Finite Group Databasebeta

← #12003529

Subgroups — #12003529

Order 1280.

506 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65377C211yesmaximal, characteristic
2C5×#1981C211yesmaximal, characteristic, complemented
3C2×#64767C211yesmaximal, characteristic, complemented
4C2×#64705C211yesmaximal, characteristic
5#10600280C211yesmaximal, characteristic
6#10600277C211yesmaximal, characteristic, complemented
7#10598194C211yesmaximal, characteristic, complemented
8C2×C5×C4⋊Q8C2211yescharacteristic
9C2×#4020C2211yescharacteristic
10C2×C5×C4⋊C8C2211yescharacteristic
11C2×C5×#103—21no—
12C2×C5×#103—21no—
13C4×C5×C4⋊C4C2211yescharacteristic
14#65377—22no—
15#65377—22no—
16C2×#3941—21no—
17C2×#3941—21no—
18C2×#3941—21no—
19C2×#3941—21no—
20C2×C4⋊#168—21no—
21C2×C4⋊#168C2211yescharacteristic
22C2×C4⋊#168C2211yescharacteristic
23C2×C4×#168C2211yescharacteristic
24#64767—22no—
25#64744—21no—
26#64705—22no—
27#10540—51nomaximal, Sylow
28C22×C5×Q8—21no—
29C22×D20—21no—
30C22×D20—21no—
31C22×D20—21no—
32C22×C5×C8—21no—
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⋊C4D411yescharacteristic
40C2×C5×C4⋊C4D411yescharacteristic
41C2×C42×C5—21no—
42C2×C42×C5C2311yescharacteristic
43C22×#168—21no—
44C22×#168—21no—
45C22×#168D411yescharacteristic
46C22×#168D411yescharacteristic
47#4020—21no—
48#4020—21no—
49#4020—21no—
50#4020D412yes—
51C5×C4⋊C8—21no—
52C5×C4⋊C8—21no—
53C5×#103—42no—
54C5×#103—42no—
55C5×#95—21no—
56#3941—24no—
57#3941—24no—
58#3941—42no—
59#3941—42no—
60C4⋊#168—21no—
61C4⋊#168—21no—
62C4⋊#168—21no—
63C4⋊#168—21no—
64C4⋊#168—42no—
65C4×#168—21no—
66C4×#168—21no—
67C2×#486—51no—
68#1982—51no—
69#1981D511yescharacteristic, complemented
70#1939—51no—
71C2×#332—51no—
72C2×#331—51no—
73#1277—51no—
74C23×D5—41no—
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—21no—
82C22×C4×C5—21no—
83C22×C4×C5—41no—
84C22×C4×C5C2×D411yescharacteristic
85C22×C4×C5C2×D411yescharacteristic
86C22×C4×C5#4111yescharacteristic
87C2×D20—22no—
88C2×D20—22no—
89C2×D20—22no—
90C2×D20—41no—
91C2×D20—41no—
92C2×D20—41no—
93C2×D20—41no—
94C2×D20—41no—
95C2×D20—41no—
96C2×D20—41no—
97C2×D20—41no—
98C2×D20—41no—
99C2×D20—41no—
100C2×D20—41no—
101C2×D20—81no—
102C2×D20—81no—
103C2×C5×C8—41no—
104C2×C5×C8—41no—
105C2×C5×C8—41no—
106C5×C4⋊C4—21no—
107C5×C4⋊C4—22no—
108C5×C4⋊C4—22no—
109C5×C4⋊C4—21no—
110C5×C4⋊C4—21no—
111C5×C4⋊C4—41no—
112C5×C4⋊C4—41no—
113C5×C4⋊C4D812yes—
114C42×C5—41no—
115C42×C5—41no—
116C42×C5C2×D411yescharacteristic
117C42×C5C2×D411yescharacteristic
118C42×C5#4111yescharacteristic
119C42×C5#4111yescharacteristic
120C2×#168—21no—
121C2×#168—21no—
122C2×#168—21no—
123C2×#168—21no—
124C2×#168—21no—
125C2×#168—21no—
126C2×#168—41no—
127C2×#168—41no—
128C2×#168—41no—
129C2×#168—41no—
130C2×#168—41no—
131C2×#168—41no—
132C2×C4⋊Q8C2×D511yescharacteristic
133C2×#127—51no—
134#486—102no—
135#486—102no—
136C2×C4⋊C8—51no—
137C2×C4⋊C8—51no—
138C2×C4⋊C8—101no—
139C2×C4⋊C8C2×D511yescharacteristic
140C2×#103—21no—
141C2×#103—21no—
142C2×#102—101no—
143C2×#102—101no—
144C2×#102—101no—
145C2×#102—101no—
146C2×C4×C8—51no—
147C4×C4⋊C4C2×D511yescharacteristic
148#336—101no—
149#332—102no—
150#331—102no—
151C23×C5#12111yescharacteristic
152C22×D5—42no—
153C22×D5—81no—
154C22×D5—81no—
155C22×D5—81no—
156C22×D5—81no—
157C22×D5—81no—
158C22×D5—81no—
159C5×Q8—42no—
160C5×Q8—42no—
161C5×Q8—81no—
162C5×Q8—81no—
163C2×C4×C5—21no—
164C2×C4×C5—21no—
165C2×C4×C5—22no—
166C2×C4×C5—41no—
167C2×C4×C5—41no—
168C2×C4×C5—42no—
169C2×C4×C5—41no—
170C2×C4×C5—41no—
171C2×C4×C5—41no—
172C2×C4×C5—81no—
173C2×C4×C5—81no—
174C2×C4×C5#12011yescharacteristic
175C2×C4×C5#12111yescharacteristic
176C2×C4×C5#12111yescharacteristic
177C2×C4×C5#12311yescharacteristic
178C2×C4×C5#12311yescharacteristic
179C2×C4×C5#12411yescharacteristic
180C2×C4×C5C2×D811yescharacteristic
181C2×C4×C5#13511yescharacteristic
182C2×C4×C5#13511yescharacteristic
183C2×C4×C5#13511yescharacteristic
184C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
185C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
186C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
187C2×C4×C5#13711yescharacteristic
188D20—42no—
189D20—42no—
190D20—42no—
191D20—42no—
192D20—82no—
193D20—82no—
194D20—81no—
195D20—81no—
196D20—81no—
197D20—81no—
198C5×C8—81no—
199#168—41no—
200#168—41no—
201#168—81no—
202#168—81no—
203C22×Q8—21no—
204C22×D4—101no—
205C22×D4—101no—
206C22×D4—101no—
207C22×C8—21no—
208C22×C8—51no—
209C22×C8—51no—
210C22×C8—101no—
211C22×C8—101no—
212C4⋊Q8—21no—
213C4⋊Q8—21no—
214C4⋊Q8—21no—
215C4⋊Q8D2012yes—
216#127—52no—
217#127—101no—
218#127—101no—
219#127—101no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4C22⋊D511yescharacteristic
223C2×C4⋊C4C22⋊D511yescharacteristic
224C2×C42—21no—
225C2×C42C22×D511yescharacteristic
226C4⋊C8—21no—
227C4⋊C8—21no—
228C4⋊C8—101no—
229C4⋊C8—101no—
230C4⋊C8—101no—
231C4⋊C8—101no—
232C4⋊C8—202no—
233#103—42no—
234#103—42no—
235#102—104no—
236#102—104no—
237#102—202no—
238#102—202no—
239C4×C8—101no—
240C4×C8—101no—
241#95—21no—
242C22×C5#39411yescharacteristic
243C22×C5#46311yescharacteristic
244C22×C5#46411yescharacteristic
245C22×C5#46611yescharacteristic
246C22×C5#46911yescharacteristic
247C22×C5#47111yescharacteristic
248C22×C5#47111yescharacteristic
249C2×D5—82no—
250C2×D5—82no—
251C2×D5—82no—
252C2×D5—161no—
253C2×D5—161no—
254C2×D5—161no—
255C2×D5—161no—
256C4×C5—21no—
257C4×C5—21no—
258C4×C5—42no—
259C4×C5—82no—
260C4×C5—81no—
261C4×C5#44911yescharacteristic
262C4×C5#45211yescharacteristic
263C4×C5#45911yescharacteristic
264C4×C5#45911yescharacteristic
265C4×C5#46311yescharacteristic
266C4×C5#46311yescharacteristic
267C4×C5#48811yescharacteristic
268C4×C5#48911yescharacteristic
269C24—201no—
270C2×Q8—22no—
271C2×Q8—41no—
272C2×Q8—41no—
273C2×Q8—41no—
274C2×Q8—41no—
275C2×Q8—41no—
276C2×D4—102no—
277C2×D4—102no—
278C2×D4—102no—
279C2×D4—201no—
280C2×D4—201no—
281C2×D4—201no—
282C2×D4—201no—
283C2×D4—201no—
284C2×D4—201no—
285C2×D4—201no—
286C2×D4—201no—
287C2×D4—201no—
288C2×D4—201no—
289C2×D4—201no—
290C2×D4—401no—
291C2×D4—401no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—41no—
295C22×C4D4×D511yescharacteristic
296C22×C4#71111yescharacteristic
297C22×C4C2×C22⋊D511yescharacteristic
298C2×C8—41no—
299C2×C8—41no—
300C2×C8—41no—
301C2×C8—101no—
302C2×C8—101no—
303C2×C8—101no—
304C2×C8—101no—
305C2×C8—101no—
306C2×C8—101no—
307C2×C8—201no—
308C2×C8—201no—
309C2×C8—201no—
310C2×C8—201no—
311C2×C8—201no—
312C2×C8—201no—
313C4⋊C4—21no—
314C4⋊C4—22no—
315C4⋊C4—22no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4#68612yes—
321C42—41no—
322C42—41no—
323C42C2×D2011yescharacteristic
324C42#70911yescharacteristic
325C42D4×D511yescharacteristic
326C42#71111yescharacteristic
327C2×C5#168111yescharacteristic
328C2×C5#168211yescharacteristic
329C2×C5#170111yescharacteristic
330C2×C5#170211yescharacteristic
331C2×C5#204211yescharacteristic
332C2×C5#204611yescharacteristic
333C2×C5#205411yescharacteristic
334D5—162no—
335C23—202no—
336C23—401no—
337C23—401no—
338C23—401no—
339C23—401no—
340C23—401no—
341C23—401no—
342C23#408511yescharacteristic
343Q8—42no—
344Q8—42no—
345Q8—81no—
346Q8—81no—
347D4—202no—
348D4—202no—
349D4—202no—
350D4—202no—
351D4—402no—
352D4—402no—
353D4—401no—
354D4—401no—
355D4—401no—
356D4—401no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—22no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—42no—
366C2×C4—81no—
367C2×C4—81no—
368C2×C4#402811yescharacteristic
369C2×C4#402911yescharacteristic
370C2×C4#403111yescharacteristic
371C2×C4#403211yescharacteristic
372C2×C4#406011yescharacteristic
373C2×C4#406211yescharacteristic
374C2×C4#406411yescharacteristic
375C2×C4#406511yescharacteristic
376C2×C4#407611yescharacteristic
377C2×C4C2×#68611yescharacteristic
378C2×C4#407811yescharacteristic
379C2×C4#408411yescharacteristic
380C2×C4#409511yescharacteristic
381C2×C4#409611yescharacteristic
382C8—81no—
383C8—201no—
384C8—201no—
385C8—401no—
386C8—401no—
387C5#1054011yescharacteristic, complemented, Sylow
388C22—402no—
389C22—402no—
390C22—402no—
391C22—801no—
392C22—801no—
393C22—801no—
394C22—801no—
395C22#6525011yescharacteristic
396C22#6532711yescharacteristic
397C22#6532811yescharacteristic
398C22#6545411yescharacteristic
399C22#6547411yescharacteristic
400C22#6549211yescharacteristic
401C22#6549211yescharacteristic
402C4—21no—
403C4—21no—
404C4—42no—
405C4—81no—
406C4—82no—
407C4#6508411yescharacteristic
408C4#6508911yescharacteristic
409C4#6509911yescharacteristic
410C4#6510011yescharacteristic
411C4#6530411yescharacteristic
412C4#6530511yescharacteristic
413C4#6534611yescharacteristic
414C4#6536111yescharacteristic
415C2—802no—
416C2#1060044311yescharacteristic
417C2#1060103811yescharacteristic
418C2#1060113211yescharacteristic
419C2#1060183211yescharacteristic
420C2#1060183611yescharacteristic
421C2#1060184811yescharacteristic
422C2#1060185211yescharacteristic
subgroupG/H
centerC23#4085
commutator, cosocleC2×C42×C5C23
FrattiniC2×C42C22×D5
FittingC5×#1981C2
socleC23×C5#121
prime radicalC2×#4020C22
hypercenter#1981D5
hypocenterC5#10540
LCSG ▷ C2×C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1981

Complements

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

NH ≅ G/Ntype
2. C5×#1981C2semidirect
3. C2×#64767C2semidirect
6. #10600277C2semidirect
7. #10598194C2semidirect
69. #1981D5semidirect
387. C5#10540semidirect

Maximal subgroups

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

subgroupindex
C2×#653772
C5×#19812
C2×#647672
C2×#647052
#106002802
#106002772
#105981942
#105405