Finite Group Databasebeta

← #11997694

Subgroups — #11997694

Order 1280.

386 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#1990C211yesmaximal, characteristic
2#10602571C211yesmaximal, characteristic
3C2×#64767C211yesmaximal, characteristic
4#10600550C211yesmaximal, characteristic
5#10600361C211yesmaximal, characteristic
6#10598145C211yesmaximal, characteristic
7#10598125C211yesmaximal, characteristic
8C2×C5×C4⋊Q8C2211yescharacteristic
9C2×C4×C5×C8C2211yescharacteristic
10C5×#384C2211yescharacteristic
11C2×#3967—21no—
12C2×#3967—21no—
13C2×#3947—21no—
14C2×#3940—21no—
15C4×C4⋊Dic5C2211yescharacteristic
16C2×C4⋊#168C2211yescharacteristic
17C2×C4⋊#168C2211yescharacteristic
18C2×C4⋊#168C2211yescharacteristic
19C5×#340—21no—
20C5×#340—21no—
21#64770—21no—
22#64767C414yescomplemented
23#64749—21no—
24#9573—51nomaximal, Sylow
25C22×C5×Q8—21no—
26C22×C5×C8D411yescharacteristic
27C22×C5×C8D411yescharacteristic
28C5×C4⋊Q8—21no—
29C5×C4⋊Q8—21no—
30C5×C4⋊Q8—21no—
31C5×C4⋊Q8C2×C412yes—
32C2×C5×C4⋊C4—21no—
33C2×C5×C4⋊C4—21no—
34C2×C5×C4⋊C4—21no—
35C2×C5×C4⋊C4—21no—
36C2×C5×C4⋊C4—21no—
37C2×C42×C5C2311yescharacteristic
38C2×C4⋊Dic5D411yescharacteristic
39C2×C4⋊Dic5D411yescharacteristic
40C2×C4×Dic5—21no—
41C22×#168—21no—
42C22×#168—21no—
43C22×#168—21no—
44C4×C5×C8—21no—
45C4×C5×C8—21no—
46#3967—42no—
47#3967—42no—
48#3963—21no—
49#3947—42no—
50#3940—42no—
51C4⋊#168—21no—
52C4⋊#168—21no—
53C4⋊#168—21no—
54C4⋊#168—21no—
55C4⋊#168C2×C412yes—
56C4⋊#168C2×C412yes—
57#1990D511yescharacteristic
58#1981—51no—
59#1948—51no—
60#1770—51no—
61C2×#332—51no—
62#1296—51no—
63#1277—51no—
64C2×C5×Q8—22no—
65C2×C5×Q8—41no—
66C2×C5×Q8—41no—
67C2×C5×Q8—41no—
68C2×C5×Q8—41no—
69C2×C5×Q8—41no—
70C22×C4×C5—41no—
71C22×C4×C5—41no—
72C22×C4×C5C2×D411yescharacteristic
73C22×C4×C5C2×D411yescharacteristic
74C22×C4×C5#4111yescharacteristic
75C22×Dic5—21no—
76C22×Dic5—21no—
77C2×C5×C8—21no—
78C2×C5×C8—21no—
79C2×C5×C8—21no—
80C2×C5×C8—21no—
81C2×C5×C8—21no—
82C2×C5×C8SD1612yes—
83C5×C4⋊C4—22no—
84C5×C4⋊C4—22no—
85C5×C4⋊C4—41no—
86C5×C4⋊C4—41no—
87C5×C4⋊C4—41no—
88C5×C4⋊C4—41no—
89C5×C4⋊C4—41no—
90C5×C4⋊C4—41no—
91C5×C4⋊C4—81no—
92C42×C5C22×C411yescharacteristic
93C42×C5#4111yescharacteristic
94C42×C5#4111yescharacteristic
95C42×C5#4111yescharacteristic
96C4⋊Dic5—21no—
97C4⋊Dic5—21no—
98C4⋊Dic5—21no—
99C4⋊Dic5—21no—
100C4×Dic5—41no—
101C4×Dic5—41no—
102C2×#168—22no—
103C2×#168—22no—
104C2×#168—41no—
105C2×#168—41no—
106C2×#168—41no—
107C2×#168—41no—
108C2×#168—41no—
109C2×#168—41no—
110C2×#168—41no—
111C2×C4⋊Q8C2×D511yescharacteristic
112C2×#106—101no—
113C2×C4⋊C8—51no—
114C2×C4⋊C8—51no—
115C2×C4⋊C8—51no—
116C2×#103—101no—
117C2×#103—101no—
118C2×#97—101no—
119C2×C4×C8C2×D511yescharacteristic
120#384C2×D511yescharacteristic
121C4×C4⋊C4—51no—
122#340—21no—
123#340—21no—
124#340—101no—
125#336—101no—
126#332—54no—
127C23×C5#12111yescharacteristic
128C5×Q8—42no—
129C5×Q8—42no—
130C5×Q8—81no—
131C5×Q8—81no—
132C2×C4×C5—21no—
133C2×C4×C5—21no—
134C2×C4×C5—42no—
135C2×C4×C5—81no—
136C2×C4×C5—81no—
137C2×C4×C5—81no—
138C2×C4×C5—81no—
139C2×C4×C5—81no—
140C2×C4×C5#11711yescharacteristic
141C2×C4×C5C4×D411yescharacteristic
142C2×C4×C5C4×D411yescharacteristic
143C2×C4×C5#12311yescharacteristic
144C2×C4×C5#12411yescharacteristic
145C2×C4×C5#12611yescharacteristic
146C2×C4×C5C2×SD1611yescharacteristic
147C2×C4×C5#13511yescharacteristic
148C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
149C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
150C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C5#13711yescharacteristic
152C2×C4×C5#13711yescharacteristic
153C2×C4×C5#13711yescharacteristic
154C2×Dic5—41no—
155C2×Dic5—41no—
156C2×Dic5—41no—
157C2×Dic5—41no—
158C2×Dic5—41no—
159C2×Dic5—41no—
160C5×C8—22no—
161C5×C8—41no—
162#168—42no—
163#168—42no—
164#168—81no—
165C22×Q8—21no—
166C22×C8—101no—
167C22×C8—101no—
168C22×C8—101no—
169C22×C8C22⋊D511yescharacteristic
170C22×C8C22⋊D511yescharacteristic
171C4⋊Q8—21no—
172C4⋊Q8—21no—
173C4⋊Q8—21no—
174C4⋊Q8C4×D512yes—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4—51no—
181C2×C4⋊C4—51no—
182C2×C42—101no—
183C2×C42C22×D511yescharacteristic
184#106—202no—
185C4⋊C8—52no—
186C4⋊C8—52no—
187C4⋊C8—101no—
188C4⋊C8—101no—
189C4⋊C8—101no—
190C4⋊C8—101no—
191#103—202no—
192#103—202no—
193#97—202no—
194C4×C8—21no—
195C4×C8—21no—
196#95—101no—
197C22×C5#38811yescharacteristic
198C22×C5#46111yescharacteristic
199C22×C5#46411yescharacteristic
200C22×C5#46811yescharacteristic
201C22×C5#46911yescharacteristic
202C22×C5#47111yescharacteristic
203C22×C5#47311yescharacteristic
204C4×C5—21no—
205C4×C5—21no—
206C4×C5—82no—
207C4×C5—161no—
208C4×C5C4×SD1611yescharacteristic
209C4×C5#44011yescharacteristic
210C4×C5#44111yescharacteristic
211C4×C5#44211yescharacteristic
212C4×C5#48311yescharacteristic
213C4×C5#48511yescharacteristic
214C4×C5#48911yescharacteristic
215C4×C5#49011yescharacteristic
216Dic5—81no—
217Dic5—81no—
218C2×Q8—22no—
219C2×Q8—41no—
220C2×Q8—41no—
221C2×Q8—41no—
222C2×Q8—41no—
223C2×Q8—41no—
224C22×C4—41no—
225C22×C4—41no—
226C22×C4—101no—
227C22×C4—101no—
228C22×C4D4×D511yescharacteristic
229C22×C4#71111yescharacteristic
230C22×C4C2×C22⋊D511yescharacteristic
231C2×C8—21no—
232C2×C8—21no—
233C2×C8—21no—
234C2×C8—21no—
235C2×C8—21no—
236C2×C8—102no—
237C2×C8—102no—
238C2×C8—201no—
239C2×C8—201no—
240C2×C8—201no—
241C2×C8—201no—
242C2×C8—201no—
243C2×C8—201no—
244C2×C8—201no—
245C2×C8#68812yes—
246C4⋊C4—22no—
247C4⋊C4—22no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—81no—
255C4⋊C4—101no—
256C4⋊C4—101no—
257C4⋊C4—101no—
258C4⋊C4—101no—
259C42—201no—
260C42—201no—
261C42C2×C4×D511yescharacteristic
262C42#70911yescharacteristic
263C42#71111yescharacteristic
264C42#71111yescharacteristic
265C2×C5#169111yescharacteristic
266C2×C5#169311yescharacteristic
267C2×C5#170011yescharacteristic
268C2×C5#170211yescharacteristic
269C2×C5#192711yescharacteristic
270C2×C5#193011yescharacteristic
271C2×C5#193611yescharacteristic
272C23#408411yescharacteristic
273Q8—42no—
274Q8—42no—
275Q8—81no—
276Q8—81no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—42no—
280C2×C4—81no—
281C2×C4—81no—
282C2×C4—81no—
283C2×C4—81no—
284C2×C4—81no—
285C2×C4—201no—
286C2×C4—201no—
287C2×C4—201no—
288C2×C4—201no—
289C2×C4—201no—
290C2×C4—201no—
291C2×C4#402311yescharacteristic
292C2×C4#402511yescharacteristic
293C2×C4#402711yescharacteristic
294C2×C4#403111yescharacteristic
295C2×C4#405711yescharacteristic
296C2×C4#405711yescharacteristic
297C2×C4#406011yescharacteristic
298C2×C4#406111yescharacteristic
299C2×C4C4×C22⋊D511yescharacteristic
300C2×C4#408111yescharacteristic
301C2×C4C2×#68811yescharacteristic
302C2×C4#408811yescharacteristic
303C2×C4#409611yescharacteristic
304C2×C4#409711yescharacteristic
305C8—22no—
306C8—41no—
307C8—202no—
308C8—202no—
309C8—401no—
310C5#957311yescharacteristic, complemented, Sylow
311C22#6523311yescharacteristic
312C22#6534311yescharacteristic
313C22#6537211yescharacteristic
314C22#6544811yescharacteristic
315C22#6546311yescharacteristic
316C22#6546611yescharacteristic
317C22#6548111yescharacteristic
318C4—21no—
319C4—21no—
320C4—82no—
321C4—161no—
322C4—401no—
323C4—401no—
324C4#6504611yescharacteristic
325C4#6505311yescharacteristic
326C4#6505411yescharacteristic
327C4#6507411yescharacteristic
328C4C4×#68811yescharacteristic
329C4#6531911yescharacteristic
330C4#6533211yescharacteristic
331C4#6533411yescharacteristic
332C2#1060045911yescharacteristic
333C2#1060098111yescharacteristic
334C2#1060105611yescharacteristic
335C2#1060200411yescharacteristic
336C2#1060203511yescharacteristic
337C2#1060213811yescharacteristic
338C2#1060216611yescharacteristic
subgroupG/H
centerC23#4084
commutatorC42×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#1990C2
socle, prime radicalC23×C5#121
cosocleC2×C42×C5C23
hypercenter#1990D5
hypocenterC5#9573
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1990

Complements

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

NH ≅ G/Ntype
22. #64767C4semidirect
310. C5#9573semidirect

Maximal subgroups

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

subgroupindex
C5×#19902
#106025712
C2×#647672
#106005502
#106003612
#105981452
#105981252
#95735