Finite Group Databasebeta

← #11994760

Subgroups — #11994760

Order 1280.

488 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2983C211yesmaximal, characteristic, complemented
2C2×#65315C211yesmaximal, characteristic
3#10602414C211yesmaximal, characteristic, complemented
4#10601576C211yesmaximal, characteristic
5#10601550C211yesmaximal, characteristic
6#10598232C211yesmaximal, characteristic, complemented
7#10598231C211yesmaximal, characteristic, complemented
8C2×C4×C5×Q8C2211yescharacteristic
9C22×#688C411yescharacteristic
10C2×C4×D20C2211yescharacteristic
11C5×#446—22no—
12C5×#446—22no—
13C5×#432—22no—
14C5×#431C2211yescharacteristic
15C5×#431C2211yescharacteristic
16C2×#3967C411yescharacteristic
17#65315—22no—
18#65315—22no—
19C2×#3941C411yescharacteristic
20C2×#3939C411yescharacteristic
21#65214C2211yescharacteristic
22#65214C2211yescharacteristic
23C2×#3935C2211yescharacteristic
24Q8⋊#168—22no—
25#64688—22no—
26#64679—22no—
27#9094—51nomaximal, Sylow
28C22×C5×Q8C2×C411yescharacteristic
29C22×D20C2×C411yescharacteristic
30C22×C4×D5—21no—
31C4×C5×Q8—21no—
32C4×C5×Q8—21no—
33C4×C5×Q8D412yes—
34C4×C5×Q8D412yes—
35C2×C5×C4⋊C4—21no—
36C2×C5×C4⋊C4C2×C411yescharacteristic
37C2×C42×C5—21no—
38C2×C42×C5C2311yescharacteristic
39C2×#688—22no—
40C2×#688—22no—
41C2×#688—22no—
42C2×#685—21no—
43C2×C4⋊Dic5C2×C411yescharacteristic
44C22×#168C2×C411yescharacteristic
45C22×#168C2×C411yescharacteristic
46C4×D20—21no—
47C4×D20—21no—
48C4×D20—21no—
49C4×D20—21no—
50C5×C4⋊C8—24no—
51C5×C4⋊C8—21no—
52C5×C4⋊C8—21no—
53C5×C22⋊C8—21no—
54C5×C22⋊C8D412yes—
55C5×#97—24no—
56C4×C5×C8—21no—
57C4×C5×C8D412yes—
58#3967—22no—
59C22⋊#168—21no—
60C22⋊#168—21no—
61#3941—22no—
62#3939—22no—
63C4⋊#168—21no—
64C4⋊#168—21no—
65#3935—21no—
66#3935—21no—
67C4×#168—21no—
68C4×#168—21no—
69#2983D511yescharacteristic, complemented
70C2×#440—51no—
71#1479—51no—
72#1478—51no—
73#1460—51no—
74#1281—51no—
75#1275—51no—
76C23×D5—21no—
77C2×C5×Q8—21no—
78C2×C5×Q8—21no—
79C2×C5×Q8—21no—
80C2×C5×Q8—21no—
81C2×C5×Q8—21no—
82C2×C5×Q8C22⋊C412yes—
83C22×C4×C5—21no—
84C22×C4×C5—21no—
85C22×C4×C5C22×C411yescharacteristic
86C22×C4×C5C2×D411yescharacteristic
87C22×C4×C5#4111yescharacteristic
88C22×Dic5—21no—
89C2×D20—21no—
90C2×D20—21no—
91C2×D20—21no—
92C2×D20—21no—
93C2×D20—21no—
94C2×D20M1612yes—
95C2×C4×D5—41no—
96C2×C4×D5—41no—
97C2×C4×D5—82no—
98C2×C5×C8—22no—
99C2×C5×C8—22no—
100C5×C4⋊C4—21no—
101C5×C4⋊C4—22no—
102C5×C4⋊C4—22no—
103C5×C4⋊C4C22⋊C412yes—
104C42×C5—22no—
105C42×C5—22no—
106C42×C5C2×D411yescharacteristic
107C42×C5C2×D411yescharacteristic
108C42×C5C2×D411yescharacteristic
109C42×C5#4111yescharacteristic
110#688—28no—
111#685—41no—
112#685—41no—
113C4⋊Dic5—21no—
114C4⋊Dic5—21no—
115C2×#168—21no—
116C2×#168—21no—
117C2×#168—21no—
118C2×#168—21no—
119C2×#168—21no—
120C2×#168—41no—
121C2×#168—41no—
122C2×#168M1612yes—
123C22×SD16—51no—
124C2×C4×Q8C2×D511yescharacteristic
125C2×C4×D4—51no—
126#446—22no—
127#446—22no—
128#440—102no—
129#440—102no—
130#432—22no—
131#431—51no—
132#431—51no—
133#431C2×D511yescharacteristic
134#431C2×D511yescharacteristic
135C2×#107—51no—
136C2×#103—51no—
137C2×#102—51no—
138C2×#97—51no—
139Q8⋊C8—102no—
140D4⋊C8—102no—
141#323—102no—
142C23×C5C4×D411yescharacteristic
143C22×D5—22no—
144C22×D5—41no—
145C22×D5—41no—
146C22×D5—81no—
147C22×D5—81no—
148C5×Q8—22no—
149C5×Q8—22no—
150C5×Q8—41no—
151C5×Q8—41no—
152C2×C4×C5—22no—
153C2×C4×C5—22no—
154C2×C4×C5—41no—
155C2×C4×C5—41no—
156C2×C4×C5—41no—
157C2×C4×C5—41no—
158C2×C4×C5—81no—
159C2×C4×C5C2×C22⋊C411yescharacteristic
160C2×C4×C5C4×D411yescharacteristic
161C2×C4×C5#12011yescharacteristic
162C2×C4×C5#12111yescharacteristic
163C2×C4×C5#12111yescharacteristic
164C2×C4×C5#12311yescharacteristic
165C2×C4×C5C2×M1611yescharacteristic
166C2×C4×C5C2×M1611yescharacteristic
167C2×C4×C5#13111yescharacteristic
168C2×C4×C5#13111yescharacteristic
169C2×Dic5—41no—
170C2×Dic5—81no—
171D20—22no—
172D20—22no—
173D20—41no—
174D20—41no—
175C4×D5—82no—
176C4×D5—82no—
177C5×C8—42no—
178C5×C8—42no—
179#168—22no—
180#168—41no—
181#168—81no—
182#168—81no—
183C22×Q8C4×D511yescharacteristic
184C22×D4—51no—
185C23×C4—101no—
186C2×SD16—102no—
187C2×SD16—102no—
188C2×SD16—102no—
189C22×C8—51no—
190C22×C8—51no—
191C4×Q8—21no—
192C4×Q8—21no—
193C4×Q8D2012yes—
194C4×Q8C22⋊D512yes—
195C4×D4—101no—
196C4×D4—101no—
197C4×D4—101no—
198C4×D4—101no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—51no—
201C2×C4⋊C4C4×D511yescharacteristic
202C2×C22⋊C4—101no—
203C2×C42—21no—
204C2×C42C22×D511yescharacteristic
205#107—102no—
206C4⋊C8—24no—
207C4⋊C8—21no—
208C4⋊C8—21no—
209C4⋊C8—101no—
210C4⋊C8—101no—
211#103—102no—
212#102—102no—
213C22⋊C8—21no—
214C22⋊C8—101no—
215C22⋊C8—101no—
216C22⋊C8C22⋊D512yes—
217#97—24no—
218#97—101no—
219#97—101no—
220C4×C8—21no—
221C4×C8—101no—
222C4×C8—101no—
223C4×C8C22⋊D512yes—
224C22×C5—21no—
225C22×C5—21no—
226C22×C5#38611yescharacteristic
227C22×C5#43511yescharacteristic
228C22×C5#43611yescharacteristic
229C2×D5—42no—
230C2×D5—82no—
231C2×D5—81no—
232C2×D5—81no—
233C2×D5—82no—
234C4×C5—21no—
235C4×C5—21no—
236C4×C5—21no—
237C4×C5—21no—
238C4×C5—42no—
239C4×C5—42no—
240C4×C5#40711yescharacteristic
241C4×C5#40811yescharacteristic
242C4×C5#43511yescharacteristic
243C4×C5#43611yescharacteristic
244Dic5—81no—
245C24—101no—
246C2×Q8—21no—
247C2×Q8—21no—
248C2×Q8—21no—
249C2×Q8—21no—
250C2×Q8—21no—
251C2×Q8#68512yes—
252C2×D4—52no—
253C2×D4—101no—
254C2×D4—101no—
255C2×D4—101no—
256C2×D4—101no—
257C2×D4—101no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—101no—
261C22×C4—201no—
262C22×C4—201no—
263C22×C4—402no—
264C22×C4C2×C4×D511yescharacteristic
265C22×C4#70911yescharacteristic
266C22×C4C2×C22⋊D511yescharacteristic
267SD16—108no—
268C2×C8—22no—
269C2×C8—22no—
270C2×C8—52no—
271C2×C8—101no—
272C2×C8—101no—
273C2×C8—101no—
274C2×C8—101no—
275C2×C8—101no—
276C2×C8—201no—
277C2×C8—201no—
278C4⋊C4—21no—
279C4⋊C4—22no—
280C4⋊C4—22no—
281C4⋊C4—101no—
282C4⋊C4—101no—
283C4⋊C4#68512yes—
284C22⋊C4—201no—
285C22⋊C4—201no—
286C42—22no—
287C42—22no—
288C42C2×D2011yescharacteristic
289C42#70911yescharacteristic
290C42C2×C22⋊D511yescharacteristic
291C42C2×C22⋊D511yescharacteristic
292C2×C5—21no—
293C2×C5—21no—
294C2×C5#187011yescharacteristic
295C2×C5#190311yescharacteristic
296C2×C5#190511yescharacteristic
297D5—82no—
298C23—102no—
299C23—201no—
300C23—201no—
301C23—401no—
302C23—401no—
303C23C4×C22⋊D511yescharacteristic
304Q8—22no—
305Q8—22no—
306Q8—41no—
307Q8—41no—
308D4—102no—
309D4—102no—
310D4—201no—
311D4—201no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—81no—
319C2×C4—201no—
320C2×C4—402no—
321C2×C4—402no—
322C2×C4—401no—
323C2×C4D5×M1611yescharacteristic
324C2×C4D5×M1611yescharacteristic
325C2×C4#405311yescharacteristic
326C2×C4#405311yescharacteristic
327C2×C4C2×#68511yescharacteristic
328C2×C4C4×C22⋊D511yescharacteristic
329C2×C4#407511yescharacteristic
330C2×C4#407611yescharacteristic
331C2×C4#407611yescharacteristic
332C2×C4#409911yescharacteristic
333C8—42no—
334C8—42no—
335C8—102no—
336C8—201no—
337C8—401no—
338C8—401no—
339C5#909411yescharacteristic, complemented, Sylow
340C22—21no—
341C22—21no—
342C22—202no—
343C22—402no—
344C22—402no—
345C22—401no—
346C22—401no—
347C22#6541611yescharacteristic
348C22#6541711yescharacteristic
349C22#6550211yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—42no—
355C4—42no—
356C4—401no—
357C4#6541511yescharacteristic
358C4#6541611yescharacteristic
359C4#6541711yescharacteristic
360C4#6541811yescharacteristic
361C2—21no—
362C2—21no—
363C2—402no—
364C2#1060245511yescharacteristic
365C2#1060278911yescharacteristic
366C2#1060281611yescharacteristic
subgroupG/H
centerC22#65502
commutatorC22×C4×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#2983C2
socleC22×C5#386
prime radicalC22×D20C2×C4
cosocleC2×C42×C5C23
hypercenter#2983D5
hypocenterC5#9094
LCSG ▷ C22×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2983

Complements

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

NH ≅ G/Ntype
1. C5×#2983C2semidirect
3. #10602414C2semidirect
6. #10598232C2semidirect
7. #10598231C2semidirect
69. #2983D5semidirect
339. C5#9094semidirect

Maximal subgroups

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

subgroupindex
C5×#29832
C2×#653152
#106024142
#106015762
#106015502
#105982322
#105982312
#90945