q8D411yescharacteristic
23C2×#709—22no—
24C22×C5×C8—21no—
25C22×C5×C8D412yes—
26C4×C5×Q8—22no—
27C4×C5×Q8—22no—
28C2×C5×C4⋊C4—21no—
29C2×C5×C4⋊C4D411yescharacteristic
30C2×C42×C5—21no—
31C2×C42×C5C2311yescharacteristic
32C2×#688—24no—
33#4076—22no—
34#4076—22no—
35C2×Dic20—22no—
36#4050—44no—
37#4050—44no—
38C2×D40—22no—
39C2×#677—24no—
40#4021—22no—
41#4020D412yes—
42C4×D20—22no—
43C4×D20—22no—
44#4015D412yes—
45C5×C4⋊C8—22no—
46C5×#97—22no—
47#3967—24no—
48C22⋊#168—22no—
49#3941—24no—
50#3940—24no—
51C4⋊#168—22no—
52C4×#168D414yes—
53#3150—51no—
54#3103—52no—
55#1985D511yescharacteristic, complemented
56#1480—52no—
57#1275—51no—
58C2×C5×Q8—22no—
59C2×C5×Q8—42no—
60C22×C4×C5—21no—
61C22×C4×C5—21no—
62C22×C4×C5C2×D411yescharacteristic
63C22×C4×C5C2×D411yescharacteristic
64C22×C4×C5#4111yescharacteristic
65C2×C22⋊D5—42no—
66#709—44no—
67#709—44no—
68C2×D20—22no—
69C2×D20—22no—
70C2×D20—22no—
71C2×C4×D5—42no—
72C2×Dic10—22no—
73C2×C5×C8—22no—
74C2×C5×C8—22no—
75C2×C5×C8—41no—
76C2×C5×C8—42no—
77C2×C5×C8SD1614yescomplemented
78C5×C4⋊C4—22no—
79C5×C4⋊C4—42no—
80C42×C5—41no—
81C42×C5—41no—
82C42×C5C2×D412yes—
83C42×C5C2×D412yes—
84#688—48no—
85#685—42no—
86#685—42no—
87C4⋊Dic5—22no—
88C4⋊Dic5—22no—
89C2×#168—24no—
90Dic20—44no—
91D40—44no—
92#677—48no—
93C2×#135—102no—
94#532—52no—
95C2×C4×Q8C2×D511yescharacteristic
96#497—102no—
97#496—102no—
98#481—102no—
99#475—102no—
100#460—102no—
101#448—102no—
102C4×SD16—104no—
103#431—52no—
104C2×C4⋊C8C2×D511yescharacteristic
105C2×#97C2×D511yescharacteristic
106#336—22no—
107D4⋊C8—104no—
108C23×C5#12111yescharacteristic
109C22×D5—42no—
110C5×Q8—24no—
111C5×Q8—42no—
112C2×C4×C5—22no—
113C2×C4×C5—41no—
114C2×C4×C5—41no—
115C2×C4×C5—41no—
116C2×C4×C5—41no—
117C2×C4×C5—42no—
118C2×C4×C5—41no—
119C2×C4×C5#12012yes—
120C2×C4×C5#12011yescharacteristic
121C2×C4×C5#12112yes—
122C2×C4×C5#12711yescharacteristic
123C2×C4×C5C2×SD1612yes—
124C2×C4×C5AGL(1,ℤ/8)12yes—
125C22⋊D5—84no—
126C2×Dic5—42no—
127D20—44no—
128D20—44no—
129D20—44no—
130C4×D5—82no—
131C4×D5—82no—
132Dic10—44no—
133C5×C8—24no—
134C5×C8—81no—
135#168—44no—
136C2×#41—102no—
137C22×Q8D2011yescharacteristic
138#135—204no—
139#135—204no—
140C2×Q16—102no—
141C2×SD16—104no—
142C2×SD16—104no—
143C2×D8—102no—
144C22×C8—21no—
145C22×C8C22⋊D512yes—
146C4⋊Q8—52no—
147#127—52no—
148#124—102no—
149#121—102no—
150#121—102no—
151C4×Q8—22no—
152C4×Q8—22no—
153C4×D4—102no—
154C4×D4—102no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4D2011yescharacteristic
157C2×C42—21no—
158C2×C42C22×D511yescharacteristic
159#106—104no—
160C4⋊C8—22no—
161C4⋊C8—102no—
162#103—104no—
163#102—104no—
164C22⋊C8—102no—
165#97—22no—
166C4×C8—54no—
167C22×C5—21no—
168C22×C5—21no—
169C22×C5#39211yescharacteristic
170C22×C5#46012yes—
171C2×D5—82no—
172C2×D5—82no—
173C2×D5—82no—
174C4×C5—22no—
175C4×C5—22no—
176C4×C5—42no—
177C4×C5—81no—
178C4×C5#45012yes—
179C4×C5#49211yescharacteristic
180C4×C5#49611yescharacteristic
181Dic5—82no—
182#41—204no—
183#41—204no—
184C2×Q8—22no—
185C2×Q8—42no—
186C2×Q8—102no—
187C2×D4—102no—
188C2×D4—102no—
189C2×D4—102no—
190C2×D4—202no—
191C22×C4—21no—
192C22×C4—21no—
193C22×C4—202no—
194C22×C4C2×D2011yescharacteristic
195C22×C4#70911yescharacteristic
196C22×C4C2×C22⋊D511yescharacteristic
197Q16—204no—
198SD16—208no—
199SD16—208no—
200D8—204no—
201C2×C8—22no—
202C2×C8—22no—
203C2×C8—41no—
204C2×C8—42no—
205C2×C8—104no—
206C2×C8#68814yescomplemented
207C4⋊C4—22no—
208C4⋊C4—42no—
209C4⋊C4—102no—
210C4⋊C4—102no—
211C22⋊C4—202no—
212C22⋊C4—202no—
213C42—41no—
214C42—41no—
215C42D4×D512yes—
216C42D4×D512yes—
217C2×C5—22no—
218C2×C5#201011yescharacteristic
219C2×C5#201411yescharacteristic
220C2×C5#201711yescharacteristic
221D5—162no—
222C23—202no—
223C23#407611yescharacteristic
224Q8—24no—
225Q8—42no—
226Q8—204no—
227D4—204no—
228D4—204no—
229D4—204no—
230D4—404no—
231C2×C4—22no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—42no—
237C2×C4—41no—
238C2×C4—202no—
239C2×C4—402no—
240C2×C4—402no—
241C2×C4#402812yes—
242C2×C4#403012yes—
243C2×C4#408311yescharacteristic
244C2×C4#408611yescharacteristic
245C2×C4C2×#68812yes—
246C2×C4#409512yes—
247C8—24no—
248C8—81no—
249C8—204no—
250C5#1003411yescharacteristic, complemented, Sylow
251C22—21no—
252C22—21no—
253C22—402no—
254C22—402no—
255C22—402no—
256C22#6524911yescharacteristic
257C22#6531612yes—
258C4—22no—
259C4—22no—
260C4—42no—
261C4—81no—
262C4—402no—
263C4#6533512yes—
264C4#6534711yescharacteristic
265C4#6537411yescharacteristic
266C2—22no—
267C2—802no—
268C2#1060048111yescharacteristic
269C2#1060078611yescharacteristic
270C2#1060080611yescharacteristic
subgroupG/H
centerC2×C4#4086
commutator, cosocleC2×C42×C5C23
FrattiniC2×C42C22×D5
FittingC5×#1985C2
socleC22×C5#392
prime radical#10610230C2
hypercenter#1985D5
hypocenterC5#10034
LCSG ▷ C2×C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1985

Complements

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

NH ≅ G/Ntype
1. #10614173C2semidirect
3. C5×#1985C2semidirect
4. #10601219C2semidirect
5. #10598151C2semidirect
55. #1985D5semidirect
77. C2×C5×C8SD16semidirect
206. C2×C8#688semidirect
250. C5#10034semidirect

Maximal subgroups

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

subgroupindex
#106141732
#106102302
C5×#19852
#106012192
#105981512
#100345