Finite Group Databasebeta

← #12001579

Subgroups — #12001579

Order 1280.

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

normal subgroups only

This group has 574 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#10614946C212yesmaximal, complemented
2#10610230C211yesmaximal, characteristic
3C5×#1960C211yesmaximal, characteristic, complemented
4#10600338C212yesmaximal, complemented
5#10598152C211yesmaximal, characteristic, complemented
6C2×C5×C4⋊Q8C2211yescharacteristic
7C2×#4050—22no—
8#65811C2212yes—
9C2×C5×#103—22no—
10C2×C5×#97C2211yescharacteristic
11C5×#382C2211yescharacteristic
12#65377—22no—
13#65376—24no—
14#65367—22no—
15#65256—24no—
16#65214C2212yes—
17#65004—22no—
18#65001—22no—
19#64671—24no—
20#10225—51nomaximal, Sylow
21C22×C5×Q8—21no—
22C2×#709—22no—
23C22×C5×C8D412yes—
24C5×C4⋊Q8—22no—
25C5×C4⋊Q8—21no—
26C5×C4⋊Q8D412yes—
27C2×C5×C4⋊C4—22no—
28C2×C5×C4⋊C4—21no—
29C2×C42×C5C2311yescharacteristic
30#4076—22no—
31#4076—22no—
32C2×Dic20—22no—
33#4050—44no—
34#4050—44no—
35C2×D40—22no—
36C2×#677—24no—
37#4021—22no—
38#4020D412yes—
39C4×D20—22no—
40C4×D20—22no—
41#4015D412yes—
42C5×#103—44no—
43C5×#97—22no—
44C5×#95—22no—
45C22⋊#168D414yes—
46#3941—28no—
47#3939—28no—
48C4⋊#168—22no—
49C4×#168—22no—
50#3226—52no—
51#3150—51no—
52#1960D511yescharacteristic, complemented
53#1517—52no—
54#1281—51no—
55C2×C5×Q8—22no—
56C2×C5×Q8—41no—
57C2×C5×Q8—42no—
58C2×C5×Q8—42no—
59C22×C4×C5—41no—
60C22×C4×C5—41no—
61C22×C4×C5C2×D412yes—
62C22×C4×C5C2×D411yescharacteristic
63C2×C22⋊D5—42no—
64#709—44no—
65#709—44no—
66C2×D20—22no—
67C2×D20—22no—
68C2×D20—22no—
69C2×C4×D5—42no—
70C2×Dic10—22no—
71C2×C5×C8—22no—
72C2×C5×C8—22no—
73C2×C5×C8D814yes—
74C5×C4⋊C4—24no—
75C5×C4⋊C4—42no—
76C5×C4⋊C4—42no—
77C42×C5C2×D411yescharacteristic
78C42×C5C2×D412yes—
79C42×C5#4111yescharacteristic
80#685—42no—
81#685—42no—
82C4⋊Dic5—22no—
83C4⋊Dic5—22no—
84C2×#168—24no—
85Dic20—44no—
86D40—44no—
87#677—48no—
88C2×#135—102no—
89#532—52no—
90C2×C4⋊Q8C2×D511yescharacteristic
91#500—102no—
92#497—102no—
93#496—102no—
94#486—102no—
95#480—104no—
96#474—104no—
97#431—52no—
98C2×#103—22no—
99C2×#97C2×D511yescharacteristic
100#382C2×D511yescharacteristic
101#327—104no—
102C23×C5#12711yescharacteristic
103C22×D5—42no—
104C5×Q8—44no—
105C5×Q8—82no—
106C2×C4×C5—42no—
107C2×C4×C5—42no—
108C2×C4×C5—81no—
109C2×C4×C5—81no—
110C2×C4×C5—82no—
111C2×C4×C5—81no—
112C2×C4×C5#12012yes—
113C2×C4×C5#12011yescharacteristic
114C2×C4×C5#12112yes—
115C2×C4×C5#12111yescharacteristic
116C2×C4×C5C2×D812yes—
117C2×C4×C5AGL(1,ℤ/8)12yes—
118C22⋊D5—82no—
119C22⋊D5—82no—
120C2×Dic5—42no—
121D20—44no—
122D20—44no—
123D20—82no—
124C4×D5—84no—
125Dic10—44no—
126C5×C8—24no—
127#168—44no—
128C2×#41—102no—
129C22×Q8—21no—
130#135—204no—
131#135—204no—
132C2×Q16—102no—
133C2×SD16—104no—
134C2×D8—102no—
135C22×C8C22⋊D512yes—
136C4⋊Q8—21no—
137C4⋊Q8—22no—
138C4⋊Q8—52no—
139C4⋊Q8D2012yes—
140#127—52no—
141#124—102no—
142#121—102no—
143#121—102no—
144C4×D4—102no—
145C4×D4—102no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—21no—
148C2×C42C22×D511yescharacteristic
149#107—108no—
150C4⋊C8—102no—
151#103—44no—
152#102—108no—
153C22⋊C8—54no—
154#97—22no—
155C4×C8—102no—
156#95—22no—
157C22×C5—22no—
158C22×C5#39211yescharacteristic
159C22×C5#49311yescharacteristic
160C22×C5#49611yescharacteristic
161C2×D5—82no—
162C2×D5—82no—
163C2×D5—82no—
164C4×C5—22no—
165C4×C5—22no—
166C4×C5—82no—
167C4×C5—161no—
168C4×C5#44712yes—
169C4×C5#45912yes—
170Dic5—82no—
171#41—204no—
172#41—204no—
173C2×Q8—22no—
174C2×Q8—41no—
175C2×Q8—42no—
176C2×Q8—42no—
177C2×Q8—102no—
178C2×D4—102no—
179C2×D4—102no—
180C2×D4—102no—
181C2×D4—202no—
182C22×C4—41no—
183C22×C4—41no—
184C22×C4—202no—
185C22×C4D4×D512yes—
186C22×C4C2×C22⋊D511yescharacteristic
187Q16—204no—
188SD16—208no—
189D8—204no—
190C2×C8—22no—
191C2×C8—22no—
192C2×C8—104no—
193C2×C8#68614yes—
194C4⋊C4—24no—
195C4⋊C4—42no—
196C4⋊C4—42no—
197C4⋊C4—102no—
198C4⋊C4—102no—
199C22⋊C4—202no—
200C22⋊C4—202no—
201C42C2×D2011yescharacteristic
202C42#70911yescharacteristic
203C42D4×D512yes—
204C2×C5—21no—
205C2×C5—21no—
206C2×C5#200912yes—
207C2×C5#201111yescharacteristic
208D5—162no—
209C23—202no—
210C23#408611yescharacteristic
211Q8—44no—
212Q8—82no—
213Q8—204no—
214D4—204no—
215D4—204no—
216D4—402no—
217D4—402no—
218D4—402no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—81no—
222C2×C4—81no—
223C2×C4—82no—
224C2×C4—81no—
225C2×C4—202no—
226C2×C4—404no—
227C2×C4#402812yes—
228C2×C4#403012yes—
229C2×C4#407611yescharacteristic
230C2×C4C2×#68612yes—
231C2×C4#408311yescharacteristic
232C2×C4#409512yes—
233C8—24no—
234C8—204no—
235C5#1022511yescharacteristic, complemented, Sylow
236C22—22no—
237C22—402no—
238C22—402no—
239C22—402no—
240C22#6524911yescharacteristic
241C22#6534711yescharacteristic
242C22#6536211yescharacteristic
243C4—22no—
244C4—22no—
245C4—82no—
246C4—161no—
247C4—402no—
248C4#6530412yes—
249C4#6532512yes—
250C2—21no—
251C2—21no—
252C2—802no—
253C2#1060045111yescharacteristic
254C2#1060114412yes—
subgroupG/H
centerC22#65249
commutator, cosocleC2×C42×C5C23
FrattiniC2×C42C22×D5
FittingC5×#1960C2
socleC22×C5#392
prime radical#10610230C2
hypercenter#1960D5
hypocenterC5#10225
LCSG ▷ C2×C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1960

Complements

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

NH ≅ G/Ntype
1. #10614946C2semidirect
3. C5×#1960C2semidirect
4. #10600338C2semidirect
5. #10598152C2semidirect
52. #1960D5semidirect
235. C5#10225semidirect

Maximal subgroups

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

subgroupindex
#106149462
#106102302
C5×#19602
#106003382
#105981522
#102255