Finite Group Databasebeta

← #11994792

Subgroups — #11994792

Order 1280.

566 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10614186C211yesmaximal, characteristic
2#10611017C211yesmaximal, characteristic
3C5×#1479C211yesmaximal, characteristic, complemented
4#10602414C211yesmaximal, characteristic, complemented
5#10601576C211yesmaximal, characteristic
6#10598228C211yesmaximal, characteristic, complemented
7#10598228C211yesmaximal, characteristic, complemented
8C2×C4×C5×Q8C2211yescharacteristic
9C2×#4093C411yescharacteristic
10C2×C4×D20C2211yescharacteristic
11C5×#431C2211yescharacteristic
12C5×#431C2211yescharacteristic
13#65519C411yescharacteristic
14#65278—22no—
15#65277C411yescharacteristic
16#65265C411yescharacteristic
17#65229—22no—
18#65221C2211yescharacteristic
19#65214C2211yescharacteristic
20#65214C2211yescharacteristic
21#65123—22no—
22D5×C22⋊C8—22no—
23C8×D20—22no—
24C5×Q8⋊C8—22no—
25Q8⋊#168—22no—
26#64688—22no—
27#9099—51nomaximal, Sylow
28C22×C5×Q8C2×C411yescharacteristic
29C22×D20C2×C411yescharacteristic
30C22×C4×D5D412yes—
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
39#4093—22no—
40#4093C814yescomplemented
41C2×#685—22no—
42C2×#685—22no—
43C2×#685D412yes—
44C2×C4⋊Dic5C2×C411yescharacteristic
45C2×#683—22no—
46C2×C4×Dic5C2×C411yescharacteristic
47C2×C4×Dic5C2×C411yescharacteristic
48C2×C8×D5—24no—
49C4×D20—21no—
50C4×D20—21no—
51C4×D20—21no—
52C4×D20—21no—
53C5×C4⋊C8—21no—
54C5×C4⋊C8—21no—
55C5×C22⋊C8—21no—
56C5×C22⋊C8—21no—
57C4×C5×C8—21no—
58C4×C5×C8D412yes—
59#3963—21no—
60#3963—21no—
61#3963—22no—
62C22⋊#168—21no—
63C22⋊#168—21no—
64#3952—24no—
65C4⋊#168—21no—
66C4⋊#168—21no—
67C4×#168—21no—
68C4×#168D412yes—
69#2972—51no—
70#2326—51no—
71#1479—51no—
72#1479D511yescharacteristic, complemented
73#1460—51no—
74#1274—51no—
75#1274—51no—
76C23×D5C22⋊C412yes—
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×C5C2×D411yescharacteristic
88C22×Dic5—21no—
89C22×Dic5—21no—
90C22×Dic5C22⋊C412yes—
91C2×D20—21no—
92C2×D20—21no—
93C2×D20—21no—
94C2×D20—21no—
95C2×D20C2×C812yes—
96C2×D20M1612yes—
97C2×C4×D5—22no—
98C2×C4×D5—22no—
99C2×C4×D5—82no—
100C2×C5×C8—22no—
101C2×C5×C8—41no—
102C5×C4⋊C4—21no—
103C5×C4⋊C4—21no—
104C5×C4⋊C4—41no—
105C5×C4⋊C4—41no—
106C42×C5—41no—
107C42×C5—41no—
108C42×C5C2×D411yescharacteristic
109C42×C5C2×D411yescharacteristic
110C42×C5#4111yescharacteristic
111C42×C5#4111yescharacteristic
112#685—28no—
113#685—22no—
114#685—22no—
115#685—82no—
116C4⋊Dic5—21no—
117C4⋊Dic5—21no—
118#683—82no—
119C4×Dic5—21no—
120C4×Dic5—21no—
121C4×Dic5—21no—
122C4×Dic5C2×C812yescomplemented
123C2×#168—22no—
124C2×#168—41no—
125C8×D5—84no—
126C2×#124—51no—
127C2×C4×Q8C2×D511yescharacteristic
128C2×C4×D4—51no—
129C8×D4—102no—
130C8×D4—102no—
131#431—51no—
132#431—51no—
133#431C2×D511yescharacteristic
134#431C2×D511yescharacteristic
135C2×C22⋊C8—102no—
136#391—51no—
137#390—51no—
138#388—102no—
139#385—102no—
140#384—51no—
141#376—51no—
142Q8⋊C8—22no—
143Q8⋊C8—102no—
144#323—102no—
145C23×C5C2×C22⋊C411yescharacteristic
146C22×D5—22no—
147C22×D5—22no—
148C22×D5—42no—
149C22×D5—42no—
150C22×D5C22⋊C814yes—
151C5×Q8—22no—
152C5×Q8—22no—
153C5×Q8—41no—
154C5×Q8—41no—
155C2×C4×C5—22no—
156C2×C4×C5—41no—
157C2×C4×C5—41no—
158C2×C4×C5—41no—
159C2×C4×C5—41no—
160C2×C4×C5—42no—
161C2×C4×C5—41no—
162C2×C4×C5C4×D411yescharacteristic
163C2×C4×C5C4×D411yescharacteristic
164C2×C4×C5#12011yescharacteristic
165C2×C4×C5#12111yescharacteristic
166C2×C4×C5#12111yescharacteristic
167C2×C4×C5#12311yescharacteristic
168C2×C4×C5C22×C811yescharacteristic
169C2×C4×C5C2×M1611yescharacteristic
170C2×C4×C5#13111yescharacteristic
171C2×C4×C5#13111yescharacteristic
172C2×Dic5—22no—
173C2×Dic5—22no—
174C2×Dic5—41no—
175C2×Dic5—41no—
176C2×Dic5—42no—
177C2×Dic5—41no—
178C2×Dic5—41no—
179C2×Dic5—41no—
180D20—22no—
181D20—22no—
182D20—22no—
183D20—22no—
184C4×D5—44no—
185C4×D5—82no—
186C5×C8—42no—
187C5×C8—81no—
188#168—42no—
189#168—81no—
190C22×Q8C4×D511yescharacteristic
191C22×D4—51no—
192C23×C4—52no—
193C22×C8—104no—
194#124—54no—
195#124—102no—
196C4×Q8—21no—
197C4×Q8—21no—
198C4×Q8—21no—
199C4×Q8—21no—
200C4×D4—101no—
201C4×D4—101no—
202C4×D4—101no—
203C4×D4—101no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—51no—
206C2×C4⋊C4—102no—
207C2×C4⋊C4C4×D511yescharacteristic
208C2×C22⋊C4—52no—
209C2×C22⋊C4—102no—
210C2×C22⋊C4—102no—
211C2×C42—21no—
212C2×C42—51no—
213C2×C42—51no—
214C2×C42C22×D511yescharacteristic
215C4⋊C8—21no—
216C4⋊C8—21no—
217C4⋊C8—101no—
218C4⋊C8—101no—
219C22⋊C8—21no—
220C22⋊C8—21no—
221C22⋊C8—104no—
222C22⋊C8—101no—
223C22⋊C8—101no—
224C4×C8—21no—
225C4×C8—52no—
226C4×C8—101no—
227C4×C8C22⋊D512yes—
228#95—102no—
229#95—101no—
230#95—101no—
231C22×C5—21no—
232C22×C5—21no—
233C22×C5#38611yescharacteristic
234C22×C5C2×C22⋊C811yescharacteristic
235C22×C5#40811yescharacteristic
236C2×D5—24no—
237C2×D5—42no—
238C2×D5—42no—
239C2×D5—44no—
240C2×D5—82no—
241C4×C5—21no—
242C4×C5—21no—
243C4×C5—21no—
244C4×C5—21no—
245C4×C5—42no—
246C4×C5—81no—
247C4×C5C8×D411yescharacteristic
248C4×C5C8×D411yescharacteristic
249C4×C5#43511yescharacteristic
250C4×C5#43511yescharacteristic
251Dic5—42no—
252Dic5—42no—
253Dic5—81no—
254C24—52no—
255C2×Q8—21no—
256C2×Q8—21no—
257C2×Q8—21no—
258C2×Q8—21no—
259C2×Q8—21no—
260C2×Q8C8×D512yescomplemented
261C2×D4—52no—
262C2×D4—52no—
263C2×D4—101no—
264C2×D4—101no—
265C2×D4—101no—
266C2×D4—101no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—52no—
270C22×C4—101no—
271C22×C4—102no—
272C22×C4—102no—
273C22×C4—101no—
274C22×C4—402no—
275C22×C4C2×C4×D511yescharacteristic
276C22×C4D4×D511yescharacteristic
277C22×C4D4×D511yescharacteristic
278C2×C8—22no—
279C2×C8—41no—
280C2×C8—102no—
281C2×C8—201no—
282C2×C8—404no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—101no—
288C4⋊C4—101no—
289C4⋊C4—402no—
290C22⋊C4—108no—
291C22⋊C4—102no—
292C22⋊C4—102no—
293C22⋊C4—402no—
294C42—41no—
295C42—41no—
296C42—52no—
297C42—101no—
298C42—101no—
299C42—101no—
300C42#70911yescharacteristic
301C42D4×D511yescharacteristic
302C42#71111yescharacteristic
303C42C2×C22⋊D511yescharacteristic
304C2×C5—21no—
305C2×C5—21no—
306C2×C5#186911yescharacteristic
307C2×C5#190911yescharacteristic
308C2×C5#191111yescharacteristic
309D5—44no—
310C23—54no—
311C23—102no—
312C23—102no—
313C23—202no—
314C23—202no—
315C23D5×C22⋊C411yescharacteristic
316Q8—22no—
317Q8—22no—
318Q8—41no—
319Q8—41no—
320D4—102no—
321D4—102no—
322D4—102no—
323D4—102no—
324C2×C4—22no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—42no—
330C2×C4—41no—
331C2×C4—102no—
332C2×C4—102no—
333C2×C4—204no—
334C2×C4—201no—
335C2×C4—201no—
336C2×C4—202no—
337C2×C4—201no—
338C2×C4—201no—
339C2×C4—201no—
340C2×C4—402no—
341C2×C4#402711yescharacteristic
342C2×C4#402911yescharacteristic
343C2×C4#403011yescharacteristic
344C2×C4C2×C8×D511yescharacteristic
345C2×C4#404711yescharacteristic
346C2×C4D5×M1611yescharacteristic
347C2×C4#405311yescharacteristic
348C2×C4C4×C22⋊D511yescharacteristic
349C2×C4#408311yescharacteristic
350C2×C4#408411yescharacteristic
351C8—42no—
352C8—81no—
353C8—202no—
354C8—401no—
355C5#909911yescharacteristic, complemented, Sylow
356C22—21no—
357C22—21no—
358C22—104no—
359C22—204no—
360C22—202no—
361C22—202no—
362C22—402no—
363C22D5×C22⋊C811yescharacteristic
364C22#6501611yescharacteristic
365C22#6524511yescharacteristic
366C4—21no—
367C4—21no—
368C4—21no—
369C4—21no—
370C4—42no—
371C4—81no—
372C4—202no—
373C4—202no—
374C4—401no—
375C4#6501411yescharacteristic
376C4#6501711yescharacteristic
377C4C8×C22⋊D511yescharacteristic
378C4#6541611yescharacteristic
379C2—21no—
380C2—21no—
381C2—204no—
382C2#1060075011yescharacteristic
383C2#1060114311yescharacteristic
384C2#1060120111yescharacteristic
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#9099
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. #10602414C2semidirect
6. #10598228C2semidirect
7. #10598228C2semidirect
40. #4093C8semidirect
72. #1479D5semidirect
82. C2×C5×Q8C2×C8semidirect
122. C4×Dic5C2×C8semidirect
260. C2×Q8C8×D5semidirect
355. C5#9099semidirect

Maximal subgroups

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

subgroupindex
#106141862
#106110172
C5×#14792
#106024142
#106015762
#105982282
#90995