Finite Group Databasebeta

← #11997635

Subgroups — #11997635

Order 1280.

466 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10601250C211yesmaximal, characteristic
2#10601247C211yesmaximal, characteristic, complemented
3C2×#64705C211yesmaximal, characteristic
4#10600565C211yesmaximal, characteristic
5C8×C4⋊Dic5C211yesmaximal, characteristic, complemented
6C5×#1277C211yesmaximal, characteristic, complemented
7#10598193C211yesmaximal, characteristic, complemented
8C2×#4020C2211yescharacteristic
9C2×C5×C4⋊C8C2211yescharacteristic
10C2×C5×C4⋊C8C2211yescharacteristic
11C2×C4×C5×C8C2211yescharacteristic
12C2×#3953—21no—
13C2×#3953—21no—
14C2×#3953—21no—
15C2×#3953—21no—
16C2×#3949—21no—
17C2×C8×Dic5—21no—
18#65224C2211yescharacteristic
19C4×C4⋊Dic5C2211yescharacteristic
20C2×C4⋊#168C2211yescharacteristic
21#64771—21no—
22#64770—21no—
23#64705C414yescomplemented
24#9564—51nomaximal, Sylow
25C22×D20—21no—
26C22×D20—21no—
27C22×D20—21no—
28C22×C5×C8—21no—
29C22×C5×C8—21no—
30C22×C5×C8D411yescharacteristic
31C22×C5×C8D411yescharacteristic
32C2×C42×C5C2311yescharacteristic
33C2×C4⋊Dic5—21no—
34C2×C4⋊Dic5—21no—
35C2×C4⋊Dic5—21no—
36C2×C4⋊Dic5D411yescharacteristic
37C2×C4⋊Dic5D411yescharacteristic
38C2×C4×Dic5—21no—
39C22×#168—21no—
40#4020—21no—
41#4020—21no—
42#4020—21no—
43#4020C2×C412yes—
44C5×C4⋊C8—21no—
45C5×C4⋊C8—21no—
46C5×C4⋊C8—21no—
47C5×C4⋊C8C2×C412yes—
48C4×C5×C8—21no—
49C4×C5×C8—21no—
50#3963—21no—
51#3953—42no—
52#3953—42no—
53#3953—42no—
54#3953—42no—
55#3949—42no—
56C8×Dic5—42no—
57C4⋊#168—21no—
58C4⋊#168C2×C412yes—
59#1982—51no—
60#1957—51no—
61#1948—51no—
62C8×C4⋊C4—51no—
63C2×#331—51no—
64#1296—51no—
65#1277D511yescharacteristic, complemented
66C23×D5—41no—
67C22×C4×C5C2×D411yescharacteristic
68C22×C4×C5C2×D411yescharacteristic
69C22×C4×C5#4111yescharacteristic
70C22×Dic5—21no—
71C22×Dic5—21no—
72C22×Dic5—41no—
73C2×D20—22no—
74C2×D20—22no—
75C2×D20—22no—
76C2×D20—41no—
77C2×D20—41no—
78C2×D20—41no—
79C2×D20—41no—
80C2×D20—41no—
81C2×D20—41no—
82C2×D20—41no—
83C2×D20—41no—
84C2×D20—41no—
85C2×D20—41no—
86C2×D20—41no—
87C2×D20—81no—
88C2×D20—81no—
89C2×C5×C8—21no—
90C2×C5×C8—21no—
91C2×C5×C8—22no—
92C2×C5×C8—21no—
93C2×C5×C8—21no—
94C2×C5×C8—21no—
95C2×C5×C8—41no—
96C2×C5×C8—41no—
97C2×C5×C8—41no—
98C2×C5×C8—41no—
99C2×C5×C8—41no—
100C2×C5×C8SD1612yes—
101C42×C5C22×C411yescharacteristic
102C42×C5#4111yescharacteristic
103C42×C5#4111yescharacteristic
104C42×C5#4111yescharacteristic
105C4⋊Dic5—21no—
106C4⋊Dic5—21no—
107C4⋊Dic5—41no—
108C4⋊Dic5—41no—
109C4⋊Dic5—41no—
110C4⋊Dic5—41no—
111C4⋊Dic5—81no—
112C4⋊Dic5D812yes—
113C4⋊Dic5SD1612yes—
114C4×Dic5—41no—
115C4×Dic5—41no—
116C2×#168—22no—
117C2×#168—41no—
118C2×#168—41no—
119C2×#127—51no—
120C2×#106—101no—
121C2×C4⋊C8—51no—
122C2×C4⋊C8C2×D511yescharacteristic
123C2×C4⋊C8C2×D511yescharacteristic
124C2×#102—101no—
125C2×#102—101no—
126C2×#102—101no—
127C2×#102—101no—
128C2×C4×C8—101no—
129C2×C4×C8C2×D511yescharacteristic
130#384—51no—
131C4×C4⋊C4—51no—
132#340—101no—
133#336—101no—
134#331—54no—
135C23×C5#12111yescharacteristic
136C22×D5—42no—
137C22×D5—81no—
138C22×D5—81no—
139C22×D5—81no—
140C22×D5—81no—
141C22×D5—81no—
142C22×D5—81no—
143C2×C4×C5—21no—
144C2×C4×C5—21no—
145C2×C4×C5#11711yescharacteristic
146C2×C4×C5C4×D411yescharacteristic
147C2×C4×C5C4×D411yescharacteristic
148C2×C4×C5#12311yescharacteristic
149C2×C4×C5#12411yescharacteristic
150C2×C4×C5#12611yescharacteristic
151C2×C4×C5C2×D811yescharacteristic
152C2×C4×C5C2×SD1611yescharacteristic
153C2×C4×C5C2×SD1611yescharacteristic
154C2×C4×C5#13511yescharacteristic
155C2×C4×C5#13511yescharacteristic
156C2×C4×C5#13511yescharacteristic
157C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
159C2×Dic5—22no—
160C2×Dic5—22no—
161C2×Dic5—41no—
162C2×Dic5—41no—
163C2×Dic5—41no—
164C2×Dic5—41no—
165C2×Dic5—81no—
166C2×Dic5—81no—
167C2×Dic5—81no—
168D20—42no—
169D20—42no—
170D20—42no—
171D20—42no—
172D20—82no—
173D20—82no—
174D20—81no—
175D20—81no—
176D20—81no—
177D20—81no—
178C5×C8—22no—
179C5×C8—42no—
180C5×C8—41no—
181C5×C8—81no—
182#168—42no—
183C22×D4—101no—
184C22×D4—101no—
185C22×D4—101no—
186C22×C8—21no—
187C22×C8—21no—
188C22×C8—101no—
189C22×C8D2011yescharacteristic
190C22×C8D2011yescharacteristic
191#127—52no—
192#127—101no—
193#127—101no—
194#127—101no—
195C2×C4⋊C4—51no—
196C2×C4⋊C4—51no—
197C2×C4⋊C4—101no—
198C2×C4⋊C4—101no—
199C2×C4⋊C4—101no—
200C2×C42—101no—
201C2×C42C22×D511yescharacteristic
202#106—202no—
203C4⋊C8—21no—
204C4⋊C8—21no—
205C4⋊C8—21no—
206C4⋊C8—52no—
207C4⋊C8—101no—
208C4⋊C8C4×D512yes—
209#102—202no—
210#102—202no—
211#102—202no—
212#102—202no—
213C4×C8—21no—
214C4×C8—21no—
215C4×C8—202no—
216#95—101no—
217C22×C5#38811yescharacteristic
218C22×C5#46011yescharacteristic
219C22×C5#46311yescharacteristic
220C22×C5#46511yescharacteristic
221C22×C5#46611yescharacteristic
222C22×C5#47111yescharacteristic
223C22×C5#47211yescharacteristic
224C2×D5—82no—
225C2×D5—82no—
226C2×D5—82no—
227C2×D5—161no—
228C2×D5—161no—
229C2×D5—161no—
230C2×D5—161no—
231C4×C5—21no—
232C4×C5—21no—
233C4×C5C4×D811yescharacteristic
234C4×C5C4×SD1611yescharacteristic
235C4×C5C4×SD1611yescharacteristic
236C4×C5#44211yescharacteristic
237C4×C5#48111yescharacteristic
238C4×C5#48211yescharacteristic
239C4×C5#48611yescharacteristic
240C4×C5#48811yescharacteristic
241Dic5—42no—
242Dic5—42no—
243Dic5—161no—
244C24—201no—
245C2×D4—102no—
246C2×D4—102no—
247C2×D4—102no—
248C2×D4—201no—
249C2×D4—201no—
250C2×D4—201no—
251C2×D4—201no—
252C2×D4—201no—
253C2×D4—201no—
254C2×D4—201no—
255C2×D4—201no—
256C2×D4—201no—
257C2×D4—201no—
258C2×D4—201no—
259C2×D4—401no—
260C2×D4—401no—
261C22×C4—101no—
262C22×C4—101no—
263C22×C4—201no—
264C22×C4C2×D2011yescharacteristic
265C22×C4D4×D511yescharacteristic
266C22×C4#71311yescharacteristic
267C2×C8—21no—
268C2×C8—21no—
269C2×C8—22no—
270C2×C8—21no—
271C2×C8—21no—
272C2×C8—21no—
273C2×C8—41no—
274C2×C8—41no—
275C2×C8—41no—
276C2×C8—41no—
277C2×C8—41no—
278C2×C8—102no—
279C2×C8—201no—
280C2×C8—201no—
281C2×C8#67712yes—
282C4⋊C4—52no—
283C4⋊C4—52no—
284C4⋊C4—101no—
285C4⋊C4—101no—
286C4⋊C4—201no—
287C4⋊C4—201no—
288C4⋊C4—201no—
289C4⋊C4—201no—
290C4⋊C4—401no—
291C42—201no—
292C42—201no—
293C42C2×C4×D511yescharacteristic
294C42#70911yescharacteristic
295C42#71111yescharacteristic
296C42#71111yescharacteristic
297C2×C5#166611yescharacteristic
298C2×C5#166811yescharacteristic
299C2×C5#167711yescharacteristic
300C2×C5#168111yescharacteristic
301C2×C5#192611yescharacteristic
302C2×C5#193111yescharacteristic
303C2×C5#193411yescharacteristic
304D5—162no—
305C23—202no—
306C23—401no—
307C23—401no—
308C23—401no—
309C23—401no—
310C23—401no—
311C23—401no—
312C23#404111yescharacteristic
313D4—202no—
314D4—202no—
315D4—202no—
316D4—202no—
317D4—402no—
318D4—402no—
319D4—401no—
320D4—401no—
321D4—401no—
322D4—401no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—102no—
326C2×C4—102no—
327C2×C4—201no—
328C2×C4—201no—
329C2×C4—201no—
330C2×C4—201no—
331C2×C4—401no—
332C2×C4—401no—
333C2×C4—401no—
334C2×C4C4×D2011yescharacteristic
335C2×C4#402711yescharacteristic
336C2×C4#403111yescharacteristic
337C2×C4#403211yescharacteristic
338C2×C4#403811yescharacteristic
339C2×C4#404411yescharacteristic
340C2×C4C2×#67711yescharacteristic
341C2×C4#405011yescharacteristic
342C2×C4#405411yescharacteristic
343C2×C4#405411yescharacteristic
344C2×C4D5×D811yescharacteristic
345C2×C4D5×SD1611yescharacteristic
346C2×C4#406211yescharacteristic
347C2×C4#406511yescharacteristic
348C8—22no—
349C8—41no—
350C8—42no—
351C8—81no—
352C8—202no—
353C5#956411yescharacteristic, complemented, Sylow
354C22—402no—
355C22—402no—
356C22—402no—
357C22—801no—
358C22—801no—
359C22—801no—
360C22—801no—
361C22#6495911yescharacteristic
362C22#6513311yescharacteristic
363C22#6513711yescharacteristic
364C22#6515311yescharacteristic
365C22#6517211yescharacteristic
366C22#6518611yescharacteristic
367C22#6518711yescharacteristic
368C4—21no—
369C4—21no—
370C4—202no—
371C4—202no—
372C4—801no—
373C4C4×#67711yescharacteristic
374C4#6500011yescharacteristic
375C4#6502411yescharacteristic
376C4#6502611yescharacteristic
377C4#6504511yescharacteristic
378C4#6504911yescharacteristic
379C4#6507711yescharacteristic
380C4#6508911yescharacteristic
381C2—802no—
382C2#1059933111yescharacteristic
383C2#1059933911yescharacteristic
384C2#1059937311yescharacteristic
385C2#1059937911yescharacteristic
386C2#1059941911yescharacteristic
387C2#1059964611yescharacteristic
388C2#1059972411yescharacteristic
subgroupG/H
centerC23#4041
commutatorC42×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#1277C2
socleC23×C5#121
prime radicalC2×#4020C22
cosocleC2×C42×C5C23
hypercenter#1277D5
hypocenterC5#9564
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1277

Complements

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

NH ≅ G/Ntype
2. #10601247C2semidirect
5. C8×C4⋊Dic5C2semidirect
6. C5×#1277C2semidirect
7. #10598193C2semidirect
23. #64705C4semidirect
65. #1277D5semidirect
353. C5#9564semidirect

Maximal subgroups

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

subgroupindex
#106012502
#106012472
C2×#647052
#106005652
C8×C4⋊Dic52
C5×#12772
#105981932
#95645