Finite Group Databasebeta

← #12068548

Subgroups — #12068548

Order 1280.

634 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10610743C211yesmaximal, characteristic
2#10610731C211yesmaximal, characteristic
3#10610178C211yesmaximal, characteristic
4C2×C5×#334C211yesmaximal, characteristic, complemented
5#10601215C211yesmaximal, characteristic, complemented
6#10601214C211yesmaximal, characteristic, complemented
7#10600524C211yesmaximal, characteristic, complemented
8#10599328C212yesmaximal, complemented
9#10599327C212yesmaximal, complemented
10#10599324C212yesmaximal, complemented
11#10599321C212yesmaximal, complemented
12C2×#4047—21no—
13C4×#709C2211yescharacteristic
14C2×C5×C4⋊C8C2211yescharacteristic
15C2×C5×C4⋊C8C2211yescharacteristic
16C2×C4×C5×C8C2211yescharacteristic
17#65400C412yes—
18#65400C412yes—
19#65399—21no—
20#65391—21no—
21#65390—21no—
22#65214C2211yescharacteristic
23#65213C2211yescharacteristic
24#65213C2211yescharacteristic
25#65129—22no—
26#65128—22no—
27#65126C2212yes—
28#65124C2212yes—
29#65122C2212yes—
30D5×C4⋊C8C2212yes—
31#64977C411yescharacteristic
32#64977C411yescharacteristic
33C4×#676C2212yes—
34#64974C2212yes—
35#64968C411yescharacteristic
36#64968C411yescharacteristic
37C5×#334C2211yescharacteristic
38C5×#334C2211yescharacteristic
39C5×#334C2211yescharacteristic
40C5×#334C2211yescharacteristic
41#64700C2212yes—
42#64700C2212yes—
43#64699C2212yes—
44#64699C2212yes—
45#64678C2212yes—
46#64678C2212yes—
47#17830—51nomaximal, Sylow
48C2×#709D411yescharacteristic
49C22×C5×C8—21no—
50C22×C5×C8—21no—
51C22×C5×C8C2×C411yescharacteristic
52C22×C5×C8C2×C411yescharacteristic
53C2×C42×C5C2311yescharacteristic
54C4×C22⋊D5C2×C412yes—
55C4×C22⋊D5Q812yes—
56#4072D411yescharacteristic
57C2×#681—21no—
58C2×#681—21no—
59#4047—44no—
60C2×#676—22no—
61C2×#676C2×C412yes—
62C2×#676C2×C412yes—
63C2×C8×D5—22no—
64C4×D20C2×C411yescharacteristic
65C4×D20Q811yescharacteristic
66#4018D412yes—
67C42×D5C2312yes—
68C4×Dic10C2×C411yescharacteristic
69C4×Dic10Q811yescharacteristic
70C5×C4⋊C8—21no—
71C5×C4⋊C8—21no—
72C5×C4⋊C8C2311yescharacteristic
73C5×C4⋊C8C2311yescharacteristic
74C5×C4⋊C8C2311yescharacteristic
75C5×C4⋊C8C2311yescharacteristic
76C4×C5×C8C2×C411yescharacteristic
77C4×C5×C8C2×C411yescharacteristic
78C4×C5×C8C2311yescharacteristic
79C4×C5×C8C2311yescharacteristic
80C22⋊#168C2×C412yes—
81#3952—22no—
82#3952—22no—
83#3952C2×C412yes—
84#3952C2×C412yes—
85#3947—22no—
86#3947C2×C412yes—
87#3947C2×C412yes—
88#3946—22no—
89#3946—22no—
90#3946C2×C412yes—
91#3946C2×C412yes—
92C8×Dic5—22no—
93C4⋊#168—21no—
94C4⋊#168—21no—
95C4⋊#168C2×C411yescharacteristic
96C4⋊#168C2×C411yescharacteristic
97C4⋊#168C2312yes—
98C4⋊#168C2312yes—
99C4×#168C2312yes—
100#2965—51no—
101#2925—51no—
102#2906—51no—
103#1574—52no—
104#1573—52no—
105#1571—51no—
106#1570—51no—
107#1569—52no—
108#1567—51no—
109#1565—52no—
110C2×#334D511yescharacteristic, complemented
111C22×C4×C5C22×C411yescharacteristic
112C22×C4×C5C2×D411yescharacteristic
113C22×C4×C5C2×Q811yescharacteristic
114C2×C22⋊D5C4⋊C412yes—
115#709—22no—
116#709—22no—
117C2×D20C4⋊C411yescharacteristic
118C2×C4×D5C22×C412yes—
119C2×C4×D5C2×D412yes—
120C2×C4×D5C2×Q812yes—
121C2×Dic10C4⋊C411yescharacteristic
122C2×C5×C8—22no—
123C2×C5×C8—21no—
124C2×C5×C8—21no—
125C2×C5×C8—21no—
126C2×C5×C8—21no—
127C2×C5×C8—41no—
128C2×C5×C8—42no—
129C2×C5×C8—42no—
130C2×C5×C8C22×C411yescharacteristic
131C2×C5×C8C22×C411yescharacteristic
132C2×C5×C8C22×C411yescharacteristic
133C2×C5×C8C22×C411yescharacteristic
134C42×C5C22×C411yescharacteristic
135C42×C5C2×D411yescharacteristic
136C42×C5C2×Q811yescharacteristic
137C42×C5C2411yescharacteristic
138C22⋊Dic5C4⋊C412yes—
139#685C4⋊C412yes—
140#685C4⋊C412yes—
141C4⋊Dic5C4⋊C411yescharacteristic
142C4⋊Dic5C4⋊C411yescharacteristic
143#683C4⋊C412yes—
144#683C4⋊C412yes—
145C4×Dic5C22×C412yes—
146C4×Dic5C2×D412yes—
147C4×Dic5C2×Q812yes—
148#681—42no—
149#681—42no—
150C2×#168—22no—
151C2×#168—22no—
152C2×#168C22×C412yes—
153C2×#168C22×C412yes—
154#676—24no—
155#676—42no—
156#676—44no—
157C8×D5—44no—
158C2×#131—101no—
159C4×#41—51no—
160#446—51no—
161#446—51no—
162#436—51no—
163#436—51no—
164#435—52no—
165#435—52no—
166#433—102no—
167#432—52no—
168#431—51no—
169#431—52no—
170#431—52no—
171#424—102no—
172#424—101no—
173#423—51no—
174#423—51no—
175#423—52no—
176C2×C4⋊C8—52no—
177C2×C4⋊C8C2×D511yescharacteristic
178C2×C4⋊C8C2×D511yescharacteristic
179#408—101no—
180#405—101no—
181C4×M16—52no—
182C2×C4×C8C2×D511yescharacteristic
183#335—52no—
184#335—52no—
185#335—52no—
186#335—52no—
187#334—52no—
188#334—52no—
189#334C2×D511yescharacteristic
190#334C2×D511yescharacteristic
191#334C2×D511yescharacteristic
192#334C2×D511yescharacteristic
193C23×C5C2×C4⋊C411yescharacteristic
194C22×D5C2×C4⋊C412yes—
195C2×C4×C5—21no—
196C2×C4×C5—21no—
197C2×C4×C5—41no—
198C2×C4×C5C2×C4⋊C411yescharacteristic
199C2×C4×C5C2×C4⋊C411yescharacteristic
200C2×C4×C5C2×C4⋊C411yescharacteristic
201C2×C4×C5AGL(1,ℤ/8)12yes—
202C2×C4×C5#13712yes—
203C2×C4×C5C23×C411yescharacteristic
204C2×C4×C5C22×D411yescharacteristic
205C2×C4×C5C22×Q811yescharacteristic
206C22⋊D5—24no—
207C2×Dic5C2×C4⋊C412yes—
208C2×Dic5C2×C4⋊C412yes—
209C2×Dic5C2×C4⋊C412yes—
210D20—22no—
211C4×D5—22no—
212C4×D5—22no—
213C4×D5—22no—
214C4×D5—22no—
215C4×D5—42no—
216Dic10—22no—
217C5×C8—21no—
218C5×C8—21no—
219C5×C8—21no—
220C5×C8—41no—
221C5×C8—41no—
222C5×C8—41no—
223C5×C8—41no—
224C5×C8#13112yescomplemented
225#168—22no—
226#168—22no—
227#168—42no—
228#168—42no—
229C2×#41—51no—
230#131—204no—
231C2×M16—52no—
232C2×M16—52no—
233C2×M16—102no—
234C2×M16—101no—
235C2×M16—101no—
236C22×C8—21no—
237C22×C8—21no—
238C22×C8—102no—
239C22×C8C4×D511yescharacteristic
240C22×C8C4×D511yescharacteristic
241C4×Q8—51no—
242C4×Q8—51no—
243C4×D4—52no—
244C4×D4—52no—
245C4×D4—51no—
246C4×D4—51no—
247#117—51no—
248#117—52no—
249C2×C42—52no—
250C2×C42C22×D511yescharacteristic
251C4⋊C8—21no—
252C4⋊C8—21no—
253C4⋊C8—52no—
254C4⋊C8—52no—
255C4⋊C8—51no—
256C4⋊C8—51no—
257C4⋊C8—52no—
258C4⋊C8—52no—
259C4⋊C8—102no—
260C4⋊C8—102no—
261C4⋊C8—101no—
262C4⋊C8—101no—
263C4⋊C8C22×D511yescharacteristic
264C4⋊C8C22×D511yescharacteristic
265C4⋊C8C22×D511yescharacteristic
266C4⋊C8C22×D511yescharacteristic
267C22⋊C8—52no—
268C22⋊C8—52no—
269C22⋊C8—52no—
270C22⋊C8—102no—
271C22⋊C8—102no—
272#97—52no—
273#97—52no—
274#97—102no—
275C4×C8—52no—
276C4×C8—102no—
277C4×C8C4×D511yescharacteristic
278C4×C8C4×D511yescharacteristic
279C4×C8C22×D511yescharacteristic
280C4×C8C22×D511yescharacteristic
281C22×C5—21no—
282C22×C5—21no—
283C22×C5#42812yes—
284C22×C5C22×C4⋊C411yescharacteristic
285C2×D5—22no—
286C2×D5—22no—
287C2×D5—22no—
288C4×C5—21no—
289C4×C5—21no—
290C4×C5—21no—
291C4×C5#42812yes—
292C4×C5C2×#13111yescharacteristic
293C4×C5#56811yescharacteristic
294C4×C5C2×AGL(1,ℤ/8)11yescharacteristic
295C4×C5C2×#13711yescharacteristic
296Dic5—22no—
297Dic5—22no—
298Dic5—22no—
299#41—102no—
300#41—102no—
301C2×Q8—51no—
302C2×D4—52no—
303C2×D4—51no—
304C22×C4—52no—
305C22×C4—52no—
306C22×C4—52no—
307C22×C4C2×C4×D511yescharacteristic
308C22×C4D4×D511yescharacteristic
309C22×C4Q8×D511yescharacteristic
310M16—104no—
311M16—202no—
312M16—204no—
313M16—202no—
314M16—202no—
315C2×C8—22no—
316C2×C8—21no—
317C2×C8—21no—
318C2×C8—21no—
319C2×C8—21no—
320C2×C8—41no—
321C2×C8—42no—
322C2×C8—42no—
323C2×C8—52no—
324C2×C8—52no—
325C2×C8—102no—
326C2×C8—102no—
327C2×C8—204no—
328C2×C8C2×C4×D511yescharacteristic
329C2×C8C2×C4×D511yescharacteristic
330C2×C8C2×C4×D511yescharacteristic
331C2×C8C2×C4×D511yescharacteristic
332C4⋊C4—52no—
333C4⋊C4—52no—
334C4⋊C4—51no—
335C4⋊C4—51no—
336C22⋊C4—52no—
337C22⋊C4—52no—
338C22⋊C4—52no—
339C42—52no—
340C42—52no—
341C42—52no—
342C42C2×C4×D511yescharacteristic
343C42D4×D511yescharacteristic
344C42Q8×D511yescharacteristic
345C42C23×D511yescharacteristic
346C2×C5—22no—
347C2×C5#290611yescharacteristic
348C2×C5C2×#42811yescharacteristic
349C2×C5#291611yescharacteristic
350D5—42no—
351C23—52no—
352C23D5×C4⋊C411yescharacteristic
353Q8—102no—
354D4—104no—
355D4—102no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—41no—
359C2×C4—52no—
360C2×C4—52no—
361C2×C4—52no—
362C2×C4—102no—
363C2×C4—102no—
364C2×C4—102no—
365C2×C4—102no—
366C2×C4—202no—
367C2×C4D5×C4⋊C411yescharacteristic
368C2×C4D5×C4⋊C411yescharacteristic
369C2×C4D5×C4⋊C411yescharacteristic
370C2×C4#406012yes—
371C2×C4#406112yes—
372C2×C4C22×C4×D511yescharacteristic
373C2×C4C2×D4×D511yescharacteristic
374C2×C4C2×Q8×D511yescharacteristic
375C8—21no—
376C8—21no—
377C8—21no—
378C8—41no—
379C8—41no—
380C8—41no—
381C8—41no—
382C8—102no—
383C8—102no—
384C8—202no—
385C8—202no—
386C8#404712yescomplemented
387C5#1783011yescharacteristic, complemented, Sylow
388C22—21no—
389C22—21no—
390C22—102no—
391C22—102no—
392C22—102no—
393C22#6515012yes—
394C22C2×D5×C4⋊C411yescharacteristic
395C4—21no—
396C4—21no—
397C4—21no—
398C4—102no—
399C4—102no—
400C4—102no—
401C4#6515012yes—
402C4C2×#404711yescharacteristic
403C4#6607911yescharacteristic
404C4C2×#406011yescharacteristic
405C4C2×#406111yescharacteristic
406C2—22no—
407C2—202no—
408C2#1061074311yescharacteristic
409C2C2×#6515011yescharacteristic
410C2#1061098311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC42C23×D5
FittingC2×C5×#334C2
socleC22×C5C22×C4⋊C4
prime radicalC2×#709D4
cosocleC42×C5C24
hypercenterC2×#334D5
hypocenterC5#17830
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×#334

Complements

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

NH ≅ G/Ntype
4. C2×C5×#334C2semidirect
5. #10601215C2semidirect
6. #10601214C2semidirect
7. #10600524C2semidirect
8. #10599328C2semidirect
9. #10599327C2semidirect
10. #10599324C2semidirect
11. #10599321C2semidirect
110. C2×#334D5semidirect
224. C5×C8#131semidirect
386. C8#4047semidirect
387. C5#17830semidirect

Maximal subgroups

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

subgroupindex
#106107432
#106107312
#106101782
C2×C5×#3342
#106012152
#106012142
#106005242
#105993282
#105993272
#105993242
#105993212
#178305