Finite Group Databasebeta

← #11995025

Subgroups — #11995025

Order 1280.

694 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 694 conjugacy classes of subgroups — too many to draw. Only its 139 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
1C2×C5×#376C211yesmaximal, characteristic
2#10613806C211yesmaximal, characteristic
3#10602324C211yesmaximal, characteristic
4C2×#64672C212yesmaximal
5#10598103C212yesmaximal
6C22×C42×C5—21no—
7C22×C42×C5C2211yescharacteristic
8C2×#4070C2211yescharacteristic
9C5×#376—24no—
10C2×C5×#95—21no—
11C2×C5×#95C2212yes—
12#65501C2211yescharacteristic
13#65500—21no—
14#65499—21no—
15C2×C22⋊#168C2212yes—
16#65222—22no—
17#65218C412yescomplemented
18#65217C412yescomplemented
19#64744—22no—
20#64672—24no—
21#9145—51nomaximal, Sylow
22C23×C4×C5—22no—
23C23×C4×C5D411yescharacteristic
24C23×C4×C5D411yescharacteristic
25C23×C4×C5C2311yescharacteristic
26C22×Dic10C2×C411yescharacteristic
27C2×C42×C5—24no—
28C2×C42×C5—28no—
29C2×C42×C5—22no—
30C2×C42×C5—22no—
31C2×C42×C5C2×C412yes—
32C2×C42×C5D412yes—
33C2×C22⋊Dic5—21no—
34C2×C22⋊Dic5—21no—
35C2×C4⋊Dic5C2×C411yescharacteristic
36C2×C4⋊Dic5C2×C412yes—
37#4070—22no—
38#4070—22no—
39C2×#683—22no—
40C2×#683—21no—
41C22×#168—22no—
42C5×#95—24no—
43C5×#95—22no—
44C5×#95D414yes—
45#3963—22no—
46#3963—22no—
47#3963—22no—
48#3963—21no—
49C22⋊#168—22no—
50C22⋊#168—22no—
51#2855—51no—
52C2×#376D511yescharacteristic
53#1817—51no—
54C2×#328—52no—
55#1294—52no—
56C24×C5C2×D411yescharacteristic
57C22×C4×C5—21no—
58C22×C4×C5—21no—
59C22×C4×C5—24no—
60C22×C4×C5—28no—
61C22×C4×C5—24no—
62C22×C4×C5—21no—
63C22×C4×C5—21no—
64C22×C4×C5—22no—
65C22×C4×C5—22no—
66C22×C4×C5—42no—
67C22×C4×C5—44no—
68C22×C4×C5—42no—
69C22×C4×C5—42no—
70C22×C4×C5C22⋊C412yes—
71C22×C4×C5C22⋊C412yes—
72C22×C4×C5C22×C411yescharacteristic
73C22×C4×C5C2×D411yescharacteristic
74C22×C4×C5C2×D412yes—
75C22×C4×C5#4112yes—
76C22×Dic5—21no—
77C22×Dic5—22no—
78C22×Dic5—21no—
79C2×Dic10—22no—
80C2×Dic10—42no—
81C42×C5—216no—
82C42×C5—24no—
83C42×C5—24no—
84C22⋊Dic5—41no—
85C22⋊Dic5—41no—
86C22⋊Dic5—42no—
87C4⋊Dic5—22no—
88C4⋊Dic5—42no—
89#683—44no—
90#683—42no—
91C2×#168—44no—
92C2×#168—42no—
93C2×C22⋊Q8—51no—
94C22×C42—21no—
95C22×C42C2×D511yescharacteristic
96C2×C22⋊C8—52no—
97#391—52no—
98#389—52no—
99#387—102no—
100#385—101no—
101#381—101no—
102#380—51no—
103#376—24no—
104C2×#95—21no—
105C2×#95C2×D512yes—
106#336—102no—
107#328—104no—
108C23×C5—22no—
109C23×C5—22no—
110C23×C5C2×C22⋊C411yescharacteristic
111C23×C5#12011yescharacteristic
112C23×C5#12311yescharacteristic
113C23×C5#13512yes—
114C23×C5#13712yes—
115C2×C4×C5—24no—
116C2×C4×C5—24no—
117C2×C4×C5—22no—
118C2×C4×C5—22no—
119C2×C4×C5—22no—
120C2×C4×C5—22no—
121C2×C4×C5—28no—
122C2×C4×C5—22no—
123C2×C4×C5—22no—
124C2×C4×C5—22no—
125C2×C4×C5—42no—
126C2×C4×C5—42no—
127C2×C4×C5—44no—
128C2×C4×C5—48no—
129C2×C4×C5—48no—
130C2×C4×C5—42no—
131C2×C4×C5—44no—
132C2×C4×C5—42no—
133C2×C4×C5#10414yes—
134C2×C4×C5C4×D412yes—
135C2×C4×C5#12112yes—
136C2×Dic5—41no—
137C2×Dic5—41no—
138C2×Dic5—42no—
139C2×Dic5—42no—
140C2×Dic5—42no—
141C2×Dic5—42no—
142C2×Dic5—42no—
143Dic10—82no—
144#168—82no—
145C22×Q8—51no—
146C23×C4—22no—
147C23×C4C22⋊D511yescharacteristic
148C23×C4C22⋊D511yescharacteristic
149C23×C4C22×D511yescharacteristic
150C22×C8—102no—
151C22⋊Q8—102no—
152C22⋊Q8—102no—
153C2×C4⋊C4—51no—
154C2×C4⋊C4—52no—
155C2×C4⋊C4—102no—
156C2×C4⋊C4—101no—
157C2×C22⋊C4—101no—
158C2×C22⋊C4—101no—
159C2×C42—24no—
160C2×C42—28no—
161C2×C42—22no—
162C2×C42—22no—
163C2×C42C4×D512yes—
164C2×C42D2012yes—
165C22⋊C8—102no—
166C22⋊C8—102no—
167#95—24no—
168#95—22no—
169#95—102no—
170#95—102no—
171#95—102no—
172#95—101no—
173#95C22⋊D514yes—
174C22×C5—21no—
175C22×C5—21no—
176C22×C5—21no—
177C22×C5—21no—
178C22×C5—24no—
179C22×C5—24no—
180C22×C5#38611yescharacteristic
181C22×C5#41012yes—
182C22×C5#41611yescharacteristic
183C22×C5#41911yescharacteristic
184C22×C5C2×#10412yes—
185C22×C5#45212yes—
186C22×C5#48512yes—
187C4×C5—24no—
188C4×C5—22no—
189C4×C5—22no—
190C4×C5—48no—
191C4×C5—42no—
192Dic5—81no—
193Dic5—81no—
194Dic5—82no—
195C24C2×C22⋊D511yescharacteristic
196C2×Q8—102no—
197C2×Q8—202no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—24no—
201C22×C4—28no—
202C22×C4—22no—
203C22×C4—22no—
204C22×C4—21no—
205C22×C4—24no—
206C22×C4—21no—
207C22×C4—42no—
208C22×C4—44no—
209C22×C4—42no—
210C22×C4—42no—
211C22×C4—102no—
212C22×C4—101no—
213C22×C4—101no—
214C22×C4#68512yes—
215C22×C4#68512yes—
216C22×C4C2×C4×D511yescharacteristic
217C22×C4C2×D2011yescharacteristic
218C22×C4#70912yes—
219C22×C4C2×C22⋊D512yes—
220C2×C8—204no—
221C2×C8—202no—
222C4⋊C4—102no—
223C4⋊C4—202no—
224C4⋊C4—204no—
225C4⋊C4—202no—
226C22⋊C4—202no—
227C22⋊C4—201no—
228C22⋊C4—201no—
229C42—216no—
230C42—24no—
231C42—24no—
232C2×C5—22no—
233C2×C5—22no—
234C2×C5#150012yes—
235C2×C5#150612yes—
236C2×C5#187311yescharacteristic
237C2×C5#189611yescharacteristic
238C2×C5#189911yescharacteristic
239C23—22no—
240C23—22no—
241C23C2×#68511yescharacteristic
242C23#407511yescharacteristic
243C23#409612yes—
244C23#409712yes—
245C23#409911yescharacteristic
246Q8—402no—
247C2×C4—24no—
248C2×C4—24no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—28no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—48no—
260C2×C4—48no—
261C2×C4—44no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—44no—
265C2×C4—202no—
266C2×C4—202no—
267C2×C4—202no—
268C2×C4—202no—
269C2×C4—202no—
270C2×C4—201no—
271C2×C4—201no—
272C2×C4#393714yes—
273C2×C4C4×C22⋊D512yes—
274C2×C4#407612yes—
275C8—402no—
276C5#914511yescharacteristic, complemented, Sylow
277C22—24no—
278C22—24no—
279C22—21no—
280C22—21no—
281C22—21no—
282C22—21no—
283C22C2×#393712yes—
284C22#6528512yes—
285C22#6529111yescharacteristic
286C22#6529311yescharacteristic
287C22#6529512yes—
288C22#6550211yescharacteristic
289C22#6552812yes—
290C4—24no—
291C4—22no—
292C4—22no—
293C4—48no—
294C4—42no—
295C4—402no—
296C4—401no—
297C4—401no—
298C2—22no—
299C2—22no—
300C2#1060022412yes—
301C2#1060022612yes—
302C2#1060232511yescharacteristic
303C2#1060237811yescharacteristic
304C2#1060238811yescharacteristic
subgroupG/H
centerC23C2×#685
commutatorC22×C4×C5C22×C4
FrattiniC23×C4C22×D5
FittingC2×C5×#376C2
socleC23×C5C2×C22⋊C4
prime radicalC24×C5C2×D4
cosocleC23×C4×C5C23
hypercenterC2×#376D5
hypocenterC5#9145
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#376

Complements

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

NH ≅ G/Ntype
17. #65218C4semidirect
18. #65217C4semidirect
276. C5#9145semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#3762
#106138062
#106023242
C2×#646722
#105981032
#91455