Finite Group Databasebeta

← #12015797

Subgroups — #12015797

Order 1280.

486 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×#107C211yesmaximal, characteristic
2C2×C5×#366C211yesmaximal, characteristic, complemented
3C2×#64727C211yesmaximal, characteristic
4#10601423C211yesmaximal, characteristic
5C2×#64709C211yesmaximal, characteristic, complemented
6#10598297C211yesmaximal, characteristic, complemented
7#10598213C211yesmaximal, characteristic, complemented
8C22×C8×D5C2211yescharacteristic
9C2×D5×C4⋊C4—21no—
10C22×C5×C16C2211yescharacteristic
11C2×C5×#107C2211yescharacteristic
12C2×C5×#107C2211yescharacteristic
13C2×#3950C2211yescharacteristic
14C2×#3950C2211yescharacteristic
15C22×#672C2211yescharacteristic
16#65276—21no—
17C2×#3939—21no—
18D5×#107—22no—
19D5×#107—22no—
20C5×#366—22no—
21#64749—21no—
22#64727C414yescomplemented
23#64709—22no—
24#12919—51nomaximal, Sylow
25C22×C4×D5—41no—
26C22×C4×D5D411yescharacteristic
27C22×C5×C8C2311yescharacteristic
28C2×C5×C4⋊C4—21no—
29C2×C5×C4⋊C4—21no—
30C2×#685—41no—
31C2×C4⋊Dic5—21no—
32C2×C4⋊Dic5—21no—
33C2×#683—41no—
34C22×#168D411yescharacteristic
35C2×C8×D5—21no—
36C2×C8×D5—21no—
37C2×C8×D5—21no—
38C2×C8×D5—21no—
39C2×C8×D5C2×C412yes—
40C2×C8×D5Q812yes—
41D5×C4⋊C4—24no—
42D5×C4⋊C4—42no—
43C2×C5×C16—21no—
44C2×C5×C16—21no—
45C2×C5×C16C2×C412yescomplemented
46C5×#107—21no—
47C5×#107—21no—
48C5×#107—21no—
49C5×#107D412yes—
50#3963—41no—
51#3950—21no—
52#3950—21no—
53#3950—21no—
54#3950D412yes—
55C2×#672—21no—
56C2×#672—21no—
57C2×#672C2×C412yescomplemented
58#3939—24no—
59C22×#107—51no—
60C2×#366—51no—
61C2×#366D511yescharacteristic, complemented
62C2×C22⋊C16—51no—
63#1808—51no—
64#1380—51no—
65#1380—51no—
66C23×D5D811yescharacteristic
67C22×C4×C5—41no—
68C22×C4×C5—41no—
69C22×C4×C5C2×D411yescharacteristic
70C22×Dic5—41no—
71C22×Dic5—41no—
72C22×Dic5D811yescharacteristic
73C2×C4×D5—21no—
74C2×C4×D5—21no—
75C2×C4×D5—21no—
76C2×C4×D5—21no—
77C2×C4×D5—44no—
78C2×C4×D5—82no—
79C2×C4×D5—82no—
80C2×C4×D5C4⋊C412yes—
81C2×C4×D5Q1612yes—
82C2×C5×C8C22×C411yescharacteristic
83C2×C5×C8C2×D411yescharacteristic
84C2×C5×C8C2×D411yescharacteristic
85C2×C5×C8C2×Q811yescharacteristic
86C2×C5×C8#4111yescharacteristic
87C2×C5×C8#4111yescharacteristic
88C5×C4⋊C4—22no—
89C5×C4⋊C4—41no—
90C5×C4⋊C4—41no—
91C5×C4⋊C4—41no—
92#685—82no—
93C4⋊Dic5—22no—
94C4⋊Dic5—41no—
95C4⋊Dic5—41no—
96C4⋊Dic5—41no—
97#683—44no—
98C2×#168—21no—
99C2×#168—21no—
100C2×#168C4⋊C412yes—
101C8×D5—22no—
102C8×D5—22no—
103C8×D5—22no—
104C8×D5—22no—
105C5×C16—22no—
106#672—22no—
107C23×C8—51no—
108C22×C4⋊C4—101no—
109C22×C16—51no—
110C22×C16C2×D511yescharacteristic
111C2×#107—51no—
112C2×#107—51no—
113C2×#107—102no—
114C2×#107—101no—
115C2×#107—102no—
116C2×#107C2×D511yescharacteristic
117C2×#107C2×D511yescharacteristic
118#380—101no—
119#366—22no—
120#366—102no—
121C22⋊C16—54no—
122#340—101no—
123C23×C5C2×D811yescharacteristic
124C22×D5—21no—
125C22×D5—21no—
126C22×D5—21no—
127C22×D5—21no—
128C22×D5#10712yes—
129C22×D5D1612yes—
130C22×D5Q3212yes—
131C2×C4×C5—42no—
132C2×C4×C5—81no—
133C2×C4×C5—81no—
134C2×C4×C5—81no—
135C2×C4×C5—81no—
136C2×C4×C5—81no—
137C2×C4×C5C2×C4⋊C411yescharacteristic
138C2×C4×C5#12011yescharacteristic
139C2×C4×C5#12311yescharacteristic
140C2×C4×C5C2×Q1611yescharacteristic
141C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C5#13711yescharacteristic
143C2×Dic5—21no—
144C2×Dic5—21no—
145C2×Dic5—42no—
146C2×Dic5—81no—
147C2×Dic5—81no—
148C2×Dic5—81no—
149C2×Dic5—81no—
150C2×Dic5—81no—
151C2×Dic5#10712yes—
152C4×D5—22no—
153C4×D5—22no—
154C4×D5—22no—
155C4×D5—22no—
156C4×D5—88no—
157C5×C8C4×D411yescharacteristic
158C5×C8C4×D411yescharacteristic
159C5×C8C22⋊Q811yescharacteristic
160C5×C8C22⋊Q811yescharacteristic
161#168—22no—
162C23×C4—51no—
163C23×C4—201no—
164C22×C8—51no—
165C22×C8—52no—
166C22×C8—52no—
167C22×C8—101no—
168C22×C8—101no—
169C22×C8—101no—
170C22×C8—101no—
171C22×C8C22×D511yescharacteristic
172C2×C4⋊C4—21no—
173C2×C4⋊C4—21no—
174C2×C4⋊C4—104no—
175C2×C4⋊C4—101no—
176C2×C4⋊C4—101no—
177C2×C4⋊C4—202no—
178C2×C4⋊C4—201no—
179C2×C22⋊C4—201no—
180C2×C16—21no—
181C2×C16—21no—
182C2×C16—52no—
183C2×C16—101no—
184C2×C16—101no—
185C2×C16C4×D512yescomplemented
186#107—21no—
187#107—21no—
188#107—21no—
189#107—52no—
190#107—104no—
191#107—101no—
192#107—101no—
193#107—101no—
194#107C22⋊D512yes—
195#95—201no—
196C22×C5C2×#10711yescharacteristic
197C22×C5#44711yescharacteristic
198C22×C5#48011yescharacteristic
199C22×C5C2×D1611yescharacteristic
200C22×C5C2×Q3211yescharacteristic
201C22×C5#50911yescharacteristic
202C22×C5#51011yescharacteristic
203C2×D5—22no—
204C2×D5—22no—
205C2×D5—22no—
206C2×D5—22no—
207C2×D5—22no—
208C2×D5—22no—
209C2×D5#36614yescomplemented
210C4×C5—82no—
211C4×C5—161no—
212C4×C5#38511yescharacteristic
213C4×C5#42811yescharacteristic
214C4×C5#45111yescharacteristic
215C4×C5#48411yescharacteristic
216Dic5—22no—
217Dic5—82no—
218Dic5—161no—
219C24—51no—
220C22×C4—41no—
221C22×C4—41no—
222C22×C4—51no—
223C22×C4—52no—
224C22×C4—52no—
225C22×C4—101no—
226C22×C4—101no—
227C22×C4—101no—
228C22×C4—101no—
229C22×C4—204no—
230C22×C4—201no—
231C22×C4—201no—
232C22×C4—402no—
233C22×C4—402no—
234C22×C4D4×D511yescharacteristic
235C2×C8—52no—
236C2×C8—101no—
237C2×C8—101no—
238C2×C8—102no—
239C2×C8—102no—
240C2×C8—102no—
241C2×C8—102no—
242C2×C8C2×C4×D511yescharacteristic
243C2×C8#70911yescharacteristic
244C2×C8D4×D511yescharacteristic
245C2×C8Q8×D511yescharacteristic
246C2×C8#71311yescharacteristic
247C2×C8C2×C22⋊D511yescharacteristic
248C4⋊C4—22no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—102no—
253C4⋊C4—204no—
254C4⋊C4—201no—
255C4⋊C4—201no—
256C4⋊C4—201no—
257C22⋊C4—402no—
258C16—22no—
259C16—102no—
260C2×C5#185211yescharacteristic
261C2×C5C2×#36611yescharacteristic
262C2×C5#215911yescharacteristic
263C2×C5#218411yescharacteristic
264C2×C5#218811yescharacteristic
265C2×C5#223211yescharacteristic
266C2×C5#223611yescharacteristic
267D5—24no—
268C23—52no—
269C23—52no—
270C23—52no—
271C23—101no—
272C23—101no—
273C23—101no—
274C23—101no—
275C23D5×D811yescharacteristic
276C2×C4—42no—
277C2×C4—52no—
278C2×C4—81no—
279C2×C4—81no—
280C2×C4—81no—
281C2×C4—81no—
282C2×C4—81no—
283C2×C4—101no—
284C2×C4—101no—
285C2×C4—102no—
286C2×C4—102no—
287C2×C4—102no—
288C2×C4—102no—
289C2×C4—202no—
290C2×C4—408no—
291C2×C4—401no—
292C2×C4—401no—
293C2×C4—401no—
294C2×C4—401no—
295C2×C4—401no—
296C2×C4D5×C4⋊C411yescharacteristic
297C2×C4#404011yescharacteristic
298C2×C4#405711yescharacteristic
299C2×C4D5×Q1611yescharacteristic
300C2×C4#406411yescharacteristic
301C2×C4#408311yescharacteristic
302C8—102no—
303C8#403911yescharacteristic
304C8#404211yescharacteristic
305C8C4×C22⋊D511yescharacteristic
306C8#409211yescharacteristic
307C5#1291911yescharacteristic, complemented, Sylow
308C22—54no—
309C22—102no—
310C22—102no—
311C22—102no—
312C22—102no—
313C22—102no—
314C22—102no—
315C22D5×#10711yescharacteristic
316C22#6517111yescharacteristic
317C22D5×D1611yescharacteristic
318C22#6520011yescharacteristic
319C22D5×Q3211yescharacteristic
320C22#6520711yescharacteristic
321C22#6544511yescharacteristic
322C4—82no—
323C4—102no—
324C4—161no—
325C4—402no—
326C4—801no—
327C4#6517011yescharacteristic
328C4#6517311yescharacteristic
329C4#6527811yescharacteristic
330C4#6547511yescharacteristic
331C2—104no—
332C2D5×#36611yescharacteristic
333C2#1060011911yescharacteristic
334C2#1060012311yescharacteristic
335C2#1060012411yescharacteristic
336C2#1060142511yescharacteristic
337C2#1060226011yescharacteristic
338C2#1060229511yescharacteristic
subgroupG/H
centerC23D5×D8
commutatorC2×C5×C8C22×C4
FrattiniC22×C8C22×D5
FittingC2×C5×#366C2
socleC23×C5C2×D8
prime radicalC23×D5D8
cosocleC22×C5×C8C23
hypercenterC2×#366D5
hypocenterC5#12919
LCSG ▷ C2×C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#366

Complements

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

NH ≅ G/Ntype
2. C2×C5×#366C2semidirect
5. C2×#64709C2semidirect
6. #10598297C2semidirect
7. #10598213C2semidirect
22. #64727C4semidirect
45. C2×C5×C16C2×C4semidirect
57. C2×#672C2×C4semidirect
61. C2×#366D5semidirect
185. C2×C16C4×D5semidirect
209. C2×D5#366semidirect
307. C5#12919semidirect

Maximal subgroups

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

subgroupindex
C2×D5×#1072
C2×C5×#3662
C2×#647272
#106014232
C2×#647092
#105982972
#105982132
#129195