Finite Group Databasebeta

← #12002846

Subgroups — #12002846

Order 1280.

478 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 133 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
1C5×#2582C211yesmaximal, characteristic
2#10602419C212yesmaximal
3C2×Q8⋊#168C212yesmaximal
4#10600369C211yesmaximal, characteristic
5#10598125C211yesmaximal, characteristic
6C2×C4×C5×Q8C2212yes—
7C5×#398—22no—
8C5×#391—22no—
9C5×#389—22no—
10C5×#384C2211yescharacteristic
11C2×#3967—22no—
12C2×#3940—22no—
13#65224C2211yescharacteristic
14C2×C4⋊#168C2212yes—
15C2×C4×#168C2211yescharacteristic
16Q8⋊#168—24no—
17#64749—22no—
18#10437—51nomaximal, Sylow
19C22×C5×Q8D412yes—
20C4×C5×Q8—22no—
21C4×C5×Q8—22no—
22C4×C5×Q8—22no—
23C4×C5×Q8—22no—
24C2×C5×C4⋊C4—22no—
25C2×C5×C4⋊C4—22no—
26C2×C5×C4⋊C4—22no—
27C2×C5×C4⋊C4D412yes—
28C2×C5×C4⋊C4D412yes—
29C2×C42×C5—22no—
30C2×C42×C5C2311yescharacteristic
31C2×C4⋊Dic5—21no—
32C2×C4⋊Dic5—22no—
33C22×#168—21no—
34C22×#168—22no—
35C5×#95—24no—
36C5×#95—22no—
37#3967—44no—
38#3940—44no—
39C4⋊#168—22no—
40C4⋊#168—22no—
41C4×#168—21no—
42C4×#168D412yes—
43#2582D511yescharacteristic
44#1844—51no—
45#1803—52no—
46C2×Q8⋊C8—52no—
47#1296—51no—
48C2×C5×Q8—22no—
49C2×C5×Q8—22no—
50C2×C5×Q8—22no—
51C2×C5×Q8—22no—
52C2×C5×Q8—22no—
53C2×C5×Q8SD1614yes—
54C22×C4×C5—22no—
55C22×C4×C5—22no—
56C22×C4×C5—22no—
57C22×C4×C5C2×D411yescharacteristic
58C22×C4×C5C2×D412yes—
59C22×Dic5—41no—
60C5×C4⋊C4—22no—
61C5×C4⋊C4—22no—
62C5×C4⋊C4—42no—
63C5×C4⋊C4—42no—
64C5×C4⋊C4—42no—
65C5×C4⋊C4—42no—
66C5×C4⋊C4—42no—
67C5×C4⋊C4—82no—
68C42×C5—42no—
69C42×C5—42no—
70C42×C5C2×D411yescharacteristic
71C42×C5#4111yescharacteristic
72C42×C5#4112yes—
73C4⋊Dic5—42no—
74C4⋊Dic5—42no—
75C4⋊Dic5—42no—
76C2×#168—22no—
77C2×#168—22no—
78C2×#168—22no—
79C2×#168—42no—
80C2×#168—42no—
81C2×#168—42no—
82C2×C4×Q8C2×D512yes—
83C2×#106—102no—
84C2×C4⋊C8—52no—
85C2×#103—102no—
86C2×C4×C8—51no—
87#398—22no—
88#391—22no—
89#389—22no—
90#384—51no—
91#384C2×D511yescharacteristic
92#340—102no—
93Q8⋊C8—104no—
94C23×C5#12011yescharacteristic
95C5×Q8—24no—
96C5×Q8—24no—
97C5×Q8—42no—
98C5×Q8—42no—
99C2×C4×C5—21no—
100C2×C4×C5—21no—
101C2×C4×C5—24no—
102C2×C4×C5—42no—
103C2×C4×C5—42no—
104C2×C4×C5—42no—
105C2×C4×C5—44no—
106C2×C4×C5—42no—
107C2×C4×C5—42no—
108C2×C4×C5—42no—
109C2×C4×C5#12111yescharacteristic
110C2×C4×C5#12112yes—
111C2×C4×C5#12312yes—
112C2×C4×C5#12411yescharacteristic
113C2×C4×C5C2×SD1612yes—
114C2×C4×C5#13512yes—
115C2×C4×C5#13712yes—
116C2×C4×C5#13712yes—
117C2×Dic5—82no—
118C2×Dic5—81no—
119#168—24no—
120#168—82no—
121C22×Q8C22⋊D512yes—
122C22×C8—101no—
123C22×C8—102no—
124C4×Q8—22no—
125C4×Q8—22no—
126C4×Q8—22no—
127C4×Q8—22no—
128C2×C4⋊C4—22no—
129C2×C4⋊C4—22no—
130C2×C4⋊C4—22no—
131C2×C4⋊C4—102no—
132C2×C4⋊C4—101no—
133C2×C4⋊C4C22⋊D512yes—
134C2×C4⋊C4C22⋊D512yes—
135C2×C42—22no—
136C2×C42C22×D511yescharacteristic
137#106—204no—
138C4⋊C8—102no—
139C4⋊C8—102no—
140#103—204no—
141C4×C8—52no—
142C4×C8—101no—
143#95—24no—
144#95—22no—
145C22×C5#39411yescharacteristic
146C22×C5#44812yes—
147C22×C5#45212yes—
148C22×C5#45311yescharacteristic
149C22×C5#45611yescharacteristic
150C4×C5—21no—
151C4×C5—21no—
152C4×C5—44no—
153C4×C5—82no—
154C4×C5—82no—
155C4×C5#46512yes—
156C4×C5#47012yes—
157C4×C5#48312yes—
158C4×C5#48512yes—
159Dic5—161no—
160C2×Q8—22no—
161C2×Q8—22no—
162C2×Q8—22no—
163C2×Q8—22no—
164C2×Q8—22no—
165C2×Q8#68814yes—
166C22×C4—22no—
167C22×C4—22no—
168C22×C4—22no—
169C22×C4—201no—
170C22×C4C2×C22⋊D511yescharacteristic
171C22×C4C2×C22⋊D512yes—
172C2×C8—102no—
173C2×C8—102no—
174C2×C8—102no—
175C2×C8—202no—
176C2×C8—202no—
177C2×C8—202no—
178C4⋊C4—22no—
179C4⋊C4—22no—
180C4⋊C4—42no—
181C4⋊C4—42no—
182C4⋊C4—42no—
183C4⋊C4—42no—
184C4⋊C4—42no—
185C4⋊C4—82no—
186C4⋊C4—202no—
187C4⋊C4—202no—
188C4⋊C4—202no—
189C42—42no—
190C42—42no—
191C42D4×D511yescharacteristic
192C42#71111yescharacteristic
193C42#71112yes—
194C2×C5#162311yescharacteristic
195C2×C5#163011yescharacteristic
196C2×C5#165312yes—
197C2×C5#203512yes—
198C2×C5#203911yescharacteristic
199C23#409911yescharacteristic
200Q8—24no—
201Q8—24no—
202Q8—42no—
203Q8—42no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—24no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—44no—
211C2×C4—42no—
212C2×C4—42no—
213C2×C4—42no—
214C2×C4—402no—
215C2×C4—401no—
216C2×C4#408112yes—
217C2×C4#408211yescharacteristic
218C2×C4#408411yescharacteristic
219C2×C4#408512yes—
220C2×C4C2×#68812yes—
221C2×C4#408812yes—
222C2×C4#409612yes—
223C2×C4#409712yes—
224C8—104no—
225C8—402no—
226C5#1043711yescharacteristic, complemented, Sylow
227C22#6551111yescharacteristic
228C22#6551612yes—
229C22#6552812yes—
230C22#6553011yescharacteristic
231C22#6553511yescharacteristic
232C4—21no—
233C4—21no—
234C4—44no—
235C4—82no—
236C4—82no—
237C4—801no—
238C4#6533212yes—
239C4#6533412yes—
240C4#6533712yes—
241C4#6534112yes—
242C2#1060248712yes—
243C2#1060266911yescharacteristic
244C2#1060273112yes—
245C2#1060273211yescharacteristic
246C2#1060273711yescharacteristic
subgroupG/H
centerC23#4099
commutator, cosocleC2×C42×C5C23
FrattiniC2×C42C22×D5
FittingC5×#2582C2
socle, prime radicalC23×C5#120
hypercenter#2582D5
hypocenterC5#10437
LCSG ▷ C2×C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2582

Complements

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

NH ≅ G/Ntype
226. C5#10437semidirect

Maximal subgroups

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

subgroupindex
C5×#25822
#106024192
C2×Q8⋊#1682
#106003692
#105981252
#104375