Finite Group Databasebeta

← #12018651

Subgroups — #12018651

Order 1280.

482 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64985C211yesmaximal, characteristic
2C5×#1942C211yesmaximal, characteristic, complemented
3C2×#64712C211yesmaximal, characteristic, complemented
4C2×#64712C211yesmaximal, characteristic, complemented
5C2×#64711C211yesmaximal, characteristic
6C2×#64711C211yesmaximal, characteristic
7#10598148C211yesmaximal, characteristic, complemented
8C22×Dic20C2211yescharacteristic
9C22×D40C2211yescharacteristic
10C22×#677—21no—
11C2×#4021—21no—
12C2×C5×#107C2211yescharacteristic
13C2×C5×#107C2211yescharacteristic
14C2×C4×C5×C8C2211yescharacteristic
15C5×#389—21no—
16C22×#672C2211yescharacteristic
17C22×#672C2211yescharacteristic
18#64985—22no—
19#64985—22no—
20C5×#340—21no—
21#64712—22no—
22#64712—22no—
23#64711—22no—
24#64711—22no—
25#13408—51nomaximal, Sylow
26C22×D20—21no—
27C22×Dic10—21no—
28C22×C5×C8D411yescharacteristic
29C22×C5×C8C2311yescharacteristic
30C2×C5×C4⋊C4—21no—
31C2×C5×C4⋊C4—21no—
32C2×C5×C4⋊C4—41no—
33C2×C42×C5D411yescharacteristic
34C2×#685—41no—
35C2×#685—41no—
36C2×Dic20—21no—
37C2×Dic20—21no—
38C2×Dic20—21no—
39C2×Dic20—21no—
40C2×Dic20—21no—
41C2×Dic20D412yes—
42C2×D40—21no—
43C2×D40—21no—
44C2×D40—21no—
45C2×D40—21no—
46C2×D40—21no—
47C2×D40D412yes—
48C2×#677—24no—
49C2×#677—42no—
50C2×#677—42no—
51#4021—24no—
52#4021—42no—
53C5×#107—21no—
54C5×#107—21no—
55C5×#107—21no—
56C5×#107D412yes—
57C4×C5×C8—21no—
58C4×C5×C8—21no—
59C5×#95—41no—
60C2×#672—21no—
61C2×#672—21no—
62C2×#672—21no—
63C2×#672—21no—
64C2×#672—21no—
65C2×#672—21no—
66C2×#495—51no—
67C2×#358—51no—
68C2×#358—51no—
69C2×#357—51no—
70C2×#357—51no—
71#1942D511yescharacteristic, complemented
72#1374—51no—
73C23×D5—41no—
74C22×C4×C5—41no—
75C22×C4×C5—41no—
76C22×C4×C5D811yescharacteristic
77C22×C4×C5D811yescharacteristic
78C22×C4×C5C2×D411yescharacteristic
79C22×Dic5—41no—
80C2×D20—22no—
81C2×D20—41no—
82C2×D20—41no—
83C2×D20—41no—
84C2×D20—41no—
85C2×D20—41no—
86C2×Dic10—22no—
87C2×Dic10—41no—
88C2×Dic10—41no—
89C2×Dic10—41no—
90C2×Dic10—41no—
91C2×Dic10—41no—
92C2×C5×C8—21no—
93C2×C5×C8—21no—
94C2×C5×C8SD1612yes—
95C2×C5×C8C2×D411yescharacteristic
96C2×C5×C8C2×D411yescharacteristic
97C2×C5×C8C2×D411yescharacteristic
98C2×C5×C8#4111yescharacteristic
99C2×C5×C8#4111yescharacteristic
100C2×C5×C8#4111yescharacteristic
101C5×C4⋊C4—22no—
102C5×C4⋊C4—41no—
103C5×C4⋊C4—41no—
104C5×C4⋊C4—41no—
105C5×C4⋊C4—82no—
106C42×C5—21no—
107C42×C5—21no—
108#685—44no—
109#685—44no—
110Dic20—22no—
111Dic20—22no—
112Dic20—41no—
113Dic20—41no—
114D40—22no—
115D40—22no—
116D40—41no—
117D40—41no—
118#677—48no—
119#672—41no—
120#672—41no—
121C22×Q16—51no—
122C22×SD16—101no—
123C22×D8—51no—
124C2×#124—101no—
125C22×C16—51no—
126C22×C16—51no—
127#495—102no—
128#495—102no—
129C2×#107C2×D511yescharacteristic
130C2×#107C2×D511yescharacteristic
131C2×C4×C8C2×D511yescharacteristic
132#389—21no—
133#358—102no—
134#358—102no—
135#357—102no—
136#357—102no—
137#340—21no—
138C23×C5C2×D811yescharacteristic
139C22×D5—42no—
140C22×D5—81no—
141C22×D5—81no—
142C22×D5—81no—
143C22×D5—81no—
144C22×D5—81no—
145C22×D5—81no—
146C2×C4×C5—21no—
147C2×C4×C5—21no—
148C2×C4×C5—21no—
149C2×C4×C5—21no—
150C2×C4×C5—21no—
151C2×C4×C5—21no—
152C2×C4×C5—42no—
153C2×C4×C5—81no—
154C2×C4×C5—81no—
155C2×C4×C5—81no—
156C2×C4×C5—81no—
157C2×C4×C5—81no—
158C2×C4×C5#12011yescharacteristic
159C2×C4×C5#12111yescharacteristic
160C2×C4×C5#12411yescharacteristic
161C2×C4×C5C2×SD1611yescharacteristic
162C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
163C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
164C2×Dic5—42no—
165C2×Dic5—81no—
166C2×Dic5—81no—
167D20—42no—
168D20—42no—
169D20—81no—
170D20—81no—
171Dic10—42no—
172Dic10—42no—
173Dic10—81no—
174Dic10—81no—
175C5×C8—22no—
176C5×C8#12111yescharacteristic
177C5×C8#12111yescharacteristic
178C5×C8#12311yescharacteristic
179C5×C8#12311yescharacteristic
180C22×Q8—101no—
181C22×D4—101no—
182C2×Q16—52no—
183C2×Q16—101no—
184C2×Q16—101no—
185C2×Q16—101no—
186C2×Q16—101no—
187C2×Q16—101no—
188C2×SD16—104no—
189C2×SD16—202no—
190C2×SD16—202no—
191C2×D8—52no—
192C2×D8—101no—
193C2×D8—101no—
194C2×D8—101no—
195C2×D8—101no—
196C2×D8—101no—
197C22×C8C22⋊D511yescharacteristic
198C22×C8C22×D511yescharacteristic
199#124—104no—
200#124—202no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—41no—
204C2×C22⋊C4—201no—
205C2×C22⋊C4—201no—
206C2×C42C22⋊D511yescharacteristic
207C2×C16—101no—
208C2×C16—101no—
209C2×C16—101no—
210C2×C16—101no—
211C2×C16—101no—
212C2×C16—101no—
213#107—21no—
214#107—21no—
215#107—21no—
216#107D2012yes—
217C4×C8—21no—
218C4×C8—21no—
219#95—41no—
220C22×C5#44711yescharacteristic
221C22×C5#45911yescharacteristic
222C22×C5#48611yescharacteristic
223C22×C5#50811yescharacteristic
224C22×C5#50811yescharacteristic
225C22×C5#50911yescharacteristic
226C22×C5#51011yescharacteristic
227C2×D5—82no—
228C2×D5—82no—
229C2×D5—82no—
230C2×D5—161no—
231C2×D5—161no—
232C2×D5—161no—
233C2×D5—161no—
234C4×C5—41no—
235C4×C5—41no—
236C4×C5—82no—
237C4×C5—161no—
238C4×C5#39411yescharacteristic
239C4×C5#45011yescharacteristic
240C4×C5#46011yescharacteristic
241C4×C5#49011yescharacteristic
242Dic5—82no—
243C24—201no—
244C2×Q8—102no—
245C2×Q8—201no—
246C2×Q8—201no—
247C2×Q8—201no—
248C2×Q8—201no—
249C2×Q8—201no—
250C2×D4—102no—
251C2×D4—201no—
252C2×D4—201no—
253C2×D4—201no—
254C2×D4—201no—
255C2×D4—201no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4—201no—
259C22×C4#68611yescharacteristic
260C22×C4#68611yescharacteristic
261C22×C4C2×C22⋊D511yescharacteristic
262Q16—102no—
263Q16—102no—
264Q16—201no—
265Q16—201no—
266SD16—208no—
267D8—102no—
268D8—102no—
269D8—201no—
270D8—201no—
271C2×C8—21no—
272C2×C8—21no—
273C2×C8#68812yes—
274C2×C8C2×D2011yescharacteristic
275C2×C8#70911yescharacteristic
276C2×C8D4×D511yescharacteristic
277C2×C8D4×D511yescharacteristic
278C2×C8#71311yescharacteristic
279C2×C8#71311yescharacteristic
280C4⋊C4—22no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—82no—
285C22⋊C4—204no—
286C22⋊C4—204no—
287C42—21no—
288C42—21no—
289C16—201no—
290C16—201no—
291C2×C5#204111yescharacteristic
292C2×C5#218611yescharacteristic
293C2×C5#218911yescharacteristic
294C2×C5#221011yescharacteristic
295C2×C5#221111yescharacteristic
296C2×C5#224211yescharacteristic
297C2×C5#224311yescharacteristic
298D5—162no—
299C23—202no—
300C23—401no—
301C23—401no—
302C23—401no—
303C23—401no—
304C23—401no—
305C23—401no—
306C23C2×#68611yescharacteristic
307Q8—202no—
308Q8—202no—
309Q8—401no—
310Q8—401no—
311D4—202no—
312D4—202no—
313D4—401no—
314D4—401no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—42no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4—81no—
326C2×C4—81no—
327C2×C4—202no—
328C2×C4—401no—
329C2×C4—401no—
330C2×C4#407611yescharacteristic
331C2×C4#408311yescharacteristic
332C2×C4C2×#68811yescharacteristic
333C2×C4#409311yescharacteristic
334C2×C4#409511yescharacteristic
335C2×C4#409511yescharacteristic
336C8—22no—
337C8#404011yescharacteristic
338C8#404011yescharacteristic
339C8#404111yescharacteristic
340C8#404111yescharacteristic
341C5#1340811yescharacteristic, complemented, Sylow
342C22—402no—
343C22—402no—
344C22—402no—
345C22—801no—
346C22—801no—
347C22—801no—
348C22—801no—
349C22#6530411yescharacteristic
350C22#6532511yescharacteristic
351C22#6537711yescharacteristic
352C22#6543611yescharacteristic
353C22#6546811yescharacteristic
354C22#6548311yescharacteristic
355C22#6548311yescharacteristic
356C4—41no—
357C4—41no—
358C4—82no—
359C4—161no—
360C4—402no—
361C4#6528011yescharacteristic
362C4#6531611yescharacteristic
363C4#6533511yescharacteristic
364C4#6535611yescharacteristic
365C2—802no—
366C2#1060042011yescharacteristic
367C2#1060168311yescharacteristic
368C2#1060170811yescharacteristic
369C2#1060186911yescharacteristic
370C2#1060187911yescharacteristic
371C2#1060214411yescharacteristic
372C2#1060217611yescharacteristic
subgroupG/H
centerC23C2×#686
commutator, cosocleC22×C5×C8C23
FrattiniC22×C8C22×D5
FittingC5×#1942C2
socleC23×C5C2×D8
prime radicalC22×D40C22
hypercenter#1942D5
hypocenterC5#13408
LCSG ▷ C22×C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ #1942

Complements

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

NH ≅ G/Ntype
2. C5×#1942C2semidirect
3. C2×#64712C2semidirect
4. C2×#64712C2semidirect
7. #10598148C2semidirect
71. #1942D5semidirect
341. C5#13408semidirect

Maximal subgroups

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

subgroupindex
C2×#649852
C5×#19422
C2×#647122
C2×#647112
#105981482
#134085