Finite Group Databasebeta

← #11998730

Subgroups — #11998730

Order 1280.

396 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×#3167C211yesmaximal, characteristic
2#10602629C211yesmaximal, characteristic, complemented
3#10602615C211yesmaximal, characteristic, complemented
4#10602605C211yesmaximal, characteristic
5#10602591C211yesmaximal, characteristic
6#10600544C211yesmaximal, characteristic, complemented
7#10600525C211yesmaximal, characteristic, complemented
8C5×#533C2211yescharacteristic
9C5×#532C2211yescharacteristic
10C5×#498C411yescharacteristic, complemented
11C5×#492C411yescharacteristic, complemented
12C5×#487C411yescharacteristic, complemented
13C5×#486C411yescharacteristic, complemented
14C5×#465—21no—
15C5×#465—21no—
16C4×C5×SD16—21no—
17C4×C5×SD16—21no—
18C2×C4×C5×C8C2211yescharacteristic
19#65221C2211yescharacteristic
20#65215C2211yescharacteristic
21#65215C2211yescharacteristic
22C2×#3935C2211yescharacteristic
23#64770—21no—
24#64770—21no—
25#64763—22no—
26#64760—22no—
27#64758—22no—
28#64757—22no—
29#64678—21no—
30#64677—21no—
31#9766—51nomaximal, Sylow
32C2×C5×#41—21no—
33C2×C5×SD16—21no—
34C2×C5×SD16—21no—
35C22×C5×C8D411yescharacteristic
36C22×C5×C8D411yescharacteristic
37C5×C4⋊Q8C2×C411yescharacteristic
38C5×C4⋊Q8C2×C411yescharacteristic
39C5×C4⋊Q8C2×C411yescharacteristic
40C5×#127C2×C411yescharacteristic
41C5×#125—21no—
42C5×#124—21no—
43C5×C22⋊Q8—21no—
44C5×C22⋊Q8—21no—
45C5×#121—21no—
46C5×#121—21no—
47C4×C5×Q8—21no—
48C4×C5×Q8—21no—
49C4×C5×D4—21no—
50C4×C5×D4—21no—
51C5×#117—21no—
52C2×C42×C5C2311yescharacteristic
53C2×C4×Dic5—21no—
54C22×#168—21no—
55C5×#106—21no—
56C5×#106—21no—
57C5×#103—21no—
58C5×#103—21no—
59C5×#102—21no—
60C5×#102—21no—
61C4×C5×C8C2×C411yescharacteristic
62C4×C5×C8C2×C411yescharacteristic
63C4×C5×C8D411yescharacteristic
64C4×C5×C8D411yescharacteristic
65#3963—21no—
66#3963D412yes—
67C22⋊#168—21no—
68C22⋊#168—21no—
69C4⋊#168—21no—
70C4⋊#168—21no—
71#3935—21no—
72#3935—21no—
73#3935—21no—
74#3935D412yes—
75#3167D511yescharacteristic
76#1746—51no—
77#1568—51no—
78#1531—51no—
79#1530—51no—
80#1506—51no—
81#1505—51no—
82C5×#41—82no—
83C2×C5×Q8—21no—
84C2×C5×Q8—21no—
85C2×C5×Q8—21no—
86C2×C5×D4—21no—
87C2×C5×D4—21no—
88C2×C5×D4—21no—
89C2×C5×D4—41no—
90C22×C4×C5—41no—
91C22×C4×C5C2×D411yescharacteristic
92C22×C4×C5C2×D411yescharacteristic
93C22×C4×C5#4111yescharacteristic
94C22×Dic5—22no—
95C5×SD16—42no—
96C5×SD16—42no—
97C2×C5×C8—41no—
98C2×C5×C8—41no—
99C2×C5×C8C22⋊C411yescharacteristic
100C2×C5×C8C22⋊C411yescharacteristic
101C2×C5×C8C22⋊C411yescharacteristic
102C2×C5×C8C22⋊C411yescharacteristic
103C5×C4⋊C4—21no—
104C5×C4⋊C4—21no—
105C5×C4⋊C4—21no—
106C5×C4⋊C4—21no—
107C5×C4⋊C4—21no—
108C5×C4⋊C4—21no—
109C5×C4⋊C4—41no—
110C5×C4⋊C4—41no—
111C5×C22⋊C4—41no—
112C5×C22⋊C4—41no—
113C5×C22⋊C4—41no—
114C42×C5—41no—
115C42×C5C22×C411yescharacteristic
116C42×C5C2×D411yescharacteristic
117C42×C5C2×D411yescharacteristic
118C42×C5#4111yescharacteristic
119C4×Dic5—41no—
120C4×Dic5—41no—
121C2×#168—22no—
122C2×#168—41no—
123C2×#168—41no—
124C2×#168—41no—
125C2×#168—41no—
126#533C2×D511yescharacteristic
127#532C2×D511yescharacteristic
128#498Dic511yescharacteristic, complemented
129#492Dic511yescharacteristic, complemented
130#487Dic511yescharacteristic, complemented
131#486Dic511yescharacteristic, complemented
132#465—21no—
133#465—21no—
134C4×SD16—21no—
135C4×SD16—21no—
136#432—51no—
137#432—51no—
138C2×#97—51no—
139C2×C4×C8C2×D511yescharacteristic
140#376—51no—
141#336—101no—
142#336—101no—
143#335—101no—
144#334—101no—
145#330—102no—
146#329—102no—
147#328—102no—
148#327—102no—
149C23×C5—41no—
150C23×C5#12111yescharacteristic
151C5×Q8—41no—
152C5×Q8—41no—
153C5×Q8—81no—
154C5×Q8—81no—
155C5×D4—41no—
156C5×D4—41no—
157C5×D4—81no—
158C5×D4—81no—
159C5×D4—82no—
160C2×C4×C5—22no—
161C2×C4×C5—21no—
162C2×C4×C5—21no—
163C2×C4×C5—41no—
164C2×C4×C5—41no—
165C2×C4×C5—41no—
166C2×C4×C5—41no—
167C2×C4×C5—82no—
168C2×C4×C5C2×C22⋊C411yescharacteristic
169C2×C4×C5C4×D411yescharacteristic
170C2×C4×C5C4×D411yescharacteristic
171C2×C4×C5#12111yescharacteristic
172C2×C4×C5#12411yescharacteristic
173C2×C4×C5#12711yescharacteristic
174C2×Dic5—42no—
175C2×Dic5—42no—
176C2×Dic5—42no—
177C5×C8—21no—
178C5×C8—21no—
179C5×C8—21no—
180C5×C8—21no—
181#168—42no—
182#168—81no—
183#168—81no—
184C2×#41—21no—
185C2×SD16—21no—
186C2×SD16—21no—
187C22×C8—101no—
188C22×C8C22⋊D511yescharacteristic
189C22×C8C22⋊D511yescharacteristic
190C4⋊Q8C2×Dic511yescharacteristic
191C4⋊Q8C2×Dic511yescharacteristic
192C4⋊Q8C2×Dic511yescharacteristic
193#127C2×Dic511yescharacteristic
194#125—21no—
195#124—21no—
196C22⋊Q8—21no—
197C22⋊Q8—21no—
198#121—21no—
199#121—21no—
200C4×Q8—21no—
201C4×Q8—21no—
202C4×D4—21no—
203C4×D4—21no—
204#117—21no—
205C2×C42—101no—
206C2×C42C22×D511yescharacteristic
207#106—21no—
208#106—21no—
209C4⋊C8—101no—
210C4⋊C8—101no—
211#103—21no—
212#103—21no—
213#102—21no—
214#102—21no—
215C22⋊C8—101no—
216C22⋊C8—101no—
217#97—52no—
218#97—101no—
219#97—101no—
220#97—101no—
221C4×C8C2×Dic511yescharacteristic
222C4×C8C2×Dic511yescharacteristic
223C4×C8C22⋊D511yescharacteristic
224C4×C8C22⋊D511yescharacteristic
225#95—52no—
226#95—101no—
227C22×C5—21no—
228C22×C5—21no—
229C22×C5—81no—
230C22×C5—81no—
231C22×C5—81no—
232C22×C5#39011yescharacteristic
233C22×C5#47112yes—
234C4×C5—21no—
235C4×C5—21no—
236C4×C5—21no—
237C4×C5—21no—
238C4×C5—21no—
239C4×C5—81no—
240C4×C5—81no—
241C4×C5—81no—
242C4×C5#42111yescharacteristic
243C4×C5#42111yescharacteristic
244Dic5—82no—
245#41—82no—
246C2×Q8—21no—
247C2×Q8—21no—
248C2×Q8—21no—
249C2×D4—21no—
250C2×D4—21no—
251C2×D4—21no—
252C2×D4—41no—
253C22×C4—41no—
254C22×C4—102no—
255C22×C4D4×D511yescharacteristic
256C22×C4#71111yescharacteristic
257C22×C4C2×C22⋊D511yescharacteristic
258SD16—42no—
259SD16—42no—
260C2×C8—41no—
261C2×C8—41no—
262C2×C8—102no—
263C2×C8—201no—
264C2×C8—201no—
265C2×C8—201no—
266C2×C8—201no—
267C2×C8C22⋊Dic511yescharacteristic
268C2×C8C22⋊Dic511yescharacteristic
269C2×C8C22⋊Dic511yescharacteristic
270C2×C8C22⋊Dic511yescharacteristic
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C22⋊C4—41no—
280C22⋊C4—41no—
281C22⋊C4—41no—
282C42—41no—
283C42—201no—
284C42—201no—
285C42D4×D511yescharacteristic
286C42#71111yescharacteristic
287C42C22×Dic511yescharacteristic
288C42C2×C22⋊D511yescharacteristic
289C2×C5—22no—
290C2×C5—161no—
291C2×C5#196311yescharacteristic
292C2×C5#197611yescharacteristic
293C2×C5#197711yescharacteristic
294C23—41no—
295C23#408411yescharacteristic
296Q8—41no—
297Q8—41no—
298Q8—81no—
299Q8—81no—
300D4—41no—
301D4—41no—
302D4—81no—
303D4—81no—
304D4—82no—
305C2×C4—22no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—82no—
313C2×C4—202no—
314C2×C4—202no—
315C2×C4—202no—
316C2×C4D4×Dic511yescharacteristic
317C2×C4D4×Dic511yescharacteristic
318C2×C4#408211yescharacteristic
319C2×C4#408411yescharacteristic
320C2×C4#408611yescharacteristic
321C2×C4C2×C22⋊Dic511yescharacteristic
322C8—21no—
323C8—21no—
324C8—21no—
325C8—21no—
326C8—202no—
327C8—401no—
328C8—401no—
329C5#976611yescharacteristic, complemented, Sylow
330C22—21no—
331C22—21no—
332C22—81no—
333C22—81no—
334C22—81no—
335C22#6546612yes—
336C22#6551011yescharacteristic
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—81no—
343C4—81no—
344C4—81no—
345C4—402no—
346C4#6552511yescharacteristic
347C4#6552511yescharacteristic
348C2—22no—
349C2—161no—
350C2#1060260911yescharacteristic
351C2#1060284511yescharacteristic
352C2#1060287911yescharacteristic
subgroupG/H
centerC22#65510
commutatorC42×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#3167C2
socleC22×C5#390
prime radicalC5×#532C22
cosocleC2×C42×C5C23
hypercenter#3167D5
hypocenterC5#9766
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3167

Complements

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

NH ≅ G/Ntype
2. #10602629C2semidirect
3. #10602615C2semidirect
6. #10600544C2semidirect
7. #10600525C2semidirect
10. C5×#498C4semidirect
11. C5×#492C4semidirect
12. C5×#487C4semidirect
13. C5×#486C4semidirect
128. #498Dic5semidirect
129. #492Dic5semidirect
130. #487Dic5semidirect
131. #486Dic5semidirect
329. C5#9766semidirect

Maximal subgroups

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

subgroupindex
C5×#31672
#106026292
#106026152
#106026052
#106025912
#106005442
#106005252
#97665