Finite Group Databasebeta

← #11993607

Subgroups — #11993607

Order 1280.

392 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2925C211yesmaximal, characteristic
2#10602439C211yesmaximal, characteristic
3#10602431C211yesmaximal, characteristic
4#10601284C211yesmaximal, characteristic, complemented
5#10601214C211yesmaximal, characteristic, complemented
6#10598206C211yesmaximal, characteristic, complemented
7#10598195C211yesmaximal, characteristic, complemented
8C4×C5×#41C2211yescharacteristic
9C5×#433—22no—
10C5×#432—21no—
11C5×#431—21no—
12C5×#423C2211yescharacteristic
13C2×C5×C4⋊C8C2211yescharacteristic
14C5×#408—21no—
15C5×#405—21no—
16C2×#3969—21no—
17C4×C4⋊Dic5C2211yescharacteristic
18#65214C2211yescharacteristic
19#65213C2211yescharacteristic
20C2×C4×#168C2211yescharacteristic
21Q8⋊#168C411yescharacteristic, complemented
22Q8⋊#168C411yescharacteristic, complemented
23D4⋊#168C411yescharacteristic, complemented
24D4⋊#168C411yescharacteristic, complemented
25#64752—21no—
26#64700—21no—
27#64700—21no—
28#64699—22no—
29#8903—51nomaximal, Sylow
30C2×C5×#41D411yescharacteristic
31C2×C5×M16—21no—
32C22×C5×C8—21no—
33C4×C5×Q8C2×C411yescharacteristic
34C4×C5×Q8Q811yescharacteristic
35C4×C5×D4—21no—
36C4×C5×D4—21no—
37C4×C5×D4C2×C411yescharacteristic
38C4×C5×D4Q811yescharacteristic
39C5×#117—21no—
40C5×#117D411yescharacteristic
41C2×C42×C5—21no—
42C2×C42×C5C2311yescharacteristic
43C2×C4⋊Dic5—21no—
44C2×C4×Dic5—21no—
45C2×#681—21no—
46C22×#168—21no—
47C5×C4⋊C8—21no—
48C5×C4⋊C8—21no—
49C5×C4⋊C8D411yescharacteristic
50C5×C4⋊C8D411yescharacteristic
51C5×C4⋊C8D412yes—
52C5×C22⋊C8—22no—
53C5×C22⋊C8—22no—
54C5×#97—22no—
55C4×C5×C8—22no—
56#3969—42no—
57#3963—21no—
58C22⋊#168—21no—
59C4⋊#168—21no—
60C4⋊#168—21no—
61C4⋊#168C2×C411yescharacteristic
62C4⋊#168C2×C411yescharacteristic
63C4×#168—21no—
64C4×#168—21no—
65C4×#168C2×C411yescharacteristic
66C4×#168C2×C411yescharacteristic
67#2925D511yescharacteristic
68#1806—51no—
69#1570—51no—
70#1567—51no—
71#1476—51no—
72#1303—51no—
73#1279—51no—
74C5×#41—21no—
75C5×#41—21no—
76C5×#41—21no—
77C5×#41—21no—
78C2×C5×Q8C4⋊C411yescharacteristic
79C2×C5×D4—21no—
80C2×C5×D4C4⋊C411yescharacteristic
81C22×C4×C5—21no—
82C22×C4×C5—21no—
83C22×C4×C5—21no—
84C22×C4×C5C2×D411yescharacteristic
85C22×C4×C5#4111yescharacteristic
86C22×C4×C5#4111yescharacteristic
87C22×Dic5—41no—
88C5×M16—41no—
89C5×M16—41no—
90C2×C5×C8—21no—
91C2×C5×C8—21no—
92C2×C5×C8—22no—
93C2×C5×C8—41no—
94C2×C5×C8—41no—
95C5×C4⋊C4—21no—
96C5×C4⋊C4—21no—
97C5×C4⋊C4C4⋊C411yescharacteristic
98C5×C4⋊C4C4⋊C411yescharacteristic
99C5×C22⋊C4—21no—
100C5×C22⋊C4—21no—
101C5×C22⋊C4—21no—
102C42×C5—21no—
103C42×C5—21no—
104C42×C5—21no—
105C42×C5C22×C411yescharacteristic
106C42×C5C2×D411yescharacteristic
107C42×C5C2×D411yescharacteristic
108C42×C5C2×Q811yescharacteristic
109C4⋊Dic5—22no—
110C4⋊Dic5—41no—
111C4×Dic5—41no—
112C4×Dic5—41no—
113#681—41no—
114#681—41no—
115C2×#168—21no—
116C2×#168—21no—
117C2×#168—21no—
118C2×#168—21no—
119C2×#168—42no—
120C2×#168—41no—
121C4×#41C2×D511yescharacteristic
122#433—22no—
123#432—21no—
124#431—21no—
125#431—51no—
126#423—51no—
127#423C2×D511yescharacteristic
128C2×C4⋊C8C2×D511yescharacteristic
129C2×#104—101no—
130#408—21no—
131#405—21no—
132C2×C4×C8—51no—
133C4×C4⋊C4—51no—
134#339—101no—
135#335—102no—
136#334—101no—
137#334—101no—
138Q8⋊C8—51no—
139Q8⋊C8—51no—
140D4⋊C8—51no—
141D4⋊C8—51no—
142C23×C5—21no—
143C23×C5#12311yescharacteristic
144C5×Q8—21no—
145C5×Q8—21no—
146C5×D4—21no—
147C5×D4—21no—
148C5×D4—41no—
149C5×D4—41no—
150C2×C4×C5—21no—
151C2×C4×C5—21no—
152C2×C4×C5—21no—
153C2×C4×C5—21no—
154C2×C4×C5—21no—
155C2×C4×C5—41no—
156C2×C4×C5—41no—
157C2×C4×C5—41no—
158C2×C4×C5—41no—
159C2×C4×C5—41no—
160C2×C4×C5—81no—
161C2×C4×C5C2×C4⋊C411yescharacteristic
162C2×C4×C5C4×D411yescharacteristic
163C2×C4×C5C4×D411yescharacteristic
164C2×C4×C5#12011yescharacteristic
165C2×C4×C5C22⋊Q811yescharacteristic
166C2×C4×C5C22⋊Q811yescharacteristic
167C2×C4×C5#13511yescharacteristic
168C2×C4×C5#13511yescharacteristic
169C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
170C2×C4×C5#13711yescharacteristic
171C2×Dic5—42no—
172C2×Dic5—81no—
173C2×Dic5—81no—
174C5×C8—42no—
175C5×C8—41no—
176C5×C8—41no—
177#168—22no—
178#168—41no—
179#168—41no—
180#168—41no—
181#168—81no—
182C2×#41C22⋊D511yescharacteristic
183C2×M16—21no—
184C2×M16—101no—
185C22×C8—21no—
186C22×C8—101no—
187C4×Q8Dic1011yescharacteristic
188C4×Q8C4×D511yescharacteristic
189C4×D4—21no—
190C4×D4—21no—
191C4×D4Dic1011yescharacteristic
192C4×D4C4×D511yescharacteristic
193#117—21no—
194#117C22⋊D511yescharacteristic
195C2×C4⋊C4—101no—
196C2×C42—21no—
197C2×C42—101no—
198C2×C42C22×D511yescharacteristic
199C4⋊C8—21no—
200C4⋊C8—21no—
201C4⋊C8—51no—
202C4⋊C8—51no—
203C4⋊C8—101no—
204C4⋊C8—101no—
205C4⋊C8C22⋊D511yescharacteristic
206C4⋊C8C22⋊D511yescharacteristic
207C4⋊C8C22⋊D512yes—
208#104—202no—
209C22⋊C8—22no—
210C22⋊C8—22no—
211C22⋊C8—101no—
212#97—22no—
213C4×C8—22no—
214C4×C8—51no—
215C4×C8—51no—
216C4×C8—101no—
217C4×C8—101no—
218#95—101no—
219C22×C5—21no—
220C22×C5—21no—
221C22×C5—41no—
222C22×C5—41no—
223C22×C5—41no—
224C22×C5#38511yescharacteristic
225C22×C5#48211yescharacteristic
226C22×C5#48511yescharacteristic
227C4×C5—21no—
228C4×C5—21no—
229C4×C5—21no—
230C4×C5—41no—
231C4×C5—41no—
232C4×C5—41no—
233C4×C5#42711yescharacteristic
234C4×C5#42811yescharacteristic
235C4×C5#44311yescharacteristic
236C4×C5#44411yescharacteristic
237C4×C5#44911yescharacteristic
238C4×C5#45211yescharacteristic
239Dic5—82no—
240#41—21no—
241#41—21no—
242#41—21no—
243#41—21no—
244C2×Q8#68311yescharacteristic
245C2×D4—21no—
246C2×D4#68311yescharacteristic
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—201no—
251C22×C4#70911yescharacteristic
252C22×C4#70911yescharacteristic
253C22×C4C2×C22⋊D511yescharacteristic
254M16—41no—
255M16—41no—
256M16—201no—
257M16—201no—
258C2×C8—21no—
259C2×C8—22no—
260C2×C8—21no—
261C2×C8—41no—
262C2×C8—41no—
263C2×C8—101no—
264C2×C8—101no—
265C2×C8—101no—
266C2×C8—101no—
267C2×C8—202no—
268C2×C8—201no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—102no—
272C4⋊C4—201no—
273C4⋊C4#68311yescharacteristic
274C4⋊C4#68311yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—21no—
278C42—21no—
279C42—21no—
280C42—21no—
281C42—201no—
282C42—201no—
283C42C2×Dic1011yescharacteristic
284C42C2×C4×D511yescharacteristic
285C42C2×C22⋊D511yescharacteristic
286C42C2×C22⋊D511yescharacteristic
287C2×C5—21no—
288C2×C5—21no—
289C2×C5—81no—
290C2×C5#185411yescharacteristic
291C2×C5#186111yescharacteristic
292C2×C5#186611yescharacteristic
293C23—21no—
294C23#407511yescharacteristic
295Q8—21no—
296Q8—21no—
297D4—21no—
298D4—21no—
299D4—41no—
300D4—41no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—81no—
312C2×C4—202no—
313C2×C4—401no—
314C2×C4—401no—
315C2×C4C2×#68311yescharacteristic
316C2×C4#407011yescharacteristic
317C2×C4#407011yescharacteristic
318C2×C4C4×C22⋊D511yescharacteristic
319C2×C4C4×C22⋊D511yescharacteristic
320C2×C4#409511yescharacteristic
321C2×C4#409611yescharacteristic
322C2×C4#409611yescharacteristic
323C2×C4#409711yescharacteristic
324C2×C4#409911yescharacteristic
325C8—42no—
326C8—41no—
327C8—41no—
328C8—102no—
329C8—201no—
330C8—201no—
331C8—201no—
332C8—401no—
333C5#890311yescharacteristic, complemented, Sylow
334C22—21no—
335C22—21no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22#6528511yescharacteristic
340C22#6529211yescharacteristic
341C22#6549911yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—402no—
349C4#6528411yescharacteristic
350C4#6528711yescharacteristic
351C4#6543311yescharacteristic
352C4#6543411yescharacteristic
353C4#6552711yescharacteristic
354C4#6552811yescharacteristic
355C2—21no—
356C2—21no—
357C2—81no—
358C2#1060236911yescharacteristic
359C2#1060281011yescharacteristic
360C2#1060282111yescharacteristic
subgroupG/H
centerC2×C4#4099
commutatorC42×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#2925C2
socleC22×C5#385
prime radicalC2×C5×#41D4
cosocleC2×C42×C5C23
hypercenter#2925D5
hypocenterC5#8903
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2925

Complements

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

NH ≅ G/Ntype
4. #10601284C2semidirect
5. #10601214C2semidirect
6. #10598206C2semidirect
7. #10598195C2semidirect
21. Q8⋊#168C4semidirect
22. Q8⋊#168C4semidirect
23. D4⋊#168C4semidirect
24. D4⋊#168C4semidirect
333. C5#8903semidirect

Maximal subgroups

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

subgroupindex
C5×#29252
#106024392
#106024312
#106012842
#106012142
#105982062
#105981952
#89035