Finite Group Databasebeta

← #12003917

Subgroups — #12003917

Order 1280.

386 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#335C211yesmaximal, characteristic
2#10601249C211yesmaximal, characteristic
3#10601247C211yesmaximal, characteristic
4C2×#64702C211yesmaximal, characteristic
5#10600579C211yesmaximal, characteristic
6#10600570C211yesmaximal, characteristic
7#10598193C211yesmaximal, characteristic
8C2×#4015C2211yescharacteristic
9C2×C5×C4⋊C8C2211yescharacteristic
10C2×C5×C4⋊C8C2211yescharacteristic
11C2×C4×C5×C8C2211yescharacteristic
12C2×#3949—21no—
13C2×#3948—21no—
14C2×#3948—21no—
15C2×#3946—21no—
16#65224C2211yescharacteristic
17C4×C4⋊Dic5C2211yescharacteristic
18C2×C4⋊#168C2211yescharacteristic
19C5×#335—22no—
20#64771—21no—
21#64771—21no—
22#64771—21no—
23#64770—21no—
24#64702—22no—
25#10602—51nomaximal, Sylow
26C22×Dic10—21no—
27C22×C5×C8—21no—
28C22×C5×C8—21no—
29C22×C5×C8D411yescharacteristic
30C22×C5×C8D411yescharacteristic
31C2×C42×C5C2311yescharacteristic
32C2×C4⋊Dic5—21no—
33C2×C4⋊Dic5—21no—
34C2×C4⋊Dic5—21no—
35C2×C4⋊Dic5—21no—
36C2×C4⋊Dic5—21no—
37C2×C4⋊Dic5D411yescharacteristic
38C2×C4⋊Dic5D411yescharacteristic
39C2×C4×Dic5—21no—
40C22×#168—21no—
41#4015—21no—
42#4015—21no—
43#4015—21no—
44#4015Q812yes—
45C5×C4⋊C8—21no—
46C5×C4⋊C8—21no—
47C5×C4⋊C8—21no—
48C5×C4⋊C8D412yes—
49C4×C5×C8—21no—
50C4×C5×C8—21no—
51#3963—21no—
52#3949—42no—
53#3948—42no—
54#3948—42no—
55#3946—42no—
56C4⋊#168—21no—
57C4⋊#168—21no—
58#1990—51no—
59#1981—51no—
60#1948—51no—
61#1939—51no—
62C2×#335D511yescharacteristic
63C2×#332—51no—
64#1296—51no—
65C22×C4×C5C2×D411yescharacteristic
66C22×C4×C5C2×D411yescharacteristic
67C22×C4×C5#4111yescharacteristic
68C22×Dic5—21no—
69C22×Dic5—21no—
70C22×Dic5—41no—
71C22×Dic5—41no—
72C2×Dic10—22no—
73C2×Dic10—41no—
74C2×Dic10—41no—
75C2×Dic10—41no—
76C2×Dic10—41no—
77C2×Dic10—41no—
78C2×C5×C8—21no—
79C2×C5×C8—21no—
80C2×C5×C8—22no—
81C2×C5×C8—21no—
82C2×C5×C8—21no—
83C2×C5×C8—21no—
84C2×C5×C8—41no—
85C2×C5×C8—41no—
86C2×C5×C8—41no—
87C2×C5×C8—41no—
88C2×C5×C8—41no—
89C2×C5×C8SD1612yes—
90C42×C5C2×D411yescharacteristic
91C42×C5C2×Q811yescharacteristic
92C42×C5#4111yescharacteristic
93C42×C5#4111yescharacteristic
94C4⋊Dic5—21no—
95C4⋊Dic5—22no—
96C4⋊Dic5—22no—
97C4⋊Dic5—21no—
98C4⋊Dic5—21no—
99C4⋊Dic5—41no—
100C4⋊Dic5—41no—
101C4⋊Dic5—41no—
102C4⋊Dic5—41no—
103C4⋊Dic5—41no—
104C4⋊Dic5—41no—
105C4⋊Dic5—81no—
106C4⋊Dic5D812yes—
107C4×Dic5—41no—
108C4×Dic5—41no—
109C2×#168—41no—
110C2×#168—41no—
111C2×#168—41no—
112C2×C4⋊Q8—51no—
113C2×#106—101no—
114C2×C4⋊C8—51no—
115C2×C4⋊C8—101no—
116C2×C4⋊C8C2×D511yescharacteristic
117C2×C4⋊C8C2×D511yescharacteristic
118C2×#103—101no—
119C2×#103—101no—
120C2×C4×C8C2×D511yescharacteristic
121#384—51no—
122C4×C4⋊C4—51no—
123#340—101no—
124#340—101no—
125#340—101no—
126#336—101no—
127#335—22no—
128#332—102no—
129C23×C5#12111yescharacteristic
130C2×C4×C5—21no—
131C2×C4×C5—21no—
132C2×C4×C5#12111yescharacteristic
133C2×C4×C5#12111yescharacteristic
134C2×C4×C5C22⋊Q811yescharacteristic
135C2×C4×C5C22⋊Q811yescharacteristic
136C2×C4×C5C22⋊Q811yescharacteristic
137C2×C4×C5#12611yescharacteristic
138C2×C4×C5C2×D811yescharacteristic
139C2×C4×C5C2×SD1611yescharacteristic
140C2×C4×C5#13511yescharacteristic
141C2×C4×C5#13511yescharacteristic
142C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C5#13711yescharacteristic
144C2×C4×C5#13711yescharacteristic
145C2×C4×C5#13711yescharacteristic
146C2×Dic5—22no—
147C2×Dic5—41no—
148C2×Dic5—41no—
149C2×Dic5—42no—
150C2×Dic5—41no—
151C2×Dic5—41no—
152C2×Dic5—41no—
153C2×Dic5—81no—
154C2×Dic5—81no—
155C2×Dic5—81no—
156C2×Dic5—81no—
157C2×Dic5—81no—
158Dic10—42no—
159Dic10—42no—
160Dic10—81no—
161Dic10—81no—
162C5×C8—22no—
163C5×C8—42no—
164C5×C8—41no—
165C5×C8—81no—
166#168—81no—
167C22×Q8—101no—
168C22×C8—21no—
169C22×C8—21no—
170C22×C8—101no—
171C22×C8D2011yescharacteristic
172C22×C8D2011yescharacteristic
173C4⋊Q8—52no—
174C4⋊Q8—101no—
175C4⋊Q8—101no—
176C4⋊Q8—101no—
177C2×C4⋊C4—51no—
178C2×C4⋊C4—51no—
179C2×C4⋊C4—101no—
180C2×C4⋊C4—101no—
181C2×C4⋊C4—101no—
182C2×C4⋊C4—101no—
183C2×C4⋊C4—101no—
184C2×C42—101no—
185C2×C42C22×D511yescharacteristic
186#106—202no—
187C4⋊C8—21no—
188C4⋊C8—21no—
189C4⋊C8—21no—
190C4⋊C8—101no—
191C4⋊C8—101no—
192C4⋊C8—202no—
193C4⋊C8C22⋊D512yes—
194#103—202no—
195#103—202no—
196C4×C8—21no—
197C4×C8—21no—
198#95—101no—
199C22×C5#39611yescharacteristic
200C22×C5#46111yescharacteristic
201C22×C5#46411yescharacteristic
202C22×C5#46611yescharacteristic
203C22×C5#46811yescharacteristic
204C22×C5#47111yescharacteristic
205C22×C5#47311yescharacteristic
206C4×C5—21no—
207C4×C5—21no—
208C4×C5#45911yescharacteristic
209C4×C5#46411yescharacteristic
210C4×C5#46511yescharacteristic
211C4×C5#47011yescharacteristic
212C4×C5#47411yescharacteristic
213C4×C5#47511yescharacteristic
214C4×C5#47811yescharacteristic
215C4×C5#47911yescharacteristic
216Dic5—42no—
217Dic5—82no—
218Dic5—81no—
219Dic5—161no—
220C2×Q8—102no—
221C2×Q8—201no—
222C2×Q8—201no—
223C2×Q8—201no—
224C2×Q8—201no—
225C2×Q8—201no—
226C22×C4—101no—
227C22×C4—101no—
228C22×C4—201no—
229C22×C4—201no—
230C22×C4C2×D2011yescharacteristic
231C22×C4D4×D511yescharacteristic
232C22×C4#71311yescharacteristic
233C2×C8—21no—
234C2×C8—21no—
235C2×C8—21no—
236C2×C8—21no—
237C2×C8—21no—
238C2×C8—22no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—201no—
245C2×C8—201no—
246C2×C8—201no—
247C2×C8#67712yes—
248C4⋊C4—52no—
249C4⋊C4—101no—
250C4⋊C4—102no—
251C4⋊C4—101no—
252C4⋊C4—101no—
253C4⋊C4—102no—
254C4⋊C4—201no—
255C4⋊C4—201no—
256C4⋊C4—201no—
257C4⋊C4—201no—
258C4⋊C4—201no—
259C4⋊C4—201no—
260C4⋊C4—401no—
261C42—201no—
262C42—201no—
263C42#70911yescharacteristic
264C42#71111yescharacteristic
265C42Q8×D511yescharacteristic
266C42C2×C22⋊D511yescharacteristic
267C2×C5#167311yescharacteristic
268C2×C5#168211yescharacteristic
269C2×C5#169111yescharacteristic
270C2×C5#170011yescharacteristic
271C2×C5#206411yescharacteristic
272C2×C5#206611yescharacteristic
273C2×C5#206711yescharacteristic
274C23#404111yescharacteristic
275Q8—202no—
276Q8—202no—
277Q8—401no—
278Q8—401no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—102no—
282C2×C4—201no—
283C2×C4—201no—
284C2×C4—202no—
285C2×C4—201no—
286C2×C4—201no—
287C2×C4—201no—
288C2×C4—401no—
289C2×C4—401no—
290C2×C4—401no—
291C2×C4—401no—
292C2×C4—401no—
293C2×C4#404211yescharacteristic
294C2×C4#404311yescharacteristic
295C2×C4#404411yescharacteristic
296C2×C4C2×#67711yescharacteristic
297C2×C4#405011yescharacteristic
298C2×C4#405511yescharacteristic
299C2×C4#405511yescharacteristic
300C2×C4D5×D811yescharacteristic
301C2×C4#405711yescharacteristic
302C2×C4#406411yescharacteristic
303C2×C4#406511yescharacteristic
304C2×C4#407611yescharacteristic
305C2×C4#408511yescharacteristic
306C2×C4#409211yescharacteristic
307C8—22no—
308C8—41no—
309C8—42no—
310C8—81no—
311C8—401no—
312C5#1060211yescharacteristic, complemented, Sylow
313C22#6513011yescharacteristic
314C22#6513411yescharacteristic
315C22#6517211yescharacteristic
316C22#6517511yescharacteristic
317C22#6518511yescharacteristic
318C22#6518711yescharacteristic
319C22#6528311yescharacteristic
320C4—21no—
321C4—21no—
322C4—202no—
323C4—401no—
324C4—402no—
325C4—801no—
326C4#6511811yescharacteristic
327C4#6514011yescharacteristic
328C4#6517911yescharacteristic
329C4#6518011yescharacteristic
330C4#6540311yescharacteristic
331C4#6542611yescharacteristic
332C4#6543911yescharacteristic
333C4#6547411yescharacteristic
334C2#1059937111yescharacteristic
335C2#1059937611yescharacteristic
336C2#1059938311yescharacteristic
337C2#1059938811yescharacteristic
338C2#1060128111yescharacteristic
339C2#1060143211yescharacteristic
340C2#1060151011yescharacteristic
subgroupG/H
centerC23#4041
commutator, cosocleC2×C42×C5C23
FrattiniC2×C42C22×D5
FittingC2×C5×#335C2
socle, prime radicalC23×C5#121
hypercenterC2×#335D5
hypocenterC5#10602
LCSG ▷ C2×C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#335

Complements

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

NH ≅ G/Ntype
312. C5#10602semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#3352
#106012492
#106012472
C2×#647022
#106005792
#106005702
#105981932
#106025