Finite Group Databasebeta

← #12002550

Subgroups — #12002550

Order 1280.

762 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 762 conjugacy classes of subgroups — too many to draw. Only its 75 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#10605575C211yesmaximal, characteristic, complemented
2C5×#1781C211yesmaximal, characteristic
3#10602923C212yesmaximal
4#10598114C211yesmaximal, characteristic, complemented
5#10598114C212yesmaximal, complemented
6C23×C5×D4C2211yescharacteristic
7C2×C5×#99—22no—
8C5×#379C2211yescharacteristic
9C5×#379C2211yescharacteristic
10#65536C2212yes—
11#65536C2212yes—
12C2×#3966—24no—
13#65236—22no—
14#65236—24no—
15#10390—51nomaximal, Sylow
16C25×C5Q811yescharacteristic, complemented
17C25×C5C2311yescharacteristic
18C22×C5×D4—21no—
19C22×C5×D4—22no—
20C22×C5×D4—21no—
21C22×C5×D4—22no—
22C22×C5×D4—44no—
23C23×C4×C5Q811yescharacteristic, complemented
24C22×Dic10—22no—
25C2×C5×C22⋊C4—21no—
26C2×C5×C22⋊C4—22no—
27C2×C5×C22⋊C4—22no—
28C2×C5×C22⋊C4D412yes—
29C2×C22⋊Dic5—22no—
30C2×C22⋊Dic5—22no—
31C2×C22⋊Dic5—22no—
32C2×C22⋊Dic5—22no—
33C2×C22⋊Dic5—22no—
34C2×C22⋊Dic5D414yes—
35C5×#99—44no—
36#3966—48no—
37#3963—26no—
38#2840—51no—
39#1781—52no—
40#1781D511yescharacteristic
41#1304—52no—
42#1304—51no—
43C24×C5—22no—
44C24×C5—21no—
45C24×C5—42no—
46C24×C5—42no—
47C24×C5—82no—
48C24×C5—82no—
49C24×C5C2×D412yes—
50C24×C5C2×D411yescharacteristic
51C24×C5C2×Q811yescharacteristic
52C24×C5#4111yescharacteristic
53C24×C5#4112yes—
54C2×C5×D4—28no—
55C2×C5×D4—24no—
56C2×C5×D4—42no—
57C2×C5×D4—44no—
58C2×C5×D4—42no—
59C2×C5×D4—44no—
60C2×C5×D4—44no—
61C2×C5×D4—42no—
62C2×C5×D4—41no—
63C2×C5×D4—42no—
64C2×C5×D4—41no—
65C22×C4×C5—22no—
66C22×C4×C5—21no—
67C22×C4×C5—22no—
68C22×C4×C5—42no—
69C22×C4×C5—41no—
70C22×Dic5—24no—
71C22×Dic5—42no—
72C2×Dic10—84no—
73C2×Dic10—82no—
74C5×C22⋊C4—42no—
75C5×C22⋊C4—42no—
76C5×C22⋊C4—82no—
77C5×C22⋊C4—82no—
78C22⋊Dic5—44no—
79C22⋊Dic5—44no—
80C22⋊Dic5—82no—
81C22⋊Dic5—82no—
82C22⋊Dic5—82no—
83C22⋊Dic5—82no—
84C23×D4C2×D511yescharacteristic
85C2×#99—22no—
86C2×#99—104no—
87#393—104no—
88#393—102no—
89#379—52no—
90#379—52no—
91#379C2×D511yescharacteristic
92#379C2×D511yescharacteristic
93C23×C5—24no—
94C23×C5—22no—
95C23×C5—24no—
96C23×C5—22no—
97C23×C5—41no—
98C23×C5—42no—
99C23×C5—42no—
100C23×C5—42no—
101C23×C5—42no—
102C23×C5—42no—
103C23×C5—42no—
104C23×C5—42no—
105C23×C5—41no—
106C23×C5—42no—
107C23×C5—42no—
108C23×C5—41no—
109C23×C5—41no—
110C23×C5—82no—
111C23×C5—82no—
112C23×C5—82no—
113C23×C5—88no—
114C23×C5—88no—
115C23×C5#12011yescharacteristic
116C23×C5C22⋊Q812yes—
117C23×C5C22⋊Q811yescharacteristic
118C23×C5#12412yes—
119C23×C5#12411yescharacteristic
120C5×D4—48no—
121C5×D4—44no—
122C5×D4—44no—
123C2×C4×C5—24no—
124C2×C4×C5—22no—
125C2×C4×C5—42no—
126C2×C4×C5—41no—
127C2×C4×C5—41no—
128C2×C4×C5—44no—
129C2×C4×C5—42no—
130C2×C4×C5—81no—
131C2×C4×C5—82no—
132C2×Dic5—44no—
133C2×Dic5—44no—
134C2×Dic5—44no—
135C2×Dic5—82no—
136C2×Dic5—82no—
137C2×Dic5—82no—
138Dic10—88no—
139C25Dic1011yescharacteristic, complemented
140C25C22×D511yescharacteristic
141C22×Q8—102no—
142C22×D4—22no—
143C22×D4—21no—
144C22×D4—21no—
145C22×D4—22no—
146C22×D4—44no—
147C23×C4Dic1011yescharacteristic, complemented
148C2×C22⋊C4—21no—
149C2×C22⋊C4—22no—
150C2×C22⋊C4—22no—
151C2×C22⋊C4—54no—
152C2×C22⋊C4—102no—
153C2×C22⋊C4—102no—
154C2×C22⋊C4—102no—
155C2×C22⋊C4—102no—
156C2×C22⋊C4—102no—
157C2×C22⋊C4C22⋊D512yes—
158#99—44no—
159#99—208no—
160#95—106no—
161C22×C5—22no—
162C22×C5—22no—
163C22×C5—22no—
164C22×C5—21no—
165C22×C5—21no—
166C22×C5—22no—
167C22×C5—22no—
168C22×C5—22no—
169C22×C5—22no—
170C22×C5—22no—
171C22×C5—22no—
172C22×C5—44no—
173C22×C5—42no—
174C22×C5—84no—
175C22×C5—82no—
176C22×C5—82no—
177C22×C5—84no—
178C22×C5—84no—
179C22×C5—82no—
180C22×C5—84no—
181C22×C5—82no—
182C22×C5—82no—
183C22×C5#39311yescharacteristic
184C22×C5B(4,𝔽2)12yes—
185C4×C5—42no—
186C4×C5—82no—
187C4×C5—161no—
188Dic5—84no—
189Dic5—162no—
190C24—22no—
191C24—21no—
192C24—42no—
193C24—42no—
194C24—82no—
195C24—82no—
196C24C2×Dic1011yescharacteristic
197C24#70911yescharacteristic
198C24D4×D512yes—
199C24#71112yes—
200C24C2×C22⋊D511yescharacteristic
201C2×Q8—404no—
202C2×Q8—402no—
203C2×D4—24no—
204C2×D4—28no—
205C2×D4—42no—
206C2×D4—44no—
207C2×D4—42no—
208C2×D4—44no—
209C2×D4—42no—
210C2×D4—44no—
211C2×D4—42no—
212C2×D4—41no—
213C2×D4—41no—
214C22×C4—22no—
215C22×C4—21no—
216C22×C4—22no—
217C22×C4—42no—
218C22×C4—41no—
219C22×C4—104no—
220C22×C4—202no—
221C22⋊C4—42no—
222C22⋊C4—42no—
223C22⋊C4—82no—
224C22⋊C4—82no—
225C22⋊C4—204no—
226C22⋊C4—204no—
227C22⋊C4—402no—
228C22⋊C4—402no—
229C22⋊C4—402no—
230C22⋊C4—402no—
231C2×C5—22no—
232C2×C5—42no—
233C2×C5—41no—
234C2×C5—42no—
235C2×C5—41no—
236C2×C5—82no—
237C2×C5#202911yescharacteristic
238C2×C5#203212yes—
239C23—22no—
240C23—24no—
241C23—24no—
242C23—22no—
243C23—41no—
244C23—42no—
245C23—42no—
246C23—42no—
247C23—42no—
248C23—42no—
249C23—42no—
250C23—42no—
251C23—41no—
252C23—42no—
253C23—42no—
254C23—41no—
255C23—41no—
256C23—82no—
257C23—82no—
258C23—82no—
259C23—88no—
260C23—88no—
261C23#402412yes—
262C23#403112yes—
263C23#407011yescharacteristic
264C23#408211yescharacteristic
265C23#408311yescharacteristic
266Q8—408no—
267D4—44no—
268D4—48no—
269D4—44no—
270C2×C4—24no—
271C2×C4—22no—
272C2×C4—42no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—44no—
276C2×C4—42no—
277C2×C4—81no—
278C2×C4—82no—
279C2×C4—204no—
280C2×C4—204no—
281C2×C4—204no—
282C2×C4—402no—
283C2×C4—402no—
284C2×C4—402no—
285C5#1039011yescharacteristic, complemented, Sylow
286C22—22no—
287C22—22no—
288C22—21no—
289C22—21no—
290C22—22no—
291C22—22no—
292C22—22no—
293C22—22no—
294C22—22no—
295C22—22no—
296C22—22no—
297C22—44no—
298C22—42no—
299C22—82no—
300C22—84no—
301C22—84no—
302C22—82no—
303C22—84no—
304C22—82no—
305C22—84no—
306C22—82no—
307C22—82no—
308C22#6523611yescharacteristic
309C22#6532112yes—
310C4—42no—
311C4—82no—
312C4—161no—
313C4—404no—
314C4—802no—
315C2—22no—
316C2—41no—
317C2—42no—
318C2—42no—
319C2—41no—
320C2—82no—
321C2#1060029011yescharacteristic
322C2#1060081812yes—
subgroupG/H
centerC22#65236
commutator, cosocleC25×C5C23
FrattiniC25C22×D5
FittingC5×#1781C2
socleC22×C5#393
prime radicalC23×C5×D4C22
hypercenter#1781D5
hypocenterC5#10390
LCSG ▷ C25×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C25 ◁ #1781

Complements

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

NH ≅ G/Ntype
1. #10605575C2semidirect
4. #10598114C2semidirect
5. #10598114C2semidirect
16. C25×C5Q8semidirect
23. C23×C4×C5Q8semidirect
139. C25Dic10semidirect
147. C23×C4Dic10semidirect
285. C5#10390semidirect

Maximal subgroups

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

subgroupindex
#106055752
C5×#17812
#106029232
#105981142
#103905