Finite Group Databasebeta

← #11995066

Subgroups — #11995066

Order 1280.

586 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 586 conjugacy classes of subgroups — too many to draw. Only its 135 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×#2855C211yesmaximal, characteristic
2C2×#65226C211yesmaximal, characteristic
3C2×#64758C212yesmaximal
4#10602324C211yesmaximal, characteristic
5#10598115C212yesmaximal
6C2×C5×C22⋊Q8C2211yescharacteristic
7C22×C42×C5C2211yescharacteristic
8C5×#391C412yescomplemented
9C5×#389C412yescomplemented
10C5×#387—22no—
11C5×#385—21no—
12C5×#381—21no—
13C5×#380C2211yescharacteristic
14C2×#3963—21no—
15C2×#3963—21no—
16C2×#3963C2212yes—
17C2×C22⋊#168C2212yes—
18#65226—24no—
19#64758—24no—
20#64744—22no—
21#9153—51nomaximal, Sylow
22C22×C5×Q8C2×C411yescharacteristic
23C23×C4×C5D411yescharacteristic
24C23×C4×C5D411yescharacteristic
25C23×C4×C5C2311yescharacteristic
26C23×Dic5—22no—
27C5×C22⋊Q8—22no—
28C5×C22⋊Q8—22no—
29C2×C5×C4⋊C4—22no—
30C2×C5×C4⋊C4—21no—
31C2×C5×C4⋊C4C2×C411yescharacteristic
32C2×C5×C4⋊C4C2×C412yes—
33C2×C5×C22⋊C4—21no—
34C2×C5×C22⋊C4—21no—
35C2×C42×C5—22no—
36C2×C42×C5—22no—
37C2×C42×C5C2×C412yes—
38C2×C42×C5D412yes—
39C22×#168—22no—
40C5×#95—22no—
41C5×#95—22no—
42C5×#95—22no—
43C5×#95—21no—
44#3963—24no—
45#3963—24no—
46#3963—22no—
47#3963D414yes—
48C22⋊#168—22no—
49C22⋊#168—22no—
50#2855D511yescharacteristic
51C2×#383—51no—
52#1817—51no—
53C2×#328—52no—
54#1294—52no—
55C24×C5C2×D411yescharacteristic
56C2×C5×Q8—22no—
57C2×C5×Q8—42no—
58C22×C4×C5—21no—
59C22×C4×C5—21no—
60C22×C4×C5—21no—
61C22×C4×C5—21no—
62C22×C4×C5—22no—
63C22×C4×C5—22no—
64C22×C4×C5—21no—
65C22×C4×C5—22no—
66C22×C4×C5—21no—
67C22×C4×C5—42no—
68C22×C4×C5—42no—
69C22×C4×C5C22⋊C412yes—
70C22×C4×C5C22⋊C412yes—
71C22×C4×C5C22×C411yescharacteristic
72C22×C4×C5C2×D412yes—
73C22×C4×C5C2×D411yescharacteristic
74C22×C4×C5#4112yes—
75C22×Dic5—24no—
76C22×Dic5—44no—
77C22×Dic5—44no—
78C22×Dic5—42no—
79C22×Dic5—42no—
80C5×C4⋊C4—22no—
81C5×C4⋊C4—42no—
82C5×C4⋊C4—44no—
83C5×C4⋊C4—42no—
84C5×C22⋊C4—41no—
85C5×C22⋊C4—41no—
86C5×C22⋊C4—42no—
87C42×C5—24no—
88C42×C5—24no—
89C2×#168—44no—
90C2×#168—42no—
91C2×C22⋊Q8C2×D511yescharacteristic
92C22×C42C2×D511yescharacteristic
93C2×C22⋊C8—52no—
94#391Dic512yescomplemented
95#389Dic512yescomplemented
96#387—22no—
97#385—21no—
98#383—104no—
99#381—21no—
100#380C2×D511yescharacteristic
101C2×#95—52no—
102C2×#95—101no—
103C2×#95—101no—
104#336—102no—
105#328—104no—
106C23×C5—22no—
107C23×C5—22no—
108C23×C5C2×C22⋊C411yescharacteristic
109C23×C5#12011yescharacteristic
110C23×C5#12311yescharacteristic
111C23×C5#13512yes—
112C23×C5#13712yes—
113C5×Q8—82no—
114C2×C4×C5—22no—
115C2×C4×C5—22no—
116C2×C4×C5—22no—
117C2×C4×C5—22no—
118C2×C4×C5—22no—
119C2×C4×C5—22no—
120C2×C4×C5—22no—
121C2×C4×C5—22no—
122C2×C4×C5—42no—
123C2×C4×C5—42no—
124C2×C4×C5—42no—
125C2×C4×C5—42no—
126C2×C4×C5—42no—
127C2×C4×C5—42no—
128C2×C4×C5—41no—
129C2×C4×C5—41no—
130C2×C4×C5—42no—
131C2×C4×C5—42no—
132C2×C4×C5—42no—
133C2×C4×C5—42no—
134C2×C4×C5—42no—
135C2×C4×C5C4×D412yes—
136C2×C4×C5#12112yes—
137C2×Dic5—44no—
138C2×Dic5—44no—
139C2×Dic5—44no—
140C2×Dic5—84no—
141C2×Dic5—84no—
142#168—82no—
143C22×Q8C2×Dic511yescharacteristic
144C23×C4—102no—
145C23×C4C22⋊D511yescharacteristic
146C23×C4C22⋊D511yescharacteristic
147C23×C4C22×D511yescharacteristic
148C22×C8—102no—
149C22⋊Q8—22no—
150C22⋊Q8—22no—
151C2×C4⋊C4—22no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4C2×Dic511yescharacteristic
154C2×C4⋊C4C2×Dic512yes—
155C2×C22⋊C4—21no—
156C2×C22⋊C4—21no—
157C2×C42—22no—
158C2×C42—22no—
159C2×C42C2×Dic512yes—
160C2×C42C22⋊D512yes—
161C22⋊C8—102no—
162C22⋊C8—102no—
163#95—22no—
164#95—22no—
165#95—22no—
166#95—21no—
167#95—54no—
168#95—104no—
169#95—104no—
170#95—102no—
171C22×C5—21no—
172C22×C5—21no—
173C22×C5—21no—
174C22×C5—21no—
175C22×C5—24no—
176C22×C5—24no—
177C22×C5#38611yescharacteristic
178C22×C5#41012yes—
179C22×C5#41611yescharacteristic
180C22×C5#41911yescharacteristic
181C22×C5#42112yes—
182C22×C5#45212yes—
183C22×C5#48512yes—
184C4×C5—22no—
185C4×C5—22no—
186C4×C5—42no—
187C4×C5—42no—
188C4×C5—81no—
189C4×C5—81no—
190C4×C5—82no—
191Dic5—84no—
192C24C2×C22⋊D511yescharacteristic
193C2×Q8—22no—
194C2×Q8—42no—
195C22×C4—22no—
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—22no—
201C22×C4—22no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—42no—
205C22×C4—42no—
206C22×C4—104no—
207C22×C4—204no—
208C22×C4—204no—
209C22×C4—202no—
210C22×C4—202no—
211C22×C4C22⋊Dic512yes—
212C22×C4C22⋊Dic512yes—
213C22×C4D4×D512yes—
214C22×C4#71112yes—
215C22×C4C22×Dic511yescharacteristic
216C22×C4C2×C22⋊D511yescharacteristic
217C2×C8—204no—
218C2×C8—202no—
219C4⋊C4—22no—
220C4⋊C4—42no—
221C4⋊C4—44no—
222C4⋊C4—42no—
223C22⋊C4—42no—
224C22⋊C4—41no—
225C22⋊C4—41no—
226C42—24no—
227C42—24no—
228C2×C5—22no—
229C2×C5—22no—
230C2×C5#151512yes—
231C2×C5#152112yes—
232C2×C5#187311yescharacteristic
233C2×C5#189711yescharacteristic
234C2×C5#189911yescharacteristic
235C23—22no—
236C23—22no—
237C23#408111yescharacteristic
238C23#408311yescharacteristic
239C23#408812yes—
240C23#409612yes—
241C23C2×C22⋊Dic511yescharacteristic
242Q8—82no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—204no—
265C2×C4—204no—
266C2×C4—204no—
267C2×C4—404no—
268C2×C4—404no—
269C2×C4D4×Dic512yes—
270C2×C4#408512yes—
271C8—402no—
272C5#915311yescharacteristic, complemented, Sylow
273C22—21no—
274C22—21no—
275C22—21no—
276C22—21no—
277C22—24no—
278C22—24no—
279C22#6533412yes—
280C22#6533612yes—
281C22#6550911yescharacteristic
282C22#6551411yescharacteristic
283C22#6552211yescharacteristic
284C22#6552512yes—
285C22#6552912yes—
286C4—22no—
287C4—22no—
288C4—42no—
289C4—42no—
290C4—81no—
291C4—81no—
292C4—82no—
293C4—404no—
294C2—22no—
295C2—22no—
296C2#1060248611yescharacteristic
297C2#1060249811yescharacteristic
298C2#1060250511yescharacteristic
299C2#1060255012yes—
300C2#1060263012yes—
subgroupG/H
centerC23C2×C22⋊Dic5
commutatorC22×C4×C5C22×C4
FrattiniC23×C4C22×D5
FittingC5×#2855C2
socleC23×C5C2×C22⋊C4
prime radicalC24×C5C2×D4
cosocleC23×C4×C5C23
hypercenter#2855D5
hypocenterC5#9153
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2855

Complements

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

NH ≅ G/Ntype
8. C5×#391C4semidirect
9. C5×#389C4semidirect
94. #391Dic5semidirect
95. #389Dic5semidirect
272. C5#9153semidirect

Maximal subgroups

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

subgroupindex
C5×#28552
C2×#652262
C2×#647582
#106023242
#105981152
#91535