Finite Group Databasebeta

← #12010389

Subgroups — #12010389

Order 1280.

416 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3050C211yesmaximal, characteristic
2#10602764C211yesmaximal, characteristic, complemented
3#10602756C211yesmaximal, characteristic, complemented
4#10598267C212yesmaximal, complemented
5#10598265C212yesmaximal, complemented
6C2×C5×#135C411yescharacteristic, complemented
7C23×C5×C8C2211yescharacteristic
8C5×#525—21no—
9C5×#467C411yescharacteristic, complemented
10C5×#467C2211yescharacteristic
11C5×#466C411yescharacteristic, complemented
12C5×#466C2211yescharacteristic
13C5×#465—21no—
14C5×#465—21no—
15C5×#427C411yescharacteristic, complemented
16C5×#416—21no—
17#65501—21no—
18C2×#3950—21no—
19C2×#3944—21no—
20#64771C2212yes—
21C22⋊#672—21no—
22C22⋊#672C2212yes—
23#11890—51nomaximal, Sylow
24C2×C5×#41—21no—
25C23×C4×C5D411yescharacteristic
26C5×#135—42no—
27C2×C5×Q16C2×C411yescharacteristic
28C2×C5×SD16—21no—
29C2×C5×D8C2×C411yescharacteristic
30C22×C5×C8—42no—
31C22×C5×C8C2×C411yescharacteristic
32C22×C5×C8C2×C411yescharacteristic
33C22×C5×C8D411yescharacteristic
34C22×C5×C8D411yescharacteristic
35C22×C5×C8D411yescharacteristic
36C22×C5×C8C2311yescharacteristic
37C5×#123—41no—
38C5×C22⋊Q8—21no—
39C5×C22⋊Q8—21no—
40C5×#121—21no—
41C5×#121—21no—
42C5×#120—41no—
43C4×C5×D4—41no—
44C4×C5×D4—41no—
45C5×#117—21no—
46C2×C22⋊Dic5—41no—
47C2×C4⋊Dic5—22no—
48C5×#107C2×C411yescharacteristic
49C5×#107C2×C411yescharacteristic
50C5×#106—21no—
51C5×#103—21no—
52C5×#103—21no—
53C5×#102—21no—
54C5×#102—21no—
55#3963—41no—
56#3950—42no—
57#3944—42no—
58C2×#672—22no—
59#3050D511yescharacteristic
60#2112—51no—
61#1808—51no—
62#1348—52no—
63#1347—52no—
64C24×C5D811yescharacteristic
65C5×#41—42no—
66C5×#41—42no—
67C2×C5×Q8—21no—
68C2×C5×D4—21no—
69C2×C5×D4—41no—
70C2×C5×D4—41no—
71C2×C5×D4—41no—
72C22×C4×C5—41no—
73C22×C4×C5—41no—
74C22×C4×C5—41no—
75C22×C4×C5C22⋊C411yescharacteristic
76C22×C4×C5C22⋊C411yescharacteristic
77C22×C4×C5D811yescharacteristic
78C22×C4×C5SD1611yescharacteristic
79C22×C4×C5SD1611yescharacteristic
80C22×C4×C5C2×D411yescharacteristic
81C22×Dic5—42no—
82C5×Q16—41no—
83C5×SD16—42no—
84C5×D8—41no—
85C2×C5×C8—22no—
86C2×C5×C8—22no—
87C2×C5×C8—22no—
88C2×C5×C8—41no—
89C2×C5×C8—41no—
90C2×C5×C8—41no—
91C2×C5×C8C22⋊C411yescharacteristic
92C2×C5×C8C22⋊C411yescharacteristic
93C2×C5×C8C22×C411yescharacteristic
94C2×C5×C8C2×D411yescharacteristic
95C5×C4⋊C4—21no—
96C5×C4⋊C4—21no—
97C5×C4⋊C4—41no—
98C5×C4⋊C4—41no—
99C5×C22⋊C4—41no—
100C5×C22⋊C4—41no—
101C5×C22⋊C4—41no—
102C5×C22⋊C4—41no—
103C5×C22⋊C4—41no—
104C42×C5—41no—
105C22⋊Dic5—82no—
106C4⋊Dic5—42no—
107C4⋊Dic5—42no—
108#672—42no—
109C2×#135Dic511yescharacteristic, complemented
110C23×C8C2×D511yescharacteristic
111#525—21no—
112C2×M32—101no—
113#467Dic511yescharacteristic, complemented
114#467C2×D511yescharacteristic
115#466Dic511yescharacteristic, complemented
116#466C2×D511yescharacteristic
117#465—21no—
118#465—21no—
119#427Dic511yescharacteristic, complemented
120C2×#107—101no—
121#416—21no—
122#380—101no—
123C22⋊C16—52no—
124C22⋊C16—101no—
125#340—52no—
126C23×C5—21no—
127C23×C5—21no—
128C23×C5—41no—
129C23×C5—41no—
130C23×C5—41no—
131C23×C5#10211yescharacteristic
132C23×C5#10211yescharacteristic
133C23×C5C2×D811yescharacteristic
134C5×Q8—41no—
135C5×Q8—41no—
136C5×D4—41no—
137C5×D4—41no—
138C5×D4—82no—
139C5×D4—82no—
140C5×D4—81no—
141C5×D4—81no—
142C2×C4×C5—21no—
143C2×C4×C5—21no—
144C2×C4×C5—21no—
145C2×C4×C5—21no—
146C2×C4×C5—21no—
147C2×C4×C5—21no—
148C2×C4×C5—41no—
149C2×C4×C5—41no—
150C2×C4×C5—41no—
151C2×C4×C5—41no—
152C2×C4×C5—41no—
153C2×C4×C5—41no—
154C2×C4×C5—82no—
155C2×C4×C5#10211yescharacteristic
156C2×C4×C5#10211yescharacteristic
157C2×C4×C5C2×C22⋊C411yescharacteristic
158C2×C4×C5C2×SD1611yescharacteristic
159C2×Dic5—82no—
160C2×Dic5—82no—
161C2×Dic5—82no—
162C5×C8—21no—
163C5×C8—21no—
164C5×C8—21no—
165C5×C8#9912yes—
166C2×#41—21no—
167C23×C4C22⋊D511yescharacteristic
168#135—42no—
169C2×Q16C2×Dic511yescharacteristic
170C2×SD16—21no—
171C2×D8C2×Dic511yescharacteristic
172C22×C8—42no—
173C22×C8C2×Dic511yescharacteristic
174C22×C8C2×Dic511yescharacteristic
175C22×C8C22⋊D511yescharacteristic
176C22×C8C22⋊D511yescharacteristic
177C22×C8C22⋊D511yescharacteristic
178C22×C8C22×D511yescharacteristic
179#123—41no—
180C22⋊Q8—21no—
181C22⋊Q8—21no—
182#121—21no—
183#121—21no—
184#120—41no—
185C4×D4—41no—
186C4×D4—41no—
187#117—21no—
188C2×C4⋊C4—102no—
189C2×C22⋊C4—201no—
190M32—202no—
191C2×C16—102no—
192#107—202no—
193#107C2×Dic511yescharacteristic
194#107C2×Dic511yescharacteristic
195#106—21no—
196#103—21no—
197#103—21no—
198#102—21no—
199#102—21no—
200#95—201no—
201C22×C5—21no—
202C22×C5—21no—
203C22×C5—21no—
204C22×C5—21no—
205C22×C5—21no—
206C22×C5—21no—
207C22×C5—21no—
208C22×C5—21no—
209C22×C5—42no—
210C22×C5—42no—
211C22×C5—81no—
212C22×C5—81no—
213C22×C5—81no—
214C22×C5C2×#10211yescharacteristic
215C22×C5#50911yescharacteristic
216C22×C5#51011yescharacteristic
217C4×C5—21no—
218C4×C5—21no—
219C4×C5—21no—
220C4×C5—81no—
221C4×C5—81no—
222C4×C5—81no—
223C4×C5C2×#9911yescharacteristic
224C4×C5#42111yescharacteristic
225Dic5—162no—
226C24#68611yescharacteristic
227#41—42no—
228#41—42no—
229C2×Q8—21no—
230C2×D4—21no—
231C2×D4—41no—
232C2×D4—41no—
233C2×D4—41no—
234C22×C4—41no—
235C22×C4—41no—
236C22×C4—41no—
237C22×C4—202no—
238C22×C4#68611yescharacteristic
239C22×C4#68711yescharacteristic
240C22×C4#68711yescharacteristic
241C22×C4C22⋊Dic511yescharacteristic
242C22×C4C22⋊Dic511yescharacteristic
243C22×C4C2×C22⋊D511yescharacteristic
244Q16—41no—
245SD16—42no—
246D8—41no—
247C2×C8—22no—
248C2×C8—22no—
249C2×C8—22no—
250C2×C8—41no—
251C2×C8—41no—
252C2×C8—41no—
253C2×C8C22⋊Dic511yescharacteristic
254C2×C8C22⋊Dic511yescharacteristic
255C2×C8C22×Dic511yescharacteristic
256C2×C8C2×C22⋊D511yescharacteristic
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—202no—
262C4⋊C4—202no—
263C22⋊C4—41no—
264C22⋊C4—41no—
265C22⋊C4—41no—
266C22⋊C4—41no—
267C22⋊C4—41no—
268C22⋊C4—402no—
269C42—41no—
270C16—202no—
271C2×C5—21no—
272C2×C5—21no—
273C2×C5—41no—
274C2×C5—41no—
275C2×C5—161no—
276C2×C5#151911yescharacteristic
277C2×C5#213911yescharacteristic
278C2×C5#214511yescharacteristic
279C23—21no—
280C23—21no—
281C23—41no—
282C23—41no—
283C23—41no—
284C23#396411yescharacteristic
285C23#396411yescharacteristic
286C23C2×#68611yescharacteristic
287Q8—41no—
288Q8—41no—
289D4—41no—
290D4—41no—
291D4—82no—
292D4—82no—
293D4—81no—
294D4—81no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—82no—
308C2×C4—402no—
309C2×C4—402no—
310C2×C4—402no—
311C2×C4#396411yescharacteristic
312C2×C4#396411yescharacteristic
313C2×C4C2×#68711yescharacteristic
314C2×C4C2×C22⋊Dic511yescharacteristic
315C8—21no—
316C8—21no—
317C8—21no—
318C8#396612yes—
319C5#1189011yescharacteristic, complemented, Sylow
320C22—21no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—42no—
329C22—42no—
330C22—81no—
331C22—81no—
332C22—81no—
333C22#6548211yescharacteristic
334C22#6548411yescharacteristic
335C22C2×#396411yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—81no—
340C4—81no—
341C4—81no—
342C4—802no—
343C4C2×#396611yescharacteristic
344C4#6552511yescharacteristic
345C2—21no—
346C2—21no—
347C2—41no—
348C2—41no—
349C2—161no—
350C2#1060246811yescharacteristic
351C2#1060286911yescharacteristic
352C2#1060287111yescharacteristic
subgroupG/H
centerC22C2×#3964
commutatorC2×C5×C8C22×C4
FrattiniC22×C8C22×D5
Fitting, prime radicalC5×#3050C2
socleC22×C5C2×#102
cosocleC22×C5×C8C23
hypercenter#3050D5
hypocenterC5#11890
LCSG ▷ C2×C5×C8 ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C23×C4 ◁ C23×C8 ◁ #3050

Complements

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

NH ≅ G/Ntype
2. #10602764C2semidirect
3. #10602756C2semidirect
4. #10598267C2semidirect
5. #10598265C2semidirect
6. C2×C5×#135C4semidirect
9. C5×#467C4semidirect
11. C5×#466C4semidirect
15. C5×#427C4semidirect
109. C2×#135Dic5semidirect
113. #467Dic5semidirect
115. #466Dic5semidirect
119. #427Dic5semidirect
319. C5#11890semidirect

Maximal subgroups

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

subgroupindex
C5×#30502
#106027642
#106027562
#105982672
#105982652
#118905