Finite Group Databasebeta

← #12003124

Subgroups — #12003124

Order 1280.

506 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65372C211yesmaximal, characteristic
2C5×#1990C211yesmaximal, characteristic, complemented
3C2×#64767C211yesmaximal, characteristic, complemented
4#10600580C211yesmaximal, characteristic
5C2×#64677C211yesmaximal, characteristic, complemented
6#10600377C211yesmaximal, characteristic
7#10598125C211yesmaximal, characteristic, complemented
8C2×C5×C4⋊Q8C2211yescharacteristic
9C22×#688—21no—
10C2×C4×D20C2211yescharacteristic
11C2×C4×C5×C8C2211yescharacteristic
12C5×#384C2211yescharacteristic
13C2×#3967—21no—
14C2×#3952—21no—
15C2×#3952—21no—
16#65372—22no—
17#65372—22no—
18C2×#3941—21no—
19C2×C4⋊#168C2211yescharacteristic
20C2×C4⋊#168C2211yescharacteristic
21C2×C4⋊#168C2211yescharacteristic
22C5×#340—21no—
23C5×#340—21no—
24#64767—22no—
25#64749—21no—
26#64677—22no—
27#10477—51nomaximal, Sylow
28C22×C5×Q8—21no—
29C22×D20D411yescharacteristic
30C22×C4×D5—21no—
31C22×C5×C8D411yescharacteristic
32C22×C5×C8D411yescharacteristic
33C5×C4⋊Q8—21no—
34C5×C4⋊Q8—21no—
35C5×C4⋊Q8—21no—
36C5×C4⋊Q8D412yes—
37C2×C5×C4⋊C4—21no—
38C2×C5×C4⋊C4—21no—
39C2×C5×C4⋊C4—21no—
40C2×C5×C4⋊C4—21no—
41C2×C5×C4⋊C4—21no—
42C2×C42×C5C2311yescharacteristic
43C2×#688—24no—
44C2×#688—42no—
45C2×#688—42no—
46C2×#685—21no—
47C2×C4⋊Dic5D411yescharacteristic
48C22×#168—21no—
49C22×#168—21no—
50C22×#168—21no—
51C4×D20—21no—
52C4×D20—21no—
53C4×D20—21no—
54C4×D20—21no—
55C4×C5×C8—21no—
56C4×C5×C8—21no—
57#3967—24no—
58#3952—42no—
59#3952—42no—
60#3941—42no—
61C4⋊#168—21no—
62C4⋊#168—21no—
63C4⋊#168—21no—
64C4⋊#168—21no—
65C4⋊#168—21no—
66C4⋊#168D412yes—
67C2×#461—51no—
68#1990D511yescharacteristic, complemented
69#1954—51no—
70#1802—51no—
71C2×#334—51no—
72C2×#332—51no—
73#1296—51no—
74C23×D5—21no—
75C2×C5×Q8—22no—
76C2×C5×Q8—41no—
77C2×C5×Q8—41no—
78C2×C5×Q8—41no—
79C2×C5×Q8—41no—
80C2×C5×Q8—41no—
81C22×C4×C5—41no—
82C22×C4×C5—41no—
83C22×C4×C5C2×D411yescharacteristic
84C22×C4×C5C2×D411yescharacteristic
85C22×C4×C5#4111yescharacteristic
86C22×Dic5—21no—
87C2×D20—21no—
88C2×D20—21no—
89C2×D20—21no—
90C2×D20—21no—
91C2×D20—21no—
92C2×D20SD1612yes—
93C2×C4×D5—41no—
94C2×C4×D5—41no—
95C2×C4×D5—41no—
96C2×C4×D5—41no—
97C2×C4×D5—41no—
98C2×C4×D5—41no—
99C2×C5×C8—21no—
100C2×C5×C8—21no—
101C2×C5×C8—21no—
102C2×C5×C8—21no—
103C2×C5×C8—21no—
104C2×C5×C8SD1612yescomplemented
105C5×C4⋊C4—22no—
106C5×C4⋊C4—22no—
107C5×C4⋊C4—41no—
108C5×C4⋊C4—41no—
109C5×C4⋊C4—41no—
110C5×C4⋊C4—41no—
111C5×C4⋊C4—41no—
112C5×C4⋊C4—41no—
113C5×C4⋊C4—81no—
114C42×C5C2×D411yescharacteristic
115C42×C5C2×D411yescharacteristic
116C42×C5#4111yescharacteristic
117C42×C5#4111yescharacteristic
118#688—48no—
119#685—41no—
120#685—41no—
121C4⋊Dic5—21no—
122C4⋊Dic5—21no—
123C2×#168—22no—
124C2×#168—41no—
125C2×#168—41no—
126C2×#168—41no—
127C2×#168—41no—
128C2×#168—41no—
129C2×#168—41no—
130C2×#168—41no—
131C2×#168—41no—
132C22×SD16—101no—
133C2×C4⋊Q8C2×D511yescharacteristic
134C2×C4×D4—51no—
135#461—102no—
136#461—102no—
137C2×C4⋊C8—51no—
138C2×C4⋊C8—51no—
139C2×C4⋊C8—51no—
140C2×#103—101no—
141C2×#102—101no—
142C2×C22⋊C8—101no—
143C2×C22⋊C8—101no—
144C2×C4×C8C2×D511yescharacteristic
145#384C2×D511yescharacteristic
146#340—21no—
147#340—21no—
148#340—101no—
149#334—102no—
150#332—102no—
151C23×C5#12111yescharacteristic
152C22×D5—22no—
153C22×D5—41no—
154C22×D5—41no—
155C22×D5—41no—
156C22×D5—41no—
157C22×D5—41no—
158C22×D5—41no—
159C5×Q8—42no—
160C5×Q8—42no—
161C5×Q8—81no—
162C5×Q8—81no—
163C2×C4×C5—21no—
164C2×C4×C5—21no—
165C2×C4×C5—42no—
166C2×C4×C5—81no—
167C2×C4×C5—81no—
168C2×C4×C5—81no—
169C2×C4×C5—81no—
170C2×C4×C5—81no—
171C2×C4×C5#12011yescharacteristic
172C2×C4×C5#12111yescharacteristic
173C2×C4×C5#12111yescharacteristic
174C2×C4×C5#12311yescharacteristic
175C2×C4×C5#12311yescharacteristic
176C2×C4×C5#12411yescharacteristic
177C2×C4×C5C2×SD1611yescharacteristic
178C2×C4×C5C2×SD1611yescharacteristic
179C2×C4×C5#13511yescharacteristic
180C2×C4×C5#13511yescharacteristic
181C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
182C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
183C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
184C2×C4×C5#13711yescharacteristic
185C2×Dic5—41no—
186C2×Dic5—41no—
187C2×Dic5—41no—
188D20—22no—
189D20—22no—
190D20—41no—
191D20—41no—
192C4×D5—81no—
193C4×D5—81no—
194C4×D5—81no—
195C4×D5—81no—
196C5×C8—22no—
197C5×C8—41no—
198#168—42no—
199#168—81no—
200#168—81no—
201C22×Q8—21no—
202C22×D4—51no—
203C23×C4—101no—
204C2×SD16—104no—
205C2×SD16—202no—
206C2×SD16—202no—
207C22×C8—101no—
208C22×C8—101no—
209C22×C8—101no—
210C22×C8C22⋊D511yescharacteristic
211C22×C8C22⋊D511yescharacteristic
212C4⋊Q8—21no—
213C4⋊Q8—21no—
214C4⋊Q8—21no—
215C4⋊Q8D2012yes—
216C4×D4—101no—
217C4×D4—101no—
218C4×D4—101no—
219C4×D4—101no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—51no—
226C2×C22⋊C4—101no—
227C2×C42C22×D511yescharacteristic
228C4⋊C8—52no—
229C4⋊C8—101no—
230C4⋊C8—101no—
231C4⋊C8—101no—
232C4⋊C8—101no—
233C4⋊C8—101no—
234#103—104no—
235#102—202no—
236C22⋊C8—202no—
237C22⋊C8—202no—
238C4×C8—21no—
239C4×C8—21no—
240C22×C5#39411yescharacteristic
241C22×C5#46111yescharacteristic
242C22×C5#46311yescharacteristic
243C22×C5#46511yescharacteristic
244C22×C5#46911yescharacteristic
245C22×C5#47111yescharacteristic
246C22×C5#47311yescharacteristic
247C2×D5—42no—
248C2×D5—42no—
249C2×D5—42no—
250C2×D5—81no—
251C2×D5—81no—
252C2×D5—81no—
253C2×D5—81no—
254C4×C5—21no—
255C4×C5—21no—
256C4×C5—82no—
257C4×C5—161no—
258C4×C5#44911yescharacteristic
259C4×C5#45011yescharacteristic
260C4×C5#46011yescharacteristic
261C4×C5#46411yescharacteristic
262C4×C5#46511yescharacteristic
263C4×C5#46811yescharacteristic
264C4×C5#48111yescharacteristic
265C4×C5#48211yescharacteristic
266Dic5—81no—
267C24—101no—
268C2×Q8—22no—
269C2×Q8—41no—
270C2×Q8—41no—
271C2×Q8—41no—
272C2×Q8—41no—
273C2×Q8—41no—
274C2×D4—52no—
275C2×D4—101no—
276C2×D4—101no—
277C2×D4—101no—
278C2×D4—101no—
279C2×D4—101no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4—101no—
283C22×C4—201no—
284C22×C4—201no—
285C22×C4—201no—
286C22×C4—201no—
287C22×C4—201no—
288C22×C4—201no—
289C22×C4D4×D511yescharacteristic
290C22×C4#71111yescharacteristic
291C22×C4C2×C22⋊D511yescharacteristic
292SD16—208no—
293C2×C8—21no—
294C2×C8—21no—
295C2×C8—21no—
296C2×C8—21no—
297C2×C8—21no—
298C2×C8—102no—
299C2×C8—201no—
300C2×C8—201no—
301C2×C8—201no—
302C2×C8—201no—
303C2×C8—201no—
304C2×C8—201no—
305C2×C8—201no—
306C2×C8—201no—
307C2×C8#68812yescomplemented
308C4⋊C4—22no—
309C4⋊C4—22no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—81no—
317C4⋊C4—101no—
318C4⋊C4—101no—
319C22⋊C4—201no—
320C22⋊C4—201no—
321C42C2×D2011yescharacteristic
322C42#70911yescharacteristic
323C42D4×D511yescharacteristic
324C42#71111yescharacteristic
325C2×C5#167111yescharacteristic
326C2×C5#167911yescharacteristic
327C2×C5#169311yescharacteristic
328C2×C5#170111yescharacteristic
329C2×C5#203411yescharacteristic
330C2×C5#205211yescharacteristic
331C2×C5#205511yescharacteristic
332D5—82no—
333C23—102no—
334C23—201no—
335C23—201no—
336C23—201no—
337C23—201no—
338C23—201no—
339C23—201no—
340C23#408411yescharacteristic
341Q8—42no—
342Q8—42no—
343Q8—81no—
344Q8—81no—
345D4—102no—
346D4—102no—
347D4—201no—
348D4—201no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—42no—
352C2×C4—81no—
353C2×C4—81no—
354C2×C4—81no—
355C2×C4—81no—
356C2×C4—81no—
357C2×C4—201no—
358C2×C4—201no—
359C2×C4—201no—
360C2×C4—401no—
361C2×C4—401no—
362C2×C4—401no—
363C2×C4—401no—
364C2×C4#402811yescharacteristic
365C2×C4#402911yescharacteristic
366C2×C4#403111yescharacteristic
367C2×C4#403211yescharacteristic
368C2×C4#405711yescharacteristic
369C2×C4#405711yescharacteristic
370C2×C4D5×SD1611yescharacteristic
371C2×C4#406211yescharacteristic
372C2×C4#407611yescharacteristic
373C2×C4#408511yescharacteristic
374C2×C4C2×#68811yescharacteristic
375C2×C4#408811yescharacteristic
376C2×C4#409511yescharacteristic
377C2×C4#409611yescharacteristic
378C8—22no—
379C8—41no—
380C8—202no—
381C8—401no—
382C8—401no—
383C5#1047711yescharacteristic, complemented, Sylow
384C22—202no—
385C22—202no—
386C22—202no—
387C22—401no—
388C22—401no—
389C22—401no—
390C22—401no—
391C22#6525011yescharacteristic
392C22#6534611yescharacteristic
393C22#6537211yescharacteristic
394C22#6544811yescharacteristic
395C22#6546011yescharacteristic
396C22#6546611yescharacteristic
397C22#6548111yescharacteristic
398C4—21no—
399C4—21no—
400C4—82no—
401C4—161no—
402C4—401no—
403C4#6506511yescharacteristic
404C4#6506611yescharacteristic
405C4#6506811yescharacteristic
406C4#6507011yescharacteristic
407C4#6531611yescharacteristic
408C4#6531711yescharacteristic
409C4#6533711yescharacteristic
410C4#6533811yescharacteristic
411C2—402no—
412C2#1060047311yescharacteristic
413C2#1060096911yescharacteristic
414C2#1060105711yescharacteristic
415C2#1060199611yescharacteristic
416C2#1060202511yescharacteristic
417C2#1060213711yescharacteristic
418C2#1060216611yescharacteristic
subgroupG/H
centerC23#4084
commutator, cosocleC2×C42×C5C23
FrattiniC2×C42C22×D5
FittingC5×#1990C2
socleC23×C5#121
prime radicalC22×D20D4
hypercenter#1990D5
hypocenterC5#10477
LCSG ▷ C2×C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1990

Complements

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

NH ≅ G/Ntype
2. C5×#1990C2semidirect
3. C2×#64767C2semidirect
5. C2×#64677C2semidirect
7. #10598125C2semidirect
68. #1990D5semidirect
104. C2×C5×C8SD16semidirect
307. C2×C8#688semidirect
383. C5#10477semidirect

Maximal subgroups

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

subgroupindex
C2×#653722
C5×#19902
C2×#647672
#106005802
C2×#646772
#106003772
#105981252
#104775