Finite Group Databasebeta

← #11987644

Subgroups — #11987644

Order 1280.

370 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 95 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#10607924C211yesmaximal, characteristic
2#10599400C211yesmaximal, characteristic
3#10599389C211yesmaximal, characteristic
4C5×#1271C211yesmaximal, characteristic
5#10598129C211yesmaximal, characteristic
6#10597969C211yesmaximal, characteristic
7#10597968C211yesmaximal, characteristic
8C5×#389C2211yescharacteristic
9C2×C8×Dic5—21no—
10#65274C411yescharacteristic
11#65270—21no—
12#65267—21no—
13#65266C411yescharacteristic
14#65266C411yescharacteristic
15#65262C411yescharacteristic
16C42×Dic5C2211yescharacteristic
17#65217C2211yescharacteristic
18#64942—21no—
19#64941—21no—
20C5×#336C2211yescharacteristic
21C5×#336C2211yescharacteristic
22#64770—21no—
23#64770—21no—
24#64770—21no—
25#64744C2211yescharacteristic
26#64744C2211yescharacteristic
27#7657—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×Dic5C2×C411yescharacteristic
40C2×C4×Dic5C2×C411yescharacteristic
41C2×C4×Dic5D411yescharacteristic
42C2×C4×Dic5D411yescharacteristic
43C2×C4×Dic5D411yescharacteristic
44C2×C4×Dic5D411yescharacteristic
45C22×#168—21no—
46C22×#168—21no—
47C5×#95—21no—
48#3963—21no—
49#3963—21no—
50#3963—21no—
51#3963—21no—
52#3963—21no—
53#3963—21no—
54#3963—21no—
55C8×Dic5—24no—
56#2864—51no—
57#1839—51no—
58#1744—51no—
59#1271—51no—
60#1271—51no—
61#1271—51no—
62#1271D511yescharacteristic
63C22×C4×C5—21no—
64C22×C4×C5—21no—
65C22×C4×C5C22×C411yescharacteristic
66C22×C4×C5C2×D411yescharacteristic
67C22×C4×C5C2×D411yescharacteristic
68C22×Dic5—21no—
69C22×Dic5—21no—
70C22×Dic5C22⋊C411yescharacteristic
71C22×Dic5C22⋊C411yescharacteristic
72C22×Dic5C22⋊C411yescharacteristic
73C22×Dic5C22⋊C411yescharacteristic
74C2×C5×C8—22no—
75C2×C5×C8—41no—
76C2×C5×C8—41no—
77C2×C5×C8—41no—
78C2×C5×C8—41no—
79C2×C5×C8—41no—
80C5×C4⋊C4—21no—
81C5×C4⋊C4—21no—
82C5×C4⋊C4—41no—
83C5×C4⋊C4—41no—
84C5×C4⋊C4—41no—
85C42×C5—41no—
86C4⋊Dic5—21no—
87C4⋊Dic5—21no—
88C4⋊Dic5—42no—
89C4⋊Dic5—41no—
90#683—41no—
91#683—41no—
92#683—42no—
93C4×Dic5—21no—
94C4×Dic5—21no—
95C4×Dic5—21no—
96C4×Dic5—21no—
97C4×Dic5—21no—
98C4×Dic5—21no—
99C4×Dic5—22no—
100C4×Dic5—22no—
101C4×Dic5—41no—
102C2×#168—22no—
103C2×#168—41no—
104C2×#168—41no—
105C2×#168—41no—
106C2×#168—41no—
107C2×#168—41no—
108C2×C4×C8—101no—
109#389—51no—
110#389—51no—
111#389—51no—
112#389C2×D511yescharacteristic
113#387—101no—
114#387—101no—
115#387—101no—
116#387—101no—
117#382—51no—
118#382—51no—
119C43—51no—
120#336—51no—
121#336—51no—
122#336—101no—
123#336—101no—
124#336—101no—
125#336C2×D511yescharacteristic
126#336C2×D511yescharacteristic
127C23×C5C2×C22⋊C411yescharacteristic
128C2×C4×C5—21no—
129C2×C4×C5—21no—
130C2×C4×C5—21no—
131C2×C4×C5—21no—
132C2×C4×C5—21no—
133C2×C4×C5—21no—
134C2×C4×C5—41no—
135C2×C4×C5—41no—
136C2×C4×C5—41no—
137C2×C4×C5—41no—
138C2×C4×C5—41no—
139C2×C4×C5—41no—
140C2×C4×C5#13111yescharacteristic
141C2×C4×C5#13111yescharacteristic
142C2×C4×C5#13511yescharacteristic
143C2×C4×C5#13511yescharacteristic
144C2×C4×C5#13511yescharacteristic
145C2×C4×C5#13511yescharacteristic
146C2×Dic5—21no—
147C2×Dic5—21no—
148C2×Dic5—21no—
149C2×Dic5—21no—
150C2×Dic5—21no—
151C2×Dic5—21no—
152C2×Dic5—21no—
153C2×Dic5—21no—
154C2×Dic5—21no—
155C2×Dic5—21no—
156C2×Dic5—41no—
157C2×Dic5—41no—
158C2×Dic5—41no—
159C2×Dic5—41no—
160C2×Dic5—41no—
161C2×Dic5—41no—
162C2×Dic5#10112yes—
163C2×Dic5#10412yes—
164C5×C8—42no—
165C5×C8—81no—
166#168—42no—
167#168—81no—
168C22×C8—21no—
169C22×C8—21no—
170C22×C8—101no—
171C22×C8—101no—
172C2×C4⋊C4—21no—
173C2×C4⋊C4—51no—
174C2×C4⋊C4—51no—
175C2×C4⋊C4—101no—
176C2×C4⋊C4—101no—
177C2×C4⋊C4—101no—
178C2×C4⋊C4C4×D511yescharacteristic
179C2×C4⋊C4C4×D511yescharacteristic
180C2×C42—51no—
181C2×C42—51no—
182C2×C42—51no—
183C2×C42—51no—
184C2×C42—51no—
185C2×C42—51no—
186C2×C42C22×D511yescharacteristic
187C4×C8—104no—
188#95—21no—
189#95—101no—
190#95—101no—
191#95—101no—
192#95—101no—
193#95—101no—
194#95—101no—
195#95—101no—
196C22×C5#40811yescharacteristic
197C22×C5#41011yescharacteristic
198C22×C5C2×#10111yescharacteristic
199C22×C5#41611yescharacteristic
200C22×C5#41611yescharacteristic
201C22×C5C2×#10411yescharacteristic
202C22×C5#42111yescharacteristic
203C4×C5—21no—
204C4×C5—21no—
205C4×C5—21no—
206C4×C5—21no—
207C4×C5—21no—
208C4×C5—21no—
209C4×C5—81no—
210C4×C5—81no—
211Dic5—22no—
212Dic5—22no—
213Dic5—41no—
214Dic5—41no—
215Dic5—81no—
216Dic5—81no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—51no—
220C22×C4—51no—
221C22×C4—51no—
222C22×C4—51no—
223C22×C4—101no—
224C22×C4—101no—
225C22×C4C2×C4×D511yescharacteristic
226C22×C4D4×D511yescharacteristic
227C22×C4D4×D511yescharacteristic
228C2×C8—22no—
229C2×C8—41no—
230C2×C8—41no—
231C2×C8—41no—
232C2×C8—41no—
233C2×C8—41no—
234C2×C8—102no—
235C2×C8—201no—
236C2×C8—201no—
237C2×C8—201no—
238C2×C8—201no—
239C2×C8—201no—
240C4⋊C4—21no—
241C4⋊C4—21no—
242C4⋊C4—41no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C4⋊C4—101no—
246C4⋊C4—101no—
247C4⋊C4—201no—
248C4⋊C4—202no—
249C4⋊C4—202no—
250C4⋊C4—201no—
251C4⋊C4—201no—
252C42—41no—
253C42—102no—
254C42—102no—
255C42—101no—
256C42—101no—
257C42—101no—
258C42—101no—
259C42—101no—
260C42—101no—
261C42—201no—
262C2×C5#147011yescharacteristic
263C2×C5#148211yescharacteristic
264C2×C5#149411yescharacteristic
265C2×C5#150011yescharacteristic
266C2×C5#152111yescharacteristic
267C2×C5#153111yescharacteristic
268C2×C5#154411yescharacteristic
269C23D5×C22⋊C411yescharacteristic
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—52no—
283C2×C4—52no—
284C2×C4—101no—
285C2×C4—101no—
286C2×C4—101no—
287C2×C4—101no—
288C2×C4—101no—
289C2×C4—101no—
290C2×C4—101no—
291C2×C4—101no—
292C2×C4—101no—
293C2×C4—101no—
294C2×C4—201no—
295C2×C4—201no—
296C2×C4—201no—
297C2×C4—201no—
298C2×C4—201no—
299C2×C4—201no—
300C2×C4#404711yescharacteristic
301C2×C4#405311yescharacteristic
302C2×C4#405811yescharacteristic
303C2×C4#406211yescharacteristic
304C2×C4#406211yescharacteristic
305C2×C4#406511yescharacteristic
306C8—42no—
307C8—81no—
308C8—202no—
309C8—401no—
310C5#765711yescharacteristic, complemented, Sylow
311C22#6501611yescharacteristic
312C22#6502911yescharacteristic
313C22D5×#10111yescharacteristic
314C22#6506111yescharacteristic
315C22#6509311yescharacteristic
316C22D5×#10411yescharacteristic
317C22#6511011yescharacteristic
318C4—21no—
319C4—21no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—81no—
325C4—81no—
326C4—102no—
327C4—102no—
328C4—201no—
329C4—201no—
330C4—401no—
331C4—401no—
332C2#1059892111yescharacteristic
333C2#1059897011yescharacteristic
334C2#1059902611yescharacteristic
335C2#1059907611yescharacteristic
336C2#1059910111yescharacteristic
337C2#1059915811yescharacteristic
338C2#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#7657
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
310. C5#7657semidirect

Maximal subgroups

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

subgroupindex
#106079242
#105994002
#105993892
C5×#12712
#105981292
#105979692
#105979682
#76575