Finite Group Databasebeta

← #11994708

Subgroups — #11994708

Order 1280.

532 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65315C211yesmaximal, characteristic
2#10611017C211yesmaximal, characteristic
3C5×#1479C211yesmaximal, characteristic, complemented
4#10602417C211yesmaximal, characteristic, complemented
5#10601550C211yesmaximal, characteristic
6#10598232C211yesmaximal, characteristic, complemented
7#10598231C211yesmaximal, characteristic, complemented
8C2×C4×C5×Q8C2211yescharacteristic
9C22×#688C411yescharacteristic
10C2×C4×D20C2211yescharacteristic
11C5×#431C2211yescharacteristic
12C5×#431C2211yescharacteristic
13C2×#3967C411yescharacteristic
14#65315—22no—
15#65315—22no—
16C2×#3941C411yescharacteristic
17C2×#3939C411yescharacteristic
18#65214C2211yescharacteristic
19#65214C2211yescharacteristic
20C2×#3935C2211yescharacteristic
21#65123—22no—
22D5×C22⋊C8—22no—
23C8×D20—22no—
24C5×Q8⋊C8—22no—
25#64748—22no—
26#64679—22no—
27#9087—51nomaximal, Sylow
28C22×C5×Q8C2×C411yescharacteristic
29C22×D20C2×C411yescharacteristic
30C22×C4×D5—21no—
31C4×C5×Q8—21no—
32C4×C5×Q8—21no—
33C4×C5×Q8—21no—
34C4×C5×Q8—21no—
35C2×C5×C4⋊C4—21no—
36C2×C5×C4⋊C4C2×C411yescharacteristic
37C2×C42×C5—21no—
38C2×C42×C5C2311yescharacteristic
39C2×#688—22no—
40C2×#688—22no—
41C2×#688C814yescomplemented
42C2×#685—21no—
43C2×C4⋊Dic5C2×C411yescharacteristic
44C22×#168C2×C411yescharacteristic
45C22×#168C2×C411yescharacteristic
46C2×C8×D5—24no—
47C4×D20—21no—
48C4×D20—21no—
49C4×D20D412yes—
50C4×D20D412yes—
51C5×C4⋊C8—21no—
52C5×C4⋊C8—21no—
53C5×C22⋊C8—21no—
54C5×C22⋊C8—21no—
55C4×C5×C8—21no—
56C4×C5×C8D412yes—
57#3967—22no—
58C22⋊#168—21no—
59C22⋊#168D412yes—
60#3952—24no—
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#2972—51no—
70C2×#440—51no—
71#1479D511yescharacteristic, complemented
72#1478—51no—
73#1461—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×Q8C2×C812yescomplemented
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×D20C22⋊C412yes—
93C2×D20C2×C812yes—
94C2×D20M1612yes—
95C2×C4×D5—22no—
96C2×C4×D5—22no—
97C2×C4×D5—82no—
98C2×C5×C8—22no—
99C2×C5×C8—41no—
100C5×C4⋊C4—21no—
101C5×C4⋊C4—21no—
102C5×C4⋊C4—41no—
103C5×C4⋊C4—41no—
104C42×C5—41no—
105C42×C5—41no—
106C42×C5C2×D411yescharacteristic
107C42×C5C2×D411yescharacteristic
108C42×C5C2×D411yescharacteristic
109C42×C5#4111yescharacteristic
110#688—28no—
111#685—22no—
112#685—22no—
113C4⋊Dic5—21no—
114C4⋊Dic5C22⋊C412yes—
115C2×#168—21no—
116C2×#168—21no—
117C2×#168—21no—
118C2×#168—22no—
119C2×#168—21no—
120C2×#168—21no—
121C2×#168—41no—
122C2×#168C2×C812yescomplemented
123C8×D5—84no—
124C22×SD16—51no—
125C2×C4×Q8C2×D511yescharacteristic
126C2×C4×D4—51no—
127#440—102no—
128#440—102no—
129C8×D4—102no—
130C8×D4—102no—
131#431—51no—
132#431—51no—
133#431C2×D511yescharacteristic
134#431C2×D511yescharacteristic
135C2×#107—51no—
136C2×#103—51no—
137C2×#102—51no—
138C2×C22⋊C8—102no—
139C2×#97—51no—
140Q8⋊C8—22no—
141D4⋊C8—102no—
142#324—102no—
143C23×C5C4×D411yescharacteristic
144C22×D5—22no—
145C22×D5—22no—
146C22×D5—22no—
147C22×D5—81no—
148C22×D5—81no—
149C5×Q8—22no—
150C5×Q8—22no—
151C5×Q8—41no—
152C5×Q8—41no—
153C2×C4×C5—22no—
154C2×C4×C5—41no—
155C2×C4×C5—41no—
156C2×C4×C5—41no—
157C2×C4×C5—41no—
158C2×C4×C5—41no—
159C2×C4×C5—81no—
160C2×C4×C5C2×C22⋊C411yescharacteristic
161C2×C4×C5C4×D411yescharacteristic
162C2×C4×C5#12011yescharacteristic
163C2×C4×C5#12111yescharacteristic
164C2×C4×C5#12111yescharacteristic
165C2×C4×C5#12311yescharacteristic
166C2×C4×C5C22×C811yescharacteristic
167C2×C4×C5C2×M1611yescharacteristic
168C2×C4×C5#13111yescharacteristic
169C2×C4×C5#13111yescharacteristic
170C2×Dic5—22no—
171C2×Dic5—81no—
172D20—22no—
173D20—22no—
174D20—22no—
175D20C22⋊C814yes—
176C4×D5—44no—
177C4×D5—82no—
178C5×C8—42no—
179C5×C8—81no—
180#168—22no—
181#168—42no—
182#168—41no—
183#168—81no—
184C22×Q8C4×D511yescharacteristic
185C22×D4—51no—
186C23×C4—101no—
187C2×SD16—54no—
188C2×SD16—102no—
189C2×SD16—102no—
190C22×C8—51no—
191C22×C8—51no—
192C22×C8—104no—
193C4×Q8—21no—
194C4×Q8—21no—
195C4×Q8—21no—
196C4×Q8—21no—
197C4×D4—52no—
198C4×D4—52no—
199C4×D4—101no—
200C4×D4—101no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—51no—
203C2×C4⋊C4C4×D511yescharacteristic
204C2×C22⋊C4—101no—
205C2×C42—21no—
206C2×C42C22×D511yescharacteristic
207#107—102no—
208C4⋊C8—21no—
209C4⋊C8—21no—
210C4⋊C8—101no—
211C4⋊C8—101no—
212#103—102no—
213#102—102no—
214C22⋊C8—21no—
215C22⋊C8—21no—
216C22⋊C8—52no—
217C22⋊C8—104no—
218C22⋊C8—101no—
219#97—101no—
220#97—101no—
221C4×C8—21no—
222C4×C8—101no—
223C4×C8—101no—
224C4×C8C22⋊D512yes—
225C22×C5—21no—
226C22×C5—21no—
227C22×C5#38611yescharacteristic
228C22×C5C8×D411yescharacteristic
229C22×C5#43511yescharacteristic
230C2×D5—24no—
231C2×D5—42no—
232C2×D5—42no—
233C2×D5—82no—
234C2×D5—82no—
235C4×C5—21no—
236C4×C5—21no—
237C4×C5—21no—
238C4×C5—21no—
239C4×C5—42no—
240C4×C5—81no—
241C4×C5C2×C22⋊C811yescharacteristic
242C4×C5#40811yescharacteristic
243C4×C5C8×D411yescharacteristic
244C4×C5#43511yescharacteristic
245Dic5—42no—
246C24—101no—
247C2×Q8—21no—
248C2×Q8—21no—
249C2×Q8—21no—
250C2×Q8—21no—
251C2×Q8—21no—
252C2×Q8C8×D512yescomplemented
253C2×D4—52no—
254C2×D4—52no—
255C2×D4—52no—
256C2×D4—101no—
257C2×D4—101no—
258C2×D4—101no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—101no—
262C22×C4—102no—
263C22×C4—102no—
264C22×C4—402no—
265C22×C4C2×C4×D511yescharacteristic
266C22×C4D4×D511yescharacteristic
267C22×C4#71111yescharacteristic
268SD16—108no—
269C2×C8—22no—
270C2×C8—41no—
271C2×C8—52no—
272C2×C8—101no—
273C2×C8—101no—
274C2×C8—101no—
275C2×C8—101no—
276C2×C8—101no—
277C2×C8—102no—
278C2×C8—201no—
279C2×C8—404no—
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—52no—
285C4⋊C4—101no—
286C22⋊C4—102no—
287C22⋊C4—102no—
288C42—41no—
289C42—41no—
290C42#70911yescharacteristic
291C42D4×D511yescharacteristic
292C42D4×D511yescharacteristic
293C42C2×C22⋊D511yescharacteristic
294C2×C5—21no—
295C2×C5—21no—
296C2×C5#186911yescharacteristic
297C2×C5#190211yescharacteristic
298C2×C5#190411yescharacteristic
299D5—44no—
300C23—102no—
301C23—102no—
302C23—102no—
303C23—401no—
304C23—401no—
305C23#402711yescharacteristic
306Q8—22no—
307Q8—22no—
308Q8—41no—
309Q8—41no—
310D4—54no—
311D4—102no—
312D4—102no—
313D4—102no—
314C2×C4—22no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—81no—
321C2×C4—102no—
322C2×C4—204no—
323C2×C4—402no—
324C2×C4—401no—
325C2×C4D5×C22⋊C411yescharacteristic
326C2×C4#402911yescharacteristic
327C2×C4#403011yescharacteristic
328C2×C4C2×C8×D511yescharacteristic
329C2×C4#404711yescharacteristic
330C2×C4D5×M1611yescharacteristic
331C2×C4#405311yescharacteristic
332C2×C4C4×C22⋊D511yescharacteristic
333C2×C4#408311yescharacteristic
334C2×C4#408411yescharacteristic
335C8—42no—
336C8—81no—
337C8—102no—
338C8—202no—
339C8—201no—
340C8—401no—
341C5#908711yescharacteristic, complemented, Sylow
342C22—21no—
343C22—21no—
344C22—104no—
345C22—202no—
346C22—202no—
347C22—402no—
348C22—402no—
349C22#6501411yescharacteristic
350C22#6501711yescharacteristic
351C22#6524511yescharacteristic
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—42no—
357C4—81no—
358C4—202no—
359C4D5×C22⋊C811yescharacteristic
360C4#6501611yescharacteristic
361C4C8×C22⋊D511yescharacteristic
362C4#6541611yescharacteristic
363C2—21no—
364C2—21no—
365C2—204no—
366C2#1060075011yescharacteristic
367C2#1060114211yescharacteristic
368C2#1060120011yescharacteristic
subgroupG/H
centerC22#65245
commutatorC2×C4×C5C22×C8
FrattiniC2×C42C22×D5
FittingC5×#1479C2
socleC22×C5#386
prime radicalC22×D20C2×C4
cosocleC2×C42×C5C23
hypercenter#1479D5
hypocenterC5#9087
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1479

Complements

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

NH ≅ G/Ntype
3. C5×#1479C2semidirect
4. #10602417C2semidirect
6. #10598232C2semidirect
7. #10598231C2semidirect
41. C2×#688C8semidirect
71. #1479D5semidirect
82. C2×C5×Q8C2×C8semidirect
122. C2×#168C2×C8semidirect
252. C2×Q8C8×D5semidirect
341. C5#9087semidirect

Maximal subgroups

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

subgroupindex
C2×#653152
#106110172
C5×#14792
#106024172
#106015502
#105982322
#105982312
#90875