Finite Group Databasebeta

← #12017527

Subgroups — #12017527

Order 1280.

522 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×#65480C211yesmaximal, characteristic
2C2×C5×#358C211yesmaximal, characteristic, complemented
3C2×#64784C211yesmaximal, characteristic, complemented
4C2×#64729C211yesmaximal, characteristic
5C2×#64722C211yesmaximal, characteristic, complemented
6#10601399C211yesmaximal, characteristic, complemented
7C2×#64711C211yesmaximal, characteristic
8C22×C5×Q16C2211yescharacteristic
9C2×#4093—21no—
10C22×#688—21no—
11C22×D40C2211yescharacteristic
12C22×C5×C16C2211yescharacteristic
13C2×C5×#107C2211yescharacteristic
14#65480—22no—
15#65480C414yescomplemented
16C2×#3950C2211yescharacteristic
17C2×C8×Dic5C2211yescharacteristic
18C22×#672C2211yescharacteristic
19#65265—21no—
20C2×#3939—21no—
21C5×#358—22no—
22#64784—22no—
23#64729—22no—
24#64722—22no—
25#64711—22no—
26#13205—51nomaximal, Sylow
27C22×C5×Q8—21no—
28C22×D20—21no—
29C2×C5×Q16—21no—
30C2×C5×Q16—21no—
31C2×C5×Q16—21no—
32C2×C5×Q16—21no—
33C2×C5×Q16—21no—
34C2×C5×Q16C2×C412yes—
35C22×C5×C8C2311yescharacteristic
36C2×C5×C4⋊C4—21no—
37#4093—24no—
38#4093—42no—
39C2×#688—24no—
40C2×#688—42no—
41C2×#688—42no—
42C2×#685—42no—
43C2×C4⋊Dic5—21no—
44C2×#683—42no—
45C2×C4×Dic5D411yescharacteristic
46C22×#168D411yescharacteristic
47C2×D40—21no—
48C2×D40—21no—
49C2×D40—21no—
50C2×D40—21no—
51C2×D40—21no—
52C2×D40C2×C412yes—
53C2×C5×C16—21no—
54C2×C5×C16—21no—
55C2×C5×C16D412yes—
56C5×#107—21no—
57C5×#107—21no—
58#3950—21no—
59#3950—21no—
60C8×Dic5C2×C412yes—
61C8×Dic5D412yes—
62C2×#672—21no—
63C2×#672—21no—
64C2×#672D412yes—
65#3939—42no—
66C2×#495—51no—
67C2×#358—51no—
68C2×#358D511yescharacteristic, complemented
69C2×#357—51no—
70C2×#357—51no—
71C2×#346—51no—
72#1845—51no—
73C23×D5—41no—
74C2×C5×Q8—22no—
75C2×C5×Q8—41no—
76C2×C5×Q8—41no—
77C2×C5×Q8—41no—
78C2×C5×Q8—41no—
79C2×C5×Q8—41no—
80C22×C4×C5—41no—
81C22×C4×C5—41no—
82C22×C4×C5C2×D411yescharacteristic
83C22×Dic5—41no—
84C22×Dic5D812yes—
85C2×D20—22no—
86C2×D20—41no—
87C2×D20—41no—
88C2×D20—41no—
89C2×D20—41no—
90C2×D20—41no—
91C5×Q16—22no—
92C5×Q16—22no—
93C5×Q16—41no—
94C5×Q16—41no—
95C2×C5×C8C22×C411yescharacteristic
96C2×C5×C8C2×D411yescharacteristic
97C2×C5×C8C2×D411yescharacteristic
98C2×C5×C8C2×D411yescharacteristic
99C2×C5×C8#4111yescharacteristic
100C2×C5×C8#4111yescharacteristic
101C5×C4⋊C4—41no—
102C5×C4⋊C4—41no—
103#688—48no—
104#685—48no—
105C4⋊Dic5—41no—
106C4⋊Dic5—41no—
107#683—84no—
108C4×Dic5C22⋊C412yes—
109C4×Dic5SD1612yes—
110C2×#168C22⋊C412yes—
111C2×#168D812yes—
112C2×#168SD1612yes—
113D40—22no—
114D40—22no—
115D40—41no—
116D40—41no—
117C5×C16—22no—
118#672—22no—
119C22×Q16C2×D511yescharacteristic
120C22×SD16—101no—
121C22×D8—51no—
122C2×#124—101no—
123C22×C16—51no—
124C22×C16C2×D511yescharacteristic
125#495—54no—
126#495—102no—
127C2×#107—51no—
128C2×#107—101no—
129C2×#107C2×D511yescharacteristic
130C2×C4×C8—51no—
131#384—101no—
132#358—22no—
133#358—102no—
134#357—102no—
135#357—102no—
136#346—102no—
137C23×C5C2×D811yescharacteristic
138C22×D5—42no—
139C22×D5—81no—
140C22×D5—81no—
141C22×D5—82no—
142C22×D5—82no—
143C5×Q8—42no—
144C5×Q8—42no—
145C5×Q8—81no—
146C5×Q8—81no—
147C2×C4×C5—42no—
148C2×C4×C5—81no—
149C2×C4×C5—81no—
150C2×C4×C5—81no—
151C2×C4×C5—82no—
152C2×C4×C5C2×C22⋊C411yescharacteristic
153C2×C4×C5#12411yescharacteristic
154C2×C4×C5#12711yescharacteristic
155C2×C4×C5C2×D811yescharacteristic
156C2×C4×C5C2×SD1611yescharacteristic
157C2×C4×C5C2×SD1611yescharacteristic
158C2×Dic5—22no—
159C2×Dic5—22no—
160C2×Dic5—81no—
161C2×Dic5—82no—
162C2×Dic5#10214yes—
163D20—42no—
164D20—42no—
165D20—81no—
166D20—81no—
167C5×C8C4×D411yescharacteristic
168C5×C8C4×D411yescharacteristic
169C5×C8#12111yescharacteristic
170C5×C8#12111yescharacteristic
171#168#10214yes—
172C22×Q8—21no—
173C22×D4—101no—
174C2×Q16—21no—
175C2×Q16—21no—
176C2×Q16—21no—
177C2×Q16—21no—
178C2×Q16—21no—
179C2×Q16C4×D512yes—
180C2×SD16—104no—
181C2×SD16—202no—
182C2×SD16—202no—
183C2×D8—52no—
184C2×D8—101no—
185C2×D8—101no—
186C2×D8—101no—
187C2×D8—101no—
188C2×D8—101no—
189C22×C8—51no—
190C22×C8C22×D511yescharacteristic
191#124—104no—
192#124—202no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—101no—
195C2×C4⋊C4—202no—
196C2×C22⋊C4—202no—
197C2×C42—51no—
198C2×C16—21no—
199C2×C16—21no—
200C2×C16—52no—
201C2×C16—101no—
202C2×C16—101no—
203C2×C16C22⋊D512yes—
204#107—21no—
205#107—21no—
206#107—101no—
207#107—101no—
208#107—202no—
209C4×C8—52no—
210C4×C8—52no—
211C22×C5C2×#10211yescharacteristic
212C22×C5#48611yescharacteristic
213C22×C5#49311yescharacteristic
214C22×C5#50912yes—
215C22×C5#51012yes—
216C2×D5—84no—
217C2×D5—82no—
218C2×D5—162no—
219C2×D5—161no—
220C2×D5—161no—
221C4×C5—82no—
222C4×C5—161no—
223C4×C5#39011yescharacteristic
224C4×C5C2×#10211yescharacteristic
225C4×C5#48611yescharacteristic
226C4×C5#49211yescharacteristic
227Dic5—24no—
228Dic5—161no—
229C24—201no—
230C2×Q8—22no—
231C2×Q8—41no—
232C2×Q8—41no—
233C2×Q8—41no—
234C2×Q8—41no—
235C2×Q8—41no—
236C2×D4—102no—
237C2×D4—201no—
238C2×D4—201no—
239C2×D4—201no—
240C2×D4—201no—
241C2×D4—201no—
242C22×C4—41no—
243C22×C4—41no—
244C22×C4—52no—
245C22×C4—201no—
246C22×C4D4×D511yescharacteristic
247Q16—22no—
248Q16—22no—
249Q16—41no—
250Q16—41no—
251SD16—208no—
252D8—102no—
253D8—102no—
254D8—201no—
255D8—201no—
256C2×C8—52no—
257C2×C8—52no—
258C2×C8—52no—
259C2×C8C2×C4×D511yescharacteristic
260C2×C8#70911yescharacteristic
261C2×C8D4×D511yescharacteristic
262C2×C8D4×D511yescharacteristic
263C2×C8#71111yescharacteristic
264C2×C8C2×C22⋊D511yescharacteristic
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—201no—
268C4⋊C4—201no—
269C4⋊C4—404no—
270C22⋊C4—208no—
271C42—52no—
272C42—52no—
273C16—22no—
274C16—102no—
275C2×C5#195711yescharacteristic
276C2×C5#213912yes—
277C2×C5#224312yes—
278C2×C5#225011yescharacteristic
279C2×C5#225111yescharacteristic
280D5—162no—
281C23—202no—
282C23—401no—
283C23—401no—
284C23—402no—
285C23—402no—
286C23D5×D811yescharacteristic
287Q8—42no—
288Q8—42no—
289Q8—81no—
290Q8—81no—
291D4—202no—
292D4—202no—
293D4—401no—
294D4—401no—
295C2×C4—42no—
296C2×C4—54no—
297C2×C4—81no—
298C2×C4—81no—
299C2×C4—81no—
300C2×C4—82no—
301C2×C4—102no—
302C2×C4—102no—
303C2×C4—401no—
304C2×C4—402no—
305C2×C4D5×C22⋊C411yescharacteristic
306C2×C4#403111yescharacteristic
307C2×C4D5×D811yescharacteristic
308C2×C4D5×SD1611yescharacteristic
309C2×C4D5×SD1611yescharacteristic
310C2×C4#408611yescharacteristic
311C8—54no—
312C8#402711yescharacteristic
313C8#403011yescharacteristic
314C8C4×C22⋊D511yescharacteristic
315C8#408511yescharacteristic
316C5#1320511yescharacteristic, complemented, Sylow
317C22—404no—
318C22—402no—
319C22—801no—
320C22—801no—
321C22—802no—
322C22#6504911yescharacteristic
323C22D5×#10211yescharacteristic
324C22#6520312yes—
325C22#6520712yes—
326C22#6544011yescharacteristic
327C4—82no—
328C4—104no—
329C4—161no—
330C4—801no—
331C4#6504911yescharacteristic
332C4D5×#10211yescharacteristic
333C4#6524611yescharacteristic
334C4#6546411yescharacteristic
335C2—802no—
336C2#1060001012yes—
337C2#1060001412yes—
338C2#1060095011yescharacteristic
339C2#1060227411yescharacteristic
340C2#1060229411yescharacteristic
subgroupG/H
centerC23D5×D8
commutatorC2×C5×C8C22×C4
FrattiniC22×C8C22×D5
FittingC2×C5×#358C2
socleC23×C5C2×D8
prime radicalC22×D40C22
cosocleC22×C5×C8C23
hypercenterC2×#358D5
hypocenterC5#13205
LCSG ▷ C2×C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#358

Complements

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

NH ≅ G/Ntype
2. C2×C5×#358C2semidirect
3. C2×#64784C2semidirect
5. C2×#64722C2semidirect
6. #10601399C2semidirect
15. #65480C4semidirect
68. C2×#358D5semidirect
316. C5#13205semidirect

Maximal subgroups

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

subgroupindex
C2×#654802
C2×C5×#3582
C2×#647842
C2×#647292
C2×#647222
#106013992
C2×#647112
#132055