Finite Group Databasebeta

← #11998653

Subgroups — #11998653

Order 1280.

428 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3131C211yesmaximal, characteristic
2#10602628C211yesmaximal, characteristic, complemented
3#10602617C211yesmaximal, characteristic, complemented
4#10602604C211yesmaximal, characteristic
5#10602593C211yesmaximal, characteristic
6C8×C4⋊Dic5C211yesmaximal, characteristic, complemented
7#10600522C211yesmaximal, characteristic, complemented
8C5×#533C2211yescharacteristic
9C5×#532C2211yescharacteristic
10C5×#488—21no—
11C5×#488—21no—
12C5×#487C411yescharacteristic, complemented
13C5×#487C411yescharacteristic, complemented
14C5×#486C411yescharacteristic, complemented
15C5×#486C411yescharacteristic, complemented
16C5×#416—21no—
17C5×#416—21no—
18C2×C4×C5×C8C2211yescharacteristic
19C2×C8×Dic5—21no—
20C4×C4⋊Dic5C2211yescharacteristic
21#65214C2211yescharacteristic
22#65214C2211yescharacteristic
23C2×C4⋊#168C2211yescharacteristic
24#64770—21no—
25#64758—22no—
26#64757—22no—
27Q8⋊#168—22no—
28D4⋊#168—22no—
29#64678—21no—
30#64677—21no—
31#9751—51nomaximal, Sylow
32C2×C5×#41—21no—
33C22×C5×C8D411yescharacteristic
34C22×C5×C8D411yescharacteristic
35C5×C4⋊Q8C2×C411yescharacteristic
36C5×C4⋊Q8C2×C411yescharacteristic
37C5×C4⋊Q8C2×C411yescharacteristic
38C5×#127C2×C411yescharacteristic
39C5×#125—21no—
40C5×#124—21no—
41C5×C22⋊Q8—21no—
42C5×C22⋊Q8—21no—
43C5×#121—21no—
44C5×#121—21no—
45C4×C5×Q8—21no—
46C4×C5×Q8—21no—
47C4×C5×D4—21no—
48C4×C5×D4—21no—
49C5×#117—21no—
50C2×C42×C5C2311yescharacteristic
51C2×C4⋊Dic5—21no—
52C2×C4×Dic5—21no—
53C22×#168—21no—
54C5×#103—21no—
55C5×#103—21no—
56C5×#103—21no—
57C5×#103—21no—
58C5×#102—21no—
59C5×#102—21no—
60C5×#102—21no—
61C5×#102—21no—
62C4×C5×C8C2×C411yescharacteristic
63C4×C5×C8C2×C411yescharacteristic
64C4×C5×C8D411yescharacteristic
65C4×C5×C8D411yescharacteristic
66#3963D412yes—
67C22⋊#168—21no—
68C22⋊#168—21no—
69C8×Dic5—42no—
70C4⋊#168—21no—
71C4⋊#168—21no—
72C4⋊#168—21no—
73C4⋊#168D412yes—
74C4×#168—21no—
75C4×#168—21no—
76#3131D511yescharacteristic
77C8×C4⋊C4—51no—
78#1564—51no—
79#1503—51no—
80#1502—51no—
81#1481—51no—
82#1480—51no—
83C5×#41—41no—
84C5×#41—41no—
85C5×#41—41no—
86C5×#41—41no—
87C2×C5×Q8—21no—
88C2×C5×Q8—21no—
89C2×C5×Q8—21no—
90C2×C5×D4—21no—
91C2×C5×D4—21no—
92C2×C5×D4—21no—
93C2×C5×D4—41no—
94C22×C4×C5—41no—
95C22×C4×C5C2×D411yescharacteristic
96C22×C4×C5C2×D411yescharacteristic
97C22×C4×C5#4111yescharacteristic
98C22×Dic5—22no—
99C2×C5×C8—21no—
100C2×C5×C8—21no—
101C2×C5×C8—21no—
102C2×C5×C8—21no—
103C2×C5×C8C22⋊C411yescharacteristic
104C2×C5×C8C22⋊C411yescharacteristic
105C2×C5×C8C22⋊C411yescharacteristic
106C2×C5×C8C22⋊C411yescharacteristic
107C5×C4⋊C4—21no—
108C5×C4⋊C4—21no—
109C5×C4⋊C4—21no—
110C5×C4⋊C4—21no—
111C5×C4⋊C4—21no—
112C5×C4⋊C4—21no—
113C5×C4⋊C4—41no—
114C5×C4⋊C4—41no—
115C5×C22⋊C4—41no—
116C5×C22⋊C4—41no—
117C5×C22⋊C4—41no—
118C42×C5—41no—
119C42×C5C22×C411yescharacteristic
120C42×C5C2×D411yescharacteristic
121C42×C5C2×D411yescharacteristic
122C42×C5#4111yescharacteristic
123C4⋊Dic5—24no—
124C4×Dic5—41no—
125C4×Dic5—41no—
126C2×#168—22no—
127C2×#168—41no—
128C2×#168—41no—
129C2×#168—41no—
130C2×#168—41no—
131#533C2×D511yescharacteristic
132#532C2×D511yescharacteristic
133#488—21no—
134#488—21no—
135#487Dic511yescharacteristic, complemented
136#487Dic511yescharacteristic, complemented
137#486Dic511yescharacteristic, complemented
138#486Dic511yescharacteristic, complemented
139#431—51no—
140#431—51no—
141C2×C4⋊C8—51no—
142#416—21no—
143#416—21no—
144C2×C4×C8—101no—
145C2×C4×C8C2×D511yescharacteristic
146C4×C4⋊C4—51no—
147#336—101no—
148#335—101no—
149#334—101no—
150#328—102no—
151#327—102no—
152Q8⋊C8—102no—
153D4⋊C8—102no—
154C23×C5—41no—
155C23×C5#12111yescharacteristic
156C5×Q8—41no—
157C5×Q8—41no—
158C5×Q8—42no—
159C5×Q8—81no—
160C5×D4—41no—
161C5×D4—41no—
162C5×D4—42no—
163C5×D4—81no—
164C5×D4—81no—
165C5×D4—81no—
166C2×C4×C5—22no—
167C2×C4×C5—41no—
168C2×C4×C5—41no—
169C2×C4×C5—41no—
170C2×C4×C5—41no—
171C2×C4×C5—81no—
172C2×C4×C5—81no—
173C2×C4×C5C2×C22⋊C411yescharacteristic
174C2×C4×C5C4×D411yescharacteristic
175C2×C4×C5C4×D411yescharacteristic
176C2×C4×C5#12111yescharacteristic
177C2×C4×C5#12411yescharacteristic
178C2×C4×C5#12711yescharacteristic
179C2×C4×C5#13511yescharacteristic
180C2×C4×C5#13511yescharacteristic
181C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
182C2×C4×C5#13711yescharacteristic
183C2×Dic5—24no—
184C2×Dic5—42no—
185C2×Dic5—42no—
186C5×C8—21no—
187C5×C8—21no—
188C5×C8—21no—
189C5×C8—21no—
190#168—42no—
191#168—81no—
192#168—81no—
193C2×#41—21no—
194C22×C8—101no—
195C22×C8C22⋊D511yescharacteristic
196C22×C8C22⋊D511yescharacteristic
197C4⋊Q8C2×Dic511yescharacteristic
198C4⋊Q8C2×Dic511yescharacteristic
199C4⋊Q8C2×Dic511yescharacteristic
200#127C2×Dic511yescharacteristic
201#125—21no—
202#124—21no—
203C22⋊Q8—21no—
204C22⋊Q8—21no—
205#121—21no—
206#121—21no—
207C4×Q8—21no—
208C4×Q8—21no—
209C4×D4—21no—
210C4×D4—21no—
211#117—21no—
212C2×C4⋊C4—101no—
213C2×C42—101no—
214C2×C42C22×D511yescharacteristic
215C4⋊C8—52no—
216C4⋊C8—101no—
217C4⋊C8—101no—
218C4⋊C8—101no—
219#103—21no—
220#103—21no—
221#103—21no—
222#103—21no—
223#102—21no—
224#102—21no—
225#102—21no—
226#102—21no—
227C22⋊C8—101no—
228C22⋊C8—101no—
229C4×C8—101no—
230C4×C8—101no—
231C4×C8—202no—
232C4×C8C2×Dic511yescharacteristic
233C4×C8C2×Dic511yescharacteristic
234C4×C8C22⋊D511yescharacteristic
235C4×C8C22⋊D511yescharacteristic
236#95—52no—
237C22×C5—21no—
238C22×C5—21no—
239C22×C5—81no—
240C22×C5—81no—
241C22×C5—81no—
242C22×C5#39011yescharacteristic
243C22×C5#46311yescharacteristic
244C22×C5#46411yescharacteristic
245C4×C5—21no—
246C4×C5—21no—
247C4×C5—21no—
248C4×C5—81no—
249C4×C5—81no—
250C4×C5—81no—
251C4×C5#41611yescharacteristic
252C4×C5#41711yescharacteristic
253C4×C5#44312yes—
254C4×C5#46311yescharacteristic
255C4×C5#46411yescharacteristic
256Dic5—44no—
257#41—41no—
258#41—41no—
259#41—41no—
260#41—41no—
261C2×Q8—21no—
262C2×Q8—21no—
263C2×Q8—21no—
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—41no—
268C22×C4—41no—
269C22×C4—102no—
270C22×C4D4×D511yescharacteristic
271C22×C4#71111yescharacteristic
272C22×C4C2×C22⋊D511yescharacteristic
273C2×C8—21no—
274C2×C8—21no—
275C2×C8—21no—
276C2×C8—21no—
277C2×C8—102no—
278C2×C8—201no—
279C2×C8—201no—
280C2×C8—201no—
281C2×C8—201no—
282C2×C8C22⋊Dic511yescharacteristic
283C2×C8C22⋊Dic511yescharacteristic
284C2×C8C22⋊Dic511yescharacteristic
285C2×C8C22⋊Dic511yescharacteristic
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—21no—
290C4⋊C4—21no—
291C4⋊C4—21no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—104no—
295C22⋊C4—41no—
296C22⋊C4—41no—
297C22⋊C4—41no—
298C42—41no—
299C42—201no—
300C42—201no—
301C42D4×D511yescharacteristic
302C42#71111yescharacteristic
303C42C22×Dic511yescharacteristic
304C42C2×C22⋊D511yescharacteristic
305C2×C5—21no—
306C2×C5—21no—
307C2×C5—161no—
308C2×C5#197411yescharacteristic
309C2×C5#197611yescharacteristic
310C2×C5#198311yescharacteristic
311C23—41no—
312C23#408411yescharacteristic
313Q8—42no—
314Q8—41no—
315Q8—41no—
316Q8—81no—
317D4—42no—
318D4—41no—
319D4—41no—
320D4—81no—
321D4—81no—
322D4—81no—
323C2×C4—22no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—81no—
329C2×C4—81no—
330C2×C4—104no—
331C2×C4—202no—
332C2×C4—202no—
333C2×C4D4×Dic511yescharacteristic
334C2×C4D4×Dic511yescharacteristic
335C2×C4#408211yescharacteristic
336C2×C4#408411yescharacteristic
337C2×C4#408611yescharacteristic
338C2×C4#409511yescharacteristic
339C2×C4#409611yescharacteristic
340C2×C4#409611yescharacteristic
341C2×C4#409711yescharacteristic
342C2×C4C2×C22⋊Dic511yescharacteristic
343C8—21no—
344C8—21no—
345C8—21no—
346C8—21no—
347C8—202no—
348C8—401no—
349C8—401no—
350C5#975111yescharacteristic, complemented, Sylow
351C22—21no—
352C22—21no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22#6534311yescharacteristic
357C22#6534611yescharacteristic
358C22#6551011yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—81no—
363C4—81no—
364C4—81no—
365C4—204no—
366C4#6534311yescharacteristic
367C4#6534611yescharacteristic
368C4#6548512yes—
369C4#6552111yescharacteristic
370C4#6552211yescharacteristic
371C2—21no—
372C2—21no—
373C2—161no—
374C2#1060251411yescharacteristic
375C2#1060287711yescharacteristic
376C2#1060287911yescharacteristic
subgroupG/H
centerC2×C4#4084
commutatorC42×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#3131C2
socleC22×C5#390
prime radicalC5×#532C22
cosocleC2×C42×C5C23
hypercenter#3131D5
hypocenterC5#9751
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3131

Complements

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

NH ≅ G/Ntype
2. #10602628C2semidirect
3. #10602617C2semidirect
6. C8×C4⋊Dic5C2semidirect
7. #10600522C2semidirect
12. C5×#487C4semidirect
13. C5×#487C4semidirect
14. C5×#486C4semidirect
15. C5×#486C4semidirect
135. #487Dic5semidirect
136. #487Dic5semidirect
137. #486Dic5semidirect
138. #486Dic5semidirect
350. C5#9751semidirect

Maximal subgroups

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

subgroupindex
C5×#31312
#106026282
#106026172
#106026042
#106025932
C8×C4⋊Dic52
#106005222
#97515