Finite Group Databasebeta

← #11987616

Subgroups — #11987616

Order 1280.

384 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 99 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#10607697C211yesmaximal, characteristic
2#10599400C211yesmaximal, characteristic
3#10599400C211yesmaximal, characteristic
4C5×#1271C211yesmaximal, characteristic
5#10598129C211yesmaximal, characteristic
6#10597969C211yesmaximal, characteristic
7#10597968C211yesmaximal, characteristic
8C2×#4036C411yescharacteristic
9C5×#389C2211yescharacteristic
10#65267—21no—
11#65266C411yescharacteristic
12C4⋊C4×Dic5—21no—
13C4⋊C4×Dic5C411yescharacteristic
14C4⋊C4×Dic5C411yescharacteristic
15C42×Dic5C2211yescharacteristic
16#65217C2211yescharacteristic
17#64942—21no—
18#64938—21no—
19C5×#336C2211yescharacteristic
20C5×#336C2211yescharacteristic
21#64770—21no—
22#64770—21no—
23#64770—21no—
24#64770—21no—
25#64744C2211yescharacteristic
26#64744C2211yescharacteristic
27#7650—51nomaximal, Sylow
28C22×C5×C8—21no—
29C22×C5×C8—21no—
30C2×C5×C4⋊C4—21no—
31C2×C5×C4⋊C4C2×C411yescharacteristic
32C2×C5×C4⋊C4C2×C411yescharacteristic
33C2×C42×C5C2311yescharacteristic
34C2×C4⋊Dic5—21no—
35C2×C4⋊Dic5C2×C411yescharacteristic
36C2×C4⋊Dic5C2×C411yescharacteristic
37C2×#683—21no—
38C2×#683—21no—
39C2×C4×Dic5—21no—
40C2×C4×Dic5—21no—
41C2×C4×Dic5C2×C411yescharacteristic
42C2×C4×Dic5C2×C411yescharacteristic
43C2×C4×Dic5D411yescharacteristic
44C2×C4×Dic5D411yescharacteristic
45C2×C4×Dic5D411yescharacteristic
46C2×C4×Dic5D411yescharacteristic
47C22×#168—21no—
48C22×#168—21no—
49#4036—22no—
50#4036—22no—
51C5×#95—21no—
52#3963—21no—
53#3963—21no—
54#3963—21no—
55#3963—21no—
56#3963—21no—
57C4×#125—51no—
58#1839—51no—
59#1839—51no—
60#1271—51no—
61#1271—51no—
62#1271—51no—
63#1271D511yescharacteristic
64C22×C4×C5—21no—
65C22×C4×C5—21no—
66C22×C4×C5C22×C411yescharacteristic
67C22×C4×C5C2×D411yescharacteristic
68C22×C4×C5C2×D411yescharacteristic
69C22×Dic5—21no—
70C22×Dic5—21no—
71C22×Dic5C22⋊C411yescharacteristic
72C22×Dic5C22⋊C411yescharacteristic
73C22×Dic5C22⋊C411yescharacteristic
74C22×Dic5C22⋊C411yescharacteristic
75C2×C5×C8—41no—
76C2×C5×C8—41no—
77C2×C5×C8—41no—
78C2×C5×C8—41no—
79C2×C5×C8—41no—
80C2×C5×C8—41no—
81C5×C4⋊C4—21no—
82C5×C4⋊C4—41no—
83C5×C4⋊C4—41no—
84C5×C4⋊C4—41no—
85C5×C4⋊C4M1612yes—
86C42×C5—41no—
87C4⋊Dic5—24no—
88C4⋊Dic5—21no—
89C4⋊Dic5—41no—
90C4⋊Dic5M1612yes—
91#683—24no—
92#683—41no—
93#683—41no—
94C4×Dic5—21no—
95C4×Dic5—21no—
96C4×Dic5—21no—
97C4×Dic5—21no—
98C4×Dic5—21no—
99C4×Dic5—21no—
100C4×Dic5—22no—
101C4×Dic5—41no—
102C4×Dic5—41no—
103C4×Dic5—42no—
104C4×Dic5—42no—
105C2×#168—41no—
106C2×#168—41no—
107C2×#168—41no—
108C2×#168—41no—
109C2×#168—41no—
110C2×#168—41no—
111C2×#125—51no—
112#389—51no—
113#389C2×D511yescharacteristic
114#387—101no—
115#387—101no—
116#382—51no—
117C4×C4⋊C4—51no—
118C4×C4⋊C4—51no—
119C4×C4⋊C4—101no—
120C4×C4⋊C4—101no—
121C43—51no—
122#336—51no—
123#336—51no—
124#336—101no—
125#336—101no—
126#336—101no—
127#336—101no—
128#336C2×D511yescharacteristic
129#336C2×D511yescharacteristic
130C23×C5C2×C22⋊C411yescharacteristic
131C2×C4×C5—21no—
132C2×C4×C5—21no—
133C2×C4×C5—21no—
134C2×C4×C5—21no—
135C2×C4×C5—21no—
136C2×C4×C5—21no—
137C2×C4×C5—22no—
138C2×C4×C5—41no—
139C2×C4×C5—41no—
140C2×C4×C5—41no—
141C2×C4×C5—41no—
142C2×C4×C5—41no—
143C2×C4×C5C2×M1611yescharacteristic
144C2×C4×C5C2×M1611yescharacteristic
145C2×C4×C5#13511yescharacteristic
146C2×C4×C5#13511yescharacteristic
147C2×C4×C5#13511yescharacteristic
148C2×C4×C5#13511yescharacteristic
149C2×Dic5—21no—
150C2×Dic5—21no—
151C2×Dic5—21no—
152C2×Dic5—21no—
153C2×Dic5—22no—
154C2×Dic5—21no—
155C2×Dic5—21no—
156C2×Dic5—21no—
157C2×Dic5—21no—
158C2×Dic5—21no—
159C2×Dic5—21no—
160C2×Dic5—21no—
161C2×Dic5—41no—
162C2×Dic5—41no—
163C2×Dic5—41no—
164C2×Dic5—41no—
165C2×Dic5—41no—
166C2×Dic5#10112yes—
167C5×C8—81no—
168C5×C8—81no—
169#168—81no—
170#168—81no—
171C22×C8—21no—
172C22×C8—21no—
173C22×C8—101no—
174C22×C8—101no—
175#125—102no—
176#125—102no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4—51no—
179C2×C4⋊C4—51no—
180C2×C4⋊C4—101no—
181C2×C4⋊C4—101no—
182C2×C4⋊C4—101no—
183C2×C4⋊C4C4×D511yescharacteristic
184C2×C4⋊C4C4×D511yescharacteristic
185C2×C42—51no—
186C2×C42—51no—
187C2×C42—51no—
188C2×C42—51no—
189C2×C42—51no—
190C2×C42—51no—
191C2×C42—101no—
192C2×C42—101no—
193C2×C42C22×D511yescharacteristic
194#95—21no—
195#95—101no—
196#95—101no—
197#95—101no—
198#95—101no—
199#95—101no—
200C22×C5#40711yescharacteristic
201C22×C5#41011yescharacteristic
202C22×C5C2×#10111yescharacteristic
203C22×C5#41611yescharacteristic
204C22×C5#41611yescharacteristic
205C22×C5#42111yescharacteristic
206C22×C5#42111yescharacteristic
207C4×C5—21no—
208C4×C5—21no—
209C4×C5—21no—
210C4×C5—21no—
211C4×C5—21no—
212C4×C5—21no—
213C4×C5—42no—
214C4×C5—81no—
215Dic5—22no—
216Dic5—41no—
217Dic5—41no—
218Dic5—41no—
219Dic5—42no—
220Dic5—81no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—51no—
224C22×C4—51no—
225C22×C4—51no—
226C22×C4—51no—
227C22×C4—101no—
228C22×C4—101no—
229C22×C4C2×C4×D511yescharacteristic
230C22×C4D4×D511yescharacteristic
231C22×C4D4×D511yescharacteristic
232C2×C8—41no—
233C2×C8—41no—
234C2×C8—41no—
235C2×C8—41no—
236C2×C8—41no—
237C2×C8—41no—
238C2×C8—201no—
239C2×C8—201no—
240C2×C8—201no—
241C2×C8—201no—
242C2×C8—201no—
243C2×C8—201no—
244C4⋊C4—21no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—52no—
249C4⋊C4—104no—
250C4⋊C4—104no—
251C4⋊C4—101no—
252C4⋊C4—201no—
253C4⋊C4—201no—
254C4⋊C4—201no—
255C4⋊C4#67612yes—
256C42—41no—
257C42—102no—
258C42—101no—
259C42—101no—
260C42—101no—
261C42—101no—
262C42—101no—
263C42—101no—
264C42—201no—
265C42—201no—
266C42—202no—
267C42—202no—
268C2×C5#146711yescharacteristic
269C2×C5#148811yescharacteristic
270C2×C5#148811yescharacteristic
271C2×C5#152111yescharacteristic
272C2×C5#152111yescharacteristic
273C2×C5#153411yescharacteristic
274C2×C5#154411yescharacteristic
275C23D5×C22⋊C411yescharacteristic
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—22no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—52no—
289C2×C4—101no—
290C2×C4—101no—
291C2×C4—101no—
292C2×C4—101no—
293C2×C4—101no—
294C2×C4—101no—
295C2×C4—101no—
296C2×C4—101no—
297C2×C4—101no—
298C2×C4—101no—
299C2×C4—101no—
300C2×C4—102no—
301C2×C4—201no—
302C2×C4—201no—
303C2×C4—201no—
304C2×C4—201no—
305C2×C4—201no—
306C2×C4C2×#67611yescharacteristic
307C2×C4D5×M1611yescharacteristic
308C2×C4#405811yescharacteristic
309C2×C4#406211yescharacteristic
310C2×C4#406211yescharacteristic
311C2×C4#406511yescharacteristic
312C8—81no—
313C8—81no—
314C8—401no—
315C8—401no—
316C5#765011yescharacteristic, complemented, Sylow
317C22#6501511yescharacteristic
318C22#6502911yescharacteristic
319C22D5×#10111yescharacteristic
320C22#6506111yescharacteristic
321C22#6509311yescharacteristic
322C22#6511011yescharacteristic
323C22#6511011yescharacteristic
324C4—21no—
325C4—21no—
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—42no—
331C4—81no—
332C4—102no—
333C4—201no—
334C4—201no—
335C4—201no—
336C4—202no—
337C4—401no—
338C2#1059892011yescharacteristic
339C2#1059896611yescharacteristic
340C2#1059903011yescharacteristic
341C2#1059907611yescharacteristic
342C2#1059910811yescharacteristic
343C2#1059916011yescharacteristic
344C2#1059921211yescharacteristic
subgroupG/H
centerC23D5×C22⋊C4
commutatorC22×C4×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#1271C2
socle, prime radicalC23×C5C2×C22⋊C4
cosocleC2×C42×C5C23
hypercenter#1271D5
hypocenterC5#7650
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
316. C5#7650semidirect

Maximal subgroups

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

subgroupindex
#106076972
#105994002
C5×#12712
#105981292
#105979692
#105979682
#76505