Finite Group Databasebeta

← #11997537

Subgroups — #11997537

Order 1280.

378 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10601550C211yesmaximal, characteristic
2C4×#3955C211yesmaximal, characteristic
3#10600643C211yesmaximal, characteristic, complemented
4C2×#64679C211yesmaximal, characteristic
5C8×#681C211yesmaximal, characteristic, complemented
6C5×#1278C211yesmaximal, characteristic, complemented
7#10598235C211yesmaximal, characteristic, complemented
8C2×C4×D20C2211yescharacteristic
9C5×#431C2211yescharacteristic
10C4×C5×M16C2211yescharacteristic
11C2×C4×C5×C8C2211yescharacteristic
12C2×#3955C411yescharacteristic
13C2×#3955C411yescharacteristic
14#65214C2211yescharacteristic
15C2×C4⋊#168C2211yescharacteristic
16C4×#681C2211yescharacteristic
17#64774C411yescharacteristic
18#64774C411yescharacteristic
19#64679—21no—
20#64679—21no—
21#64679—21no—
22#64679—21no—
23#64678—21no—
24#64677—21no—
25#64674—21no—
26C8×#168—21no—
27#9550—51nomaximal, Sylow
28C22×D20C2×C411yescharacteristic
29C22×C4×D5—21no—
30C2×C5×M16C2×C411yescharacteristic
31C2×C5×M16C2×C411yescharacteristic
32C22×C5×C8—21no—
33C2×C42×C5C2311yescharacteristic
34C2×#685—21no—
35C2×C4⋊Dic5C2×C411yescharacteristic
36C2×#681C2×C411yescharacteristic
37C2×#681C2×C411yescharacteristic
38C22×#168—21no—
39C4×D20—21no—
40C4×D20—21no—
41C4×D20—21no—
42C4×D20—21no—
43C5×C4⋊C8—21no—
44C5×C22⋊C8—21no—
45C5×#97—21no—
46C4×C5×C8—21no—
47C4×C5×C8—21no—
48C4×C5×C8—21no—
49C4×C5×C8D411yescharacteristic
50C4×C5×C8D411yescharacteristic
51C22⋊#168—21no—
52#3955—22no—
53#3955C814yescomplemented
54C4⋊#168—21no—
55C4⋊#168—21no—
56C4⋊#168D411yescharacteristic
57C4⋊#168D411yescharacteristic
58#3935—21no—
59C4×#168—21no—
60C4×#168—21no—
61C4×#100—51no—
62#1565—51no—
63#1478—51no—
64C2×D4⋊C8—51no—
65C8×M16—51no—
66#1283—51no—
67#1278D511yescharacteristic, complemented
68C23×D5—21no—
69C22×C4×C5C22×C411yescharacteristic
70C22×C4×C5#4111yescharacteristic
71C22×C4×C5#4111yescharacteristic
72C22×Dic5—21no—
73C2×D20—21no—
74C2×D20—21no—
75C2×D20—21no—
76C2×D20—21no—
77C2×D20—21no—
78C2×D20C2×C812yes—
79C2×C4×D5—41no—
80C2×C4×D5—41no—
81C2×C4×D5—81no—
82C2×C4×D5—81no—
83C5×M16—21no—
84C5×M16—21no—
85C5×M16—21no—
86C5×M16C2×C812yes—
87C2×C5×C8—21no—
88C2×C5×C8—21no—
89C2×C5×C8—21no—
90C2×C5×C8—21no—
91C2×C5×C8—42no—
92C2×C5×C8—41no—
93C42×C5C2×D411yescharacteristic
94C42×C5C2×D411yescharacteristic
95C42×C5#4111yescharacteristic
96C42×C5#4111yescharacteristic
97#685—41no—
98#685—41no—
99C4⋊Dic5—21no—
100C4⋊Dic5—21no—
101#681—21no—
102#681—21no—
103#681C2×C812yes—
104#681M1612yes—
105C2×#168—21no—
106C2×#168—21no—
107C2×#168—21no—
108C2×#168—21no—
109C2×#168—41no—
110C2×#168—81no—
111C2×C4×D4—51no—
112#431—51no—
113#431C2×D511yescharacteristic
114C2×C4⋊C8—51no—
115C2×#100—51no—
116C2×#100—51no—
117C4×M16—51no—
118C4×M16C2×D511yescharacteristic
119C2×C4×C8C2×D511yescharacteristic
120#343—51no—
121#343—51no—
122#335—101no—
123#334—101no—
124D4⋊C8—101no—
125D4⋊C8—101no—
126D4⋊C8—101no—
127D4⋊C8—101no—
128#322—101no—
129C82—101no—
130C23×C5#11711yescharacteristic
131C22×D5—22no—
132C22×D5—41no—
133C22×D5—41no—
134C22×D5—81no—
135C22×D5—81no—
136C2×C4×C5—21no—
137C2×C4×C5—21no—
138C2×C4×C5—41no—
139C2×C4×C5C4×D411yescharacteristic
140C2×C4×C5C4×D411yescharacteristic
141C2×C4×C5#12111yescharacteristic
142C2×C4×C5#12311yescharacteristic
143C2×C4×C5#12411yescharacteristic
144C2×C4×C5#12611yescharacteristic
145C2×C4×C5C22×C811yescharacteristic
146C2×C4×C5C2×M1611yescharacteristic
147C2×C4×C5#13111yescharacteristic
148C2×C4×C5#13111yescharacteristic
149C2×Dic5—41no—
150C2×Dic5—81no—
151D20—22no—
152D20—22no—
153D20—41no—
154D20—41no—
155C4×D5—82no—
156C4×D5—81no—
157C4×D5—81no—
158C5×C8—22no—
159C5×C8—22no—
160C5×C8—41no—
161C5×C8—41no—
162C5×C8—81no—
163#168—22no—
164#168—22no—
165#168—41no—
166#168—41no—
167#168—81no—
168C22×D4—51no—
169C23×C4—101no—
170C2×M16—51no—
171C2×M16—51no—
172C2×M16C4×D511yescharacteristic
173C2×M16C4×D511yescharacteristic
174C22×C8—21no—
175C22×C8—101no—
176C4×D4—101no—
177C4×D4—101no—
178C4×D4—101no—
179C4×D4—101no—
180C2×C4⋊C4—51no—
181C2×C22⋊C4—101no—
182C2×C42C22×D511yescharacteristic
183C4⋊C8—21no—
184C4⋊C8—51no—
185C4⋊C8—51no—
186C4⋊C8—101no—
187C4⋊C8—101no—
188#100—54no—
189#100—102no—
190C22⋊C8—21no—
191C22⋊C8—101no—
192#97—21no—
193#97—101no—
194C4×C8—21no—
195C4×C8—21no—
196C4×C8—21no—
197C4×C8—101no—
198C4×C8—101no—
199C4×C8D2011yescharacteristic
200C4×C8D2011yescharacteristic
201C22×C5—21no—
202C22×C5—21no—
203C22×C5#38811yescharacteristic
204C22×C5#43111yescharacteristic
205C22×C5#43311yescharacteristic
206C2×D5—42no—
207C2×D5—82no—
208C2×D5—81no—
209C2×D5—81no—
210C2×D5—82no—
211C4×C5—21no—
212C4×C5—21no—
213C4×C5—21no—
214C4×C5C8×D411yescharacteristic
215C4×C5C8×D411yescharacteristic
216C4×C5#43511yescharacteristic
217C4×C5#43611yescharacteristic
218C4×C5#47111yescharacteristic
219C4×C5#47211yescharacteristic
220Dic5—81no—
221C24—101no—
222C2×D4—52no—
223C2×D4—101no—
224C2×D4—101no—
225C2×D4—101no—
226C2×D4—101no—
227C2×D4—101no—
228C22×C4—101no—
229C22×C4—201no—
230C22×C4—201no—
231C22×C4—401no—
232C22×C4—401no—
233C22×C4C2×C4×D511yescharacteristic
234C22×C4#71111yescharacteristic
235C22×C4#71311yescharacteristic
236M16—21no—
237M16—21no—
238M16—21no—
239M16—52no—
240M16—52no—
241M16—101no—
242M16—101no—
243M16C8×D512yes—
244C2×C8—21no—
245C2×C8—21no—
246C2×C8—21no—
247C2×C8—21no—
248C2×C8—42no—
249C2×C8—41no—
250C2×C8—101no—
251C2×C8—101no—
252C2×C8—101no—
253C2×C8—101no—
254C2×C8—201no—
255C2×C8—401no—
256C4⋊C4—101no—
257C4⋊C4—101no—
258C22⋊C4—201no—
259C22⋊C4—201no—
260C42C2×D2011yescharacteristic
261C42#70911yescharacteristic
262C42D4×D511yescharacteristic
263C42#71111yescharacteristic
264C2×C5—21no—
265C2×C5—21no—
266C2×C5#192311yescharacteristic
267C2×C5#193111yescharacteristic
268C2×C5#193211yescharacteristic
269D5—82no—
270C23—102no—
271C23—201no—
272C23—201no—
273C23—401no—
274C23—401no—
275C23#403811yescharacteristic
276D4—102no—
277D4—102no—
278D4—201no—
279D4—201no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—41no—
283C2×C4—201no—
284C2×C4—402no—
285C2×C4—401no—
286C2×C4—401no—
287C2×C4—401no—
288C2×C4C4×D2011yescharacteristic
289C2×C4#402711yescharacteristic
290C2×C4#403111yescharacteristic
291C2×C4#403211yescharacteristic
292C2×C4#404111yescharacteristic
293C2×C4#404411yescharacteristic
294C2×C4C2×C8×D511yescharacteristic
295C2×C4#404711yescharacteristic
296C2×C4D5×M1611yescharacteristic
297C2×C4#405311yescharacteristic
298C8—22no—
299C8—22no—
300C8—41no—
301C8—41no—
302C8—81no—
303C8—102no—
304C8—102no—
305C8—201no—
306C8—201no—
307C8—401no—
308C5#955011yescharacteristic, complemented, Sylow
309C22—21no—
310C22—21no—
311C22—202no—
312C22—402no—
313C22—402no—
314C22—401no—
315C22—401no—
316C22#6495911yescharacteristic
317C22#6512211yescharacteristic
318C22#6512911yescharacteristic
319C4—21no—
320C4—21no—
321C4—21no—
322C4—401no—
323C4C8×D2011yescharacteristic
324C4#6499511yescharacteristic
325C4#6501411yescharacteristic
326C4#6501811yescharacteristic
327C4#6518611yescharacteristic
328C4#6518711yescharacteristic
329C2—21no—
330C2—21no—
331C2—402no—
332C2#1059940811yescharacteristic
333C2#1059954311yescharacteristic
334C2#1059972411yescharacteristic
subgroupG/H
centerC2×C4#4041
commutatorC2×C4×C5C22×C8
FrattiniC2×C42C22×D5
FittingC5×#1278C2
socleC22×C5#388
prime radicalC22×D20C2×C4
cosocleC2×C42×C5C23
hypercenter#1278D5
hypocenterC5#9550
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1278

Complements

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

NH ≅ G/Ntype
3. #10600643C2semidirect
5. C8×#681C2semidirect
6. C5×#1278C2semidirect
7. #10598235C2semidirect
53. #3955C8semidirect
67. #1278D5semidirect
308. C5#9550semidirect

Maximal subgroups

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

subgroupindex
#106015502
C4×#39552
#106006432
C2×#646792
C8×#6812
C5×#12782
#105982352
#95505