Finite Group Databasebeta

← #11992171

Subgroups — #11992171

Order 1280.

462 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#4047C211yesmaximal, characteristic
2C5×#1564C211yesmaximal, characteristic, complemented
3#10601548C212yesmaximal
4C2×#64677C211yesmaximal, characteristic, complemented
5#10598235C212yesmaximal, complemented
6C2×#4047C411yescharacteristic
7C2×#4047C411yescharacteristic
8C4×#709C2211yescharacteristic
9C5×#431C2212yes—
10C2×C4×C5×C8C2211yescharacteristic
11#65390C411yescharacteristic
12#65390C411yescharacteristic
13C2×C4⋊#168C2212yes—
14C4×#681C2211yescharacteristic
15#64978—21no—
16#64978—21no—
17C4×#676—21no—
18C4×C8×D5—21no—
19C5×#335—21no—
20C5×#334—21no—
21#64679—22no—
22#64677—21no—
23#64677—21no—
24#64676—22no—
25#8604—51nomaximal, Sylow
26C2×#709C2×C411yescharacteristic
27C22×C5×C8C2×C411yescharacteristic
28C22×C5×C8C2×C411yescharacteristic
29C2×C42×C5C2311yescharacteristic
30C4×C22⋊D5—21no—
31C4×C22⋊D5—21no—
32#4072C2×C411yescharacteristic
33C2×#681C2×C411yescharacteristic
34C2×#681C2×C411yescharacteristic
35C22×#168—22no—
36#4047—22no—
37#4047—22no—
38#4047—22no—
39#4047C814yescomplemented
40C2×#676—21no—
41C2×#676—21no—
42C2×C8×D5—21no—
43C2×C8×D5—21no—
44C4×D20D411yescharacteristic
45C4×D20Q811yescharacteristic
46#4018—21no—
47C42×D5—21no—
48C4×Dic10D411yescharacteristic
49C4×Dic10Q811yescharacteristic
50C5×C4⋊C8—22no—
51C5×C22⋊C8—22no—
52C4×C5×C8—22no—
53C4×C5×C8D411yescharacteristic
54C4×C5×C8D411yescharacteristic
55C4×C5×C8D411yescharacteristic
56C4×C5×C8D411yescharacteristic
57#3947—21no—
58#3947—21no—
59C8×Dic5—21no—
60C8×Dic5—21no—
61C4⋊#168—22no—
62C4⋊#168—22no—
63#3935—21no—
64C4×#168—21no—
65C4×#131—51no—
66#1564D511yescharacteristic, complemented
67C2×#334—51no—
68#1477—52no—
69#1283—52no—
70C22×C4×C5C22×C411yescharacteristic
71C22×C4×C5#4111yescharacteristic
72C22×C4×C5#4111yescharacteristic
73C2×C22⋊D5—21no—
74#709—21no—
75#709—21no—
76#709C2×C812yes—
77#709M1612yes—
78C2×D20C4⋊C411yescharacteristic
79C2×C4×D5—21no—
80C2×C4×D5—21no—
81C2×C4×D5—21no—
82C2×Dic10C4⋊C411yescharacteristic
83C2×C5×C8—21no—
84C2×C5×C8—21no—
85C2×C5×C8—42no—
86C2×C5×C8C22⋊C411yescharacteristic
87C2×C5×C8C22⋊C411yescharacteristic
88C2×C5×C8C22⋊C411yescharacteristic
89C2×C5×C8C22⋊C411yescharacteristic
90C2×C5×C8C2×C812yes—
91C2×C5×C8M1612yes—
92C42×C5C2×D411yescharacteristic
93C42×C5C2×D411yescharacteristic
94C42×C5C2×D411yescharacteristic
95C42×C5C2×Q811yescharacteristic
96C22⋊Dic5—21no—
97#685—21no—
98#685—21no—
99C4⋊Dic5C4⋊C411yescharacteristic
100C4⋊Dic5C4⋊C411yescharacteristic
101#683—21no—
102#683—21no—
103C4×Dic5—21no—
104C4×Dic5—21no—
105C4×Dic5—21no—
106#681—21no—
107#681—21no—
108#681C2×C812yes—
109#681M1612yes—
110C2×#168—21no—
111C2×#168—21no—
112C2×#168—42no—
113C2×#168—82no—
114#676—24no—
115#676—24no—
116C8×D5—24no—
117C8×D5—24no—
118C2×#131—51no—
119C2×#131—51no—
120C4×#41—51no—
121#431C2×D512yes—
122C2×C4⋊C8—52no—
123#405—51no—
124#405—51no—
125#405—101no—
126#405—101no—
127C4×M16—51no—
128C4×M16—101no—
129C2×C4×C8—101no—
130C2×C4×C8C2×D511yescharacteristic
131#335—21no—
132#334—21no—
133#334—101no—
134#334—101no—
135Q8⋊C8—102no—
136D4⋊C8—102no—
137C23×C5#11711yescharacteristic
138C22×D5—21no—
139C2×C4×C5—22no—
140C2×C4×C5—41no—
141C2×C4×C5C2×C22⋊C411yescharacteristic
142C2×C4×C5C2×C4⋊C411yescharacteristic
143C2×C4×C5#12111yescharacteristic
144C2×C4×C5#12111yescharacteristic
145C2×C4×C5C22⋊Q811yescharacteristic
146C2×C4×C5C22⋊Q811yescharacteristic
147C2×C4×C5C22×C811yescharacteristic
148C2×C4×C5C2×M1611yescharacteristic
149C2×C4×C5C2×M1611yescharacteristic
150C2×C4×C5C2×M1611yescharacteristic
151C22⋊D5—22no—
152C22⋊D5—22no—
153C2×Dic5—21no—
154C2×Dic5—21no—
155C2×Dic5—21no—
156D20—21no—
157D20C4⋊C812yes—
158C4×D5—22no—
159C4×D5—22no—
160C4×D5—42no—
161C4×D5—42no—
162Dic10—21no—
163Dic10C4⋊C812yes—
164C5×C8—21no—
165C5×C8—21no—
166C5×C8—82no—
167C5×C8C22⋊C812yes—
168C5×C8C22⋊C812yes—
169#168—22no—
170#168—22no—
171#168—82no—
172C2×#41—51no—
173#131—54no—
174#131—102no—
175#131—102no—
176#131—102no—
177C2×M16—51no—
178C2×M16—51no—
179C2×M16—101no—
180C2×M16—101no—
181C22×C8—101no—
182C22×C8—101no—
183C22×C8—102no—
184C22×C8C4×D511yescharacteristic
185C22×C8C4×D511yescharacteristic
186C4×Q8—51no—
187C4×Q8—51no—
188C4×D4—51no—
189C4×D4—51no—
190C4×D4—101no—
191C4×D4—101no—
192#117—51no—
193#117—101no—
194C2×C42—101no—
195C2×C42C22×D511yescharacteristic
196C4⋊C8—22no—
197C4⋊C8—102no—
198C4⋊C8—102no—
199C22⋊C8—22no—
200#97—101no—
201#97—101no—
202#97—101no—
203C4×C8—22no—
204C4×C8—101no—
205C4×C8—101no—
206C4×C8—101no—
207C4×C8D2011yescharacteristic
208C4×C8D2011yescharacteristic
209C4×C8C22⋊D511yescharacteristic
210C4×C8C22⋊D511yescharacteristic
211C22×C5—21no—
212C22×C5—21no—
213C22×C5#38011yescharacteristic
214C22×C5#43111yescharacteristic
215C22×C5#43211yescharacteristic
216C2×D5—22no—
217C2×D5—41no—
218C2×D5—41no—
219C4×C5—21no—
220C4×C5—21no—
221C4×C5—21no—
222C4×C5C2×C22⋊C811yescharacteristic
223C4×C5#40711yescharacteristic
224C4×C5C2×C4⋊C811yescharacteristic
225C4×C5#42311yescharacteristic
226C4×C5#47112yes—
227Dic5—22no—
228Dic5—41no—
229Dic5—41no—
230#41—52no—
231#41—52no—
232#41—101no—
233#41—101no—
234C2×Q8—51no—
235C2×D4—51no—
236C2×D4—101no—
237C22×C4—101no—
238C22×C4—101no—
239C22×C4—101no—
240C22×C4C2×C4×D511yescharacteristic
241C22×C4#71111yescharacteristic
242C22×C4#71311yescharacteristic
243M16—52no—
244M16—52no—
245M16—104no—
246M16—101no—
247M16—101no—
248M16—104no—
249C2×C8—21no—
250C2×C8—21no—
251C2×C8—42no—
252C2×C8—104no—
253C2×C8—101no—
254C2×C8—101no—
255C2×C8—104no—
256C2×C8—202no—
257C2×C8—402no—
258C2×C8C8×D512yes—
259C2×C8#67612yes—
260C2×C8#68511yescharacteristic
261C2×C8#68511yescharacteristic
262C2×C8#68511yescharacteristic
263C2×C8#68511yescharacteristic
264C4⋊C4—51no—
265C4⋊C4—51no—
266C4⋊C4—101no—
267C4⋊C4—101no—
268C22⋊C4—101no—
269C22⋊C4—101no—
270C22⋊C4—101no—
271C42—101no—
272C42—101no—
273C42—101no—
274C42C2×D2011yescharacteristic
275C42D4×D511yescharacteristic
276C42Q8×D511yescharacteristic
277C42C2×C22⋊D511yescharacteristic
278C2×C5—21no—
279C2×C5—21no—
280C2×C5#179711yescharacteristic
281C2×C5#181411yescharacteristic
282C2×C5#181511yescharacteristic
283D5—42no—
284C23—101no—
285C23#403811yescharacteristic
286Q8—52no—
287Q8—101no—
288D4—52no—
289D4—102no—
290D4—102no—
291D4—101no—
292C2×C4—22no—
293C2×C4—41no—
294C2×C4—101no—
295C2×C4—102no—
296C2×C4—102no—
297C2×C4—101no—
298C2×C4—101no—
299C2×C4—202no—
300C2×C4—202no—
301C2×C4D5×C4⋊C411yescharacteristic
302C2×C4#404111yescharacteristic
303C2×C4#404311yescharacteristic
304C2×C4C2×C8×D511yescharacteristic
305C2×C4C2×#67611yescharacteristic
306C2×C4D5×M1611yescharacteristic
307C2×C4D5×M1611yescharacteristic
308C2×C4C2×#68511yescharacteristic
309C2×C4#408411yescharacteristic
310C2×C4#409211yescharacteristic
311C8—21no—
312C8—21no—
313C8—82no—
314C8—102no—
315C8—102no—
316C8—402no—
317C8#395212yes—
318C8#395212yes—
319C5#860411yescharacteristic, complemented, Sylow
320C22—21no—
321C22—21no—
322C22—102no—
323C22—201no—
324C22—201no—
325C22#6512211yescharacteristic
326C22#6512411yescharacteristic
327C22#6527611yescharacteristic
328C4—21no—
329C4—21no—
330C4—21no—
331C4—102no—
332C4—201no—
333C4—201no—
334C4D5×C4⋊C811yescharacteristic
335C4#6512611yescharacteristic
336C4#6518712yes—
337C4C2×#395211yescharacteristic
338C4#6541511yescharacteristic
339C2—21no—
340C2—21no—
341C2—202no—
342C2#1060126811yescharacteristic
343C2#1060145811yescharacteristic
344C2#1060151311yescharacteristic
subgroupG/H
centerC2×C4#4041
commutatorC2×C4×C5C22×C8
FrattiniC2×C42C22×D5
FittingC5×#1564C2
socleC22×C5#380
prime radicalC2×#709C2×C4
cosocleC2×C42×C5C23
hypercenter#1564D5
hypocenterC5#8604
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1564

Complements

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

NH ≅ G/Ntype
2. C5×#1564C2semidirect
4. C2×#64677C2semidirect
5. #10598235C2semidirect
39. #4047C8semidirect
66. #1564D5semidirect
319. C5#8604semidirect

Maximal subgroups

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

subgroupindex
C4×#40472
C5×#15642
#106015482
C2×#646772
#105982352
#86045