Finite Group Databasebeta

← #11986622

Subgroups — #11986622

Order 1280.

374 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 71 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×#1463C211yesmaximal, characteristic
2#10602362C211yesmaximal, characteristic
3#10602345C211yesmaximal, characteristic
4C22×C5×C4⋊C4C2211yescharacteristic
5C5×#407—21no—
6C2×#3963—21no—
7C2×#3963—21no—
8C2×#3963C411yescharacteristic
9C2×#3963C411yescharacteristic
10#65496—21no—
11C5×#324—21no—
12C5×#324C412yescomplemented
13#64748—21no—
14#64748C412yescomplemented
15#7326—51nomaximal, Sylow
16C23×C4×C5C2×C411yescharacteristic
17C23×C4×C5D411yescharacteristic
18C23×C4×C5D411yescharacteristic
19C23×Dic5—21no—
20C23×Dic5—21no—
21C2×C5×M16—41no—
22C2×C5×C4⋊C4—41no—
23C2×C5×C4⋊C4—41no—
24C2×C5×C4⋊C4C2×C411yescharacteristic
25C2×C5×C4⋊C4C2×C411yescharacteristic
26C2×C5×C4⋊C4D411yescharacteristic
27C2×C5×C4⋊C4Q811yescharacteristic
28C2×#681—41no—
29C5×C22⋊C8—22no—
30C5×C22⋊C8—41no—
31#3963—42no—
32#3963—42no—
33#3963—41no—
34#3963—41no—
35C22⋊#168—22no—
36C22⋊#168—41no—
37#1463—51no—
38#1463D511yescharacteristic
39#1445—51no—
40C24×C5C22⋊C411yescharacteristic
41C22×C4×C5—21no—
42C22×C4×C5—21no—
43C22×C4×C5—21no—
44C22×C4×C5—21no—
45C22×C4×C5—21no—
46C22×C4×C5—21no—
47C22×C4×C5—41no—
48C22×C4×C5—41no—
49C22×C4×C5—41no—
50C22×C4×C5—41no—
51C22×C4×C5—41no—
52C22×C4×C5—41no—
53C22×C4×C5C4211yescharacteristic
54C22×C4×C5C22⋊C411yescharacteristic
55C22×C4×C5C22⋊C411yescharacteristic
56C22×C4×C5C4⋊C411yescharacteristic
57C22×C4×C5C4⋊C411yescharacteristic
58C22×C4×C5C4⋊C411yescharacteristic
59C22×Dic5—22no—
60C22×Dic5—22no—
61C22×Dic5—41no—
62C22×Dic5—41no—
63C22×Dic5—41no—
64C22×Dic5—41no—
65C22×Dic5—41no—
66C22×Dic5—41no—
67C22×Dic5—41no—
68C22×Dic5—41no—
69C22×Dic5—41no—
70C22×Dic5—41no—
71C22×Dic5—41no—
72C22×Dic5—41no—
73C5×M16—81no—
74C5×M16—81no—
75C2×C5×C8—42no—
76C5×C4⋊C4—41no—
77C5×C4⋊C4—41no—
78C5×C4⋊C4—41no—
79C5×C4⋊C4—41no—
80#681—81no—
81#681—81no—
82C2×#168—42no—
83C22×C4⋊C4C2×D511yescharacteristic
84#407—21no—
85#407—101no—
86C2×#95—51no—
87C2×#95—51no—
88C2×#95—101no—
89C2×#95—101no—
90#324—21no—
91#324—52no—
92#324—101no—
93#324Dic512yescomplemented
94C23×C5—21no—
95C23×C5—21no—
96C23×C5—21no—
97C23×C5—21no—
98C23×C5—21no—
99C23×C5—21no—
100C23×C5#9511yescharacteristic
101C23×C5#9911yescharacteristic
102C23×C5#9911yescharacteristic
103C2×C4×C5—21no—
104C2×C4×C5—21no—
105C2×C4×C5—21no—
106C2×C4×C5—21no—
107C2×C4×C5—21no—
108C2×C4×C5—21no—
109C2×C4×C5—21no—
110C2×C4×C5—21no—
111C2×C4×C5—21no—
112C2×C4×C5—21no—
113C2×C4×C5—42no—
114C2×C4×C5—42no—
115C2×C4×C5—41no—
116C2×C4×C5—41no—
117C2×C4×C5—41no—
118C2×C4×C5—41no—
119C2×C4×C5—41no—
120C2×C4×C5—41no—
121C2×C4×C5—41no—
122C2×C4×C5—41no—
123C2×C4×C5—81no—
124C2×C4×C5—81no—
125C2×Dic5—42no—
126C2×Dic5—42no—
127C2×Dic5—42no—
128C2×Dic5—42no—
129C2×Dic5—42no—
130C2×Dic5—42no—
131C2×Dic5—81no—
132C2×Dic5—81no—
133C2×Dic5—81no—
134C2×Dic5—81no—
135C2×Dic5—81no—
136C2×Dic5—81no—
137C2×Dic5—81no—
138C2×Dic5—81no—
139C5×C8—82no—
140#168—82no—
141C23×C4—101no—
142C23×C4—101no—
143C23×C4C4×D511yescharacteristic
144C23×C4D2011yescharacteristic
145C23×C4C22⋊D511yescharacteristic
146C2×M16—41no—
147C2×M16—201no—
148C2×C4⋊C4—41no—
149C2×C4⋊C4—41no—
150C2×C4⋊C4Dic1011yescharacteristic
151C2×C4⋊C4C4×D511yescharacteristic
152C2×C4⋊C4C2×Dic511yescharacteristic
153C2×C4⋊C4C22⋊D511yescharacteristic
154C22⋊C8—22no—
155C22⋊C8—41no—
156C22⋊C8—102no—
157C22⋊C8—201no—
158#95—201no—
159#95—201no—
160#95—202no—
161#95—202no—
162C22×C5—21no—
163C22×C5—21no—
164C22×C5—21no—
165C22×C5—21no—
166C22×C5—21no—
167C22×C5—21no—
168C22×C5—21no—
169C22×C5—21no—
170C22×C5—21no—
171C22×C5—21no—
172C22×C5—21no—
173C22×C5—21no—
174C22×C5—21no—
175C22×C5—21no—
176C22×C5#34211yescharacteristic
177C22×C5#34411yescharacteristic
178C22×C5#34411yescharacteristic
179C22×C5#35311yescharacteristic
180C22×C5#35411yescharacteristic
181C22×C5#35511yescharacteristic
182C22×C5#35611yescharacteristic
183C4×C5—41no—
184C4×C5—41no—
185C4×C5—41no—
186C4×C5—41no—
187C4×C5—41no—
188C4×C5—41no—
189Dic5—82no—
190Dic5—82no—
191C24#68511yescharacteristic
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—21no—
195C22×C4—21no—
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—41no—
199C22×C4—41no—
200C22×C4—41no—
201C22×C4—41no—
202C22×C4—41no—
203C22×C4—41no—
204C22×C4—102no—
205C22×C4—102no—
206C22×C4—201no—
207C22×C4—201no—
208C22×C4—201no—
209C22×C4—201no—
210C22×C4—201no—
211C22×C4—201no—
212C22×C4—201no—
213C22×C4—201no—
214C22×C4—201no—
215C22×C4—201no—
216C22×C4—201no—
217C22×C4—201no—
218C22×C4C4×Dic511yescharacteristic
219C22×C4#68311yescharacteristic
220C22×C4#68311yescharacteristic
221C22×C4C4⋊Dic511yescharacteristic
222C22×C4#68511yescharacteristic
223C22×C4C22⋊Dic511yescharacteristic
224M16—81no—
225M16—81no—
226M16—401no—
227M16—401no—
228C2×C8—42no—
229C2×C8—202no—
230C4⋊C4—41no—
231C4⋊C4—41no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C2×C5—21no—
235C2×C5—21no—
236C2×C5—21no—
237C2×C5—21no—
238C2×C5—21no—
239C2×C5—21no—
240C2×C5#130611yescharacteristic
241C2×C5#139311yescharacteristic
242C2×C5#139411yescharacteristic
243C23—21no—
244C23—21no—
245C23—21no—
246C23—21no—
247C23—21no—
248C23—21no—
249C23#393811yescharacteristic
250C23#393811yescharacteristic
251C23#396311yescharacteristic
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—81no—
273C2×C4—81no—
274C2×C4—202no—
275C2×C4—202no—
276C2×C4—202no—
277C2×C4—202no—
278C2×C4—202no—
279C2×C4—202no—
280C2×C4—401no—
281C2×C4—401no—
282C2×C4—401no—
283C2×C4—401no—
284C2×C4—401no—
285C2×C4—401no—
286C2×C4—401no—
287C2×C4—401no—
288C8—82no—
289C8—402no—
290C5#732611yescharacteristic, complemented, Sylow
291C22—21no—
292C22—21no—
293C22—21no—
294C22—21no—
295C22—21no—
296C22—21no—
297C22—21no—
298C22—21no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22#6469311yescharacteristic
306C22#6469411yescharacteristic
307C22#6469711yescharacteristic
308C22#6469811yescharacteristic
309C22#6474711yescharacteristic
310C22#6477611yescharacteristic
311C22#6477911yescharacteristic
312C4—41no—
313C4—41no—
314C4—41no—
315C4—41no—
316C4—41no—
317C4—41no—
318C4—402no—
319C4—402no—
320C2—21no—
321C2—21no—
322C2—21no—
323C2—21no—
324C2—21no—
325C2—21no—
326C2#1059817711yescharacteristic
327C2#1059818611yescharacteristic
328C2#1059819011yescharacteristic
subgroupG/H
centerC22#64747
commutatorC22×C4×C5C42
FrattiniC22×C4⋊C4C2×D5
FittingC5×#1463C2
socleC22×C5#342
prime radicalC24×C5C22⋊C4
cosocleC22×C5×C4⋊C4C22
hypercenter#1463D5
hypocenterC5#7326
LCSG ▷ C22×C4×C5 ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #1463

Complements

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

NH ≅ G/Ntype
12. C5×#324C4semidirect
14. #64748C4semidirect
93. #324Dic5semidirect
290. C5#7326semidirect

Maximal subgroups

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

subgroupindex
C5×#14632
#106023622
#106023452
#73265