Finite Group Databasebeta

← #11995486

Subgroups — #11995486

Order 1280.

590 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65316C211yesmaximal, characteristic
2C2×Q8×#168C211yesmaximal, characteristic, complemented
3C5×#1803C211yesmaximal, characteristic, complemented
4C2×#64705C211yesmaximal, characteristic
5#10600373C211yesmaximal, characteristic
6#10598194C211yesmaximal, characteristic, complemented
7#10598125C211yesmaximal, characteristic, complemented
8C2×C4×C5×Q8C2211yescharacteristic
9C22×#688—21no—
10C2×#4020C2211yescharacteristic
11C2×C5×C4⋊C8C2211yescharacteristic
12C2×C5×#103—21no—
13C5×#384C2211yescharacteristic
14#65316—22no—
15#65316C414yescomplemented
16Q8×#168—22no—
17Q8×#168—22no—
18C2×#3941—21no—
19C2×#3941—21no—
20C2×#3941—21no—
21C2×C4⋊#168—21no—
22C2×C4⋊#168C2211yescharacteristic
23C2×C4⋊#168C2211yescharacteristic
24C2×C4×#168—21no—
25C2×C4×#168C2211yescharacteristic
26C5×#340—21no—
27#64705—22no—
28#9222—51nomaximal, Sylow
29C22×C5×Q8D411yescharacteristic
30C22×D20—21no—
31C22×D20—21no—
32C22×D20—21no—
33C22×C5×C8—21no—
34C4×C5×Q8—21no—
35C4×C5×Q8—21no—
36C4×C5×Q8C2×C412yes—
37C4×C5×Q8D412yes—
38C2×C5×C4⋊C4—21no—
39C2×C5×C4⋊C4—21no—
40C2×C5×C4⋊C4—21no—
41C2×C5×C4⋊C4—21no—
42C2×C5×C4⋊C4D411yescharacteristic
43C2×C42×C5—21no—
44C2×C42×C5C2311yescharacteristic
45C2×#688—24no—
46C2×#688—42no—
47C2×#688—42no—
48C22×#168—21no—
49C22×#168—21no—
50C22×#168D411yescharacteristic
51C22×#168D411yescharacteristic
52#4020—21no—
53#4020—21no—
54#4020—21no—
55#4020C2×C412yes—
56C5×C4⋊C8—21no—
57C5×C4⋊C8—21no—
58C5×#103—42no—
59#3941—24no—
60#3941—42no—
61#3941—42no—
62C4⋊#168—24no—
63C4⋊#168—21no—
64C4⋊#168—21no—
65C4⋊#168C2×C412yes—
66C4⋊#168D412yes—
67C4×#168—24no—
68C4×#168—21no—
69C4×#168—21no—
70C2×#460—51no—
71C2×C8×Q8—51no—
72#1957—51no—
73#1803D511yescharacteristic, complemented
74C2×#331—51no—
75#1296—51no—
76#1277—51no—
77C23×D5—41no—
78C2×C5×Q8—21no—
79C2×C5×Q8—21no—
80C2×C5×Q8—21no—
81C2×C5×Q8C22⋊C412yes—
82C2×C5×Q8D812yes—
83C2×C5×Q8SD1612yes—
84C22×C4×C5—21no—
85C22×C4×C5—21no—
86C22×C4×C5—41no—
87C22×C4×C5C2×D411yescharacteristic
88C22×C4×C5C2×D411yescharacteristic
89C22×C4×C5#4111yescharacteristic
90C2×D20—22no—
91C2×D20—22no—
92C2×D20—22no—
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—41no—
102C2×D20—41no—
103C2×D20—41no—
104C2×D20—81no—
105C2×D20—81no—
106C2×C5×C8—41no—
107C2×C5×C8—41no—
108C2×C5×C8—41no—
109C5×C4⋊C4—22no—
110C5×C4⋊C4—21no—
111C5×C4⋊C4—22no—
112C5×C4⋊C4—41no—
113C5×C4⋊C4—41no—
114C5×C4⋊C4—41no—
115C5×C4⋊C4—41no—
116C5×C4⋊C4—81no—
117C5×C4⋊C4C22⋊C412yes—
118C42×C5—22no—
119C42×C5—22no—
120C42×C5C22×C411yescharacteristic
121C42×C5C2×D411yescharacteristic
122C42×C5C2×D411yescharacteristic
123C42×C5#4111yescharacteristic
124#688—48no—
125C2×#168—21no—
126C2×#168—21no—
127C2×#168—22no—
128C2×#168—21no—
129C2×#168—22no—
130C2×#168—21no—
131C2×#168—21no—
132C2×#168—41no—
133C2×#168—41no—
134C2×#168—41no—
135C2×#168—41no—
136C2×#168SD1612yescomplemented
137C22×SD16—101no—
138C2×#127—51no—
139C2×C4×Q8C2×D511yescharacteristic
140#460—54no—
141#460—102no—
142C8×Q8—102no—
143C8×Q8—102no—
144C2×C4⋊C8—51no—
145C2×C4⋊C8—51no—
146C2×C4⋊C8—101no—
147C2×C4⋊C8C2×D511yescharacteristic
148C2×#103—21no—
149C2×#102—101no—
150C2×#102—101no—
151C2×#102—101no—
152C2×C4×C8—51no—
153C2×C4×C8—101no—
154#384C2×D511yescharacteristic
155#340—21no—
156#331—102no—
157C23×C5#12111yescharacteristic
158C22×D5—42no—
159C22×D5—81no—
160C22×D5—81no—
161C22×D5—81no—
162C22×D5—81no—
163C22×D5—81no—
164C22×D5—81no—
165C5×Q8—22no—
166C5×Q8—22no—
167C5×Q8—22no—
168C5×Q8#10214yescomplemented
169C2×C4×C5—22no—
170C2×C4×C5—22no—
171C2×C4×C5—22no—
172C2×C4×C5—21no—
173C2×C4×C5—21no—
174C2×C4×C5—22no—
175C2×C4×C5—41no—
176C2×C4×C5—41no—
177C2×C4×C5—81no—
178C2×C4×C5—81no—
179C2×C4×C5—81no—
180C2×C4×C5C2×C22⋊C411yescharacteristic
181C2×C4×C5C4×D411yescharacteristic
182C2×C4×C5C4×D411yescharacteristic
183C2×C4×C5#12011yescharacteristic
184C2×C4×C5#12111yescharacteristic
185C2×C4×C5#12311yescharacteristic
186C2×C4×C5C2×D811yescharacteristic
187C2×C4×C5C2×SD1611yescharacteristic
188C2×C4×C5C2×SD1611yescharacteristic
189C2×C4×C5#13511yescharacteristic
190C2×C4×C5#13511yescharacteristic
191C2×C4×C5#13511yescharacteristic
192C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
193C2×C4×C5#13711yescharacteristic
194D20—42no—
195D20—42no—
196D20—42no—
197D20—42no—
198D20—82no—
199D20—82no—
200D20—81no—
201D20—81no—
202D20—81no—
203D20—81no—
204C5×C8—81no—
205#168—22no—
206#168—42no—
207#168—41no—
208#168—42no—
209C22×Q8C22⋊D511yescharacteristic
210C22×D4—101no—
211C22×D4—101no—
212C22×D4—101no—
213C2×SD16—104no—
214C2×SD16—202no—
215C2×SD16—202no—
216C22×C8—21no—
217C22×C8—51no—
218C22×C8—51no—
219C22×C8—101no—
220C22×C8—101no—
221#127—52no—
222#127—101no—
223#127—101no—
224#127—101no—
225C4×Q8—21no—
226C4×Q8—21no—
227C4×Q8C4×D512yes—
228C4×Q8D2012yes—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4C22⋊D511yescharacteristic
234C2×C42—21no—
235C2×C42C22×D511yescharacteristic
236C4⋊C8—21no—
237C4⋊C8—21no—
238C4⋊C8—52no—
239C4⋊C8—52no—
240C4⋊C8—104no—
241C4⋊C8—101no—
242C4⋊C8—101no—
243#103—42no—
244#102—104no—
245#102—202no—
246#102—202no—
247C4×C8—104no—
248C4×C8—101no—
249C4×C8—101no—
250C22×C5#38611yescharacteristic
251C22×C5#46011yescharacteristic
252C22×C5#46411yescharacteristic
253C22×C5#46511yescharacteristic
254C22×C5#46611yescharacteristic
255C22×C5#47111yescharacteristic
256C22×C5#47211yescharacteristic
257C2×D5—82no—
258C2×D5—82no—
259C2×D5—82no—
260C2×D5—161no—
261C2×D5—161no—
262C2×D5—161no—
263C2×D5—161no—
264C4×C5—24no—
265C4×C5—21no—
266C4×C5—21no—
267C4×C5—42no—
268C4×C5—161no—
269C4×C5C2×#10211yescharacteristic
270C4×C5#41611yescharacteristic
271C4×C5C4×SD1611yescharacteristic
272C4×C5#44011yescharacteristic
273C4×C5#44811yescharacteristic
274C4×C5#44911yescharacteristic
275C4×C5#46511yescharacteristic
276C4×C5#46611yescharacteristic
277C24—201no—
278C2×Q8—21no—
279C2×Q8—21no—
280C2×Q8—21no—
281C2×Q8#68512yes—
282C2×Q8#68612yes—
283C2×Q8#68812yes—
284C2×D4—102no—
285C2×D4—102no—
286C2×D4—102no—
287C2×D4—201no—
288C2×D4—201no—
289C2×D4—201no—
290C2×D4—201no—
291C2×D4—201no—
292C2×D4—201no—
293C2×D4—201no—
294C2×D4—201no—
295C2×D4—201no—
296C2×D4—201no—
297C2×D4—201no—
298C2×D4—401no—
299C2×D4—401no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—41no—
303C22×C4D4×D511yescharacteristic
304C22×C4#71111yescharacteristic
305C22×C4C2×C22⋊D511yescharacteristic
306SD16—208no—
307C2×C8—41no—
308C2×C8—41no—
309C2×C8—41no—
310C2×C8—52no—
311C2×C8—101no—
312C2×C8—101no—
313C2×C8—102no—
314C2×C8—101no—
315C2×C8—101no—
316C2×C8—101no—
317C2×C8—102no—
318C2×C8—201no—
319C2×C8—201no—
320C2×C8—201no—
321C2×C8—201no—
322C4⋊C4—22no—
323C4⋊C4—22no—
324C4⋊C4—21no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—81no—
330C4⋊C4#68512yes—
331C42—22no—
332C42—22no—
333C42C2×C4×D511yescharacteristic
334C42C2×D2011yescharacteristic
335C42D4×D511yescharacteristic
336C42#71111yescharacteristic
337C2×C5#166611yescharacteristic
338C2×C5#166811yescharacteristic
339C2×C5#167811yescharacteristic
340C2×C5#168211yescharacteristic
341C2×C5#188011yescharacteristic
342C2×C5#189311yescharacteristic
343C2×C5#190711yescharacteristic
344D5—162no—
345C23—202no—
346C23—401no—
347C23—401no—
348C23—401no—
349C23—401no—
350C23—401no—
351C23—401no—
352C23#408511yescharacteristic
353Q8—22no—
354Q8—22no—
355Q8—22no—
356Q8#394114yescomplemented
357D4—202no—
358D4—202no—
359D4—202no—
360D4—202no—
361D4—402no—
362D4—402no—
363D4—401no—
364D4—401no—
365D4—401no—
366D4—401no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—81no—
376C2×C4—81no—
377C2×C4—81no—
378C2×C4#402711yescharacteristic
379C2×C4#402711yescharacteristic
380C2×C4#402811yescharacteristic
381C2×C4#403211yescharacteristic
382C2×C4D5×SD1611yescharacteristic
383C2×C4#406011yescharacteristic
384C2×C4#406411yescharacteristic
385C2×C4#406511yescharacteristic
386C2×C4C2×#68511yescharacteristic
387C2×C4C2×#68611yescharacteristic
388C2×C4#408511yescharacteristic
389C2×C4C2×#68811yescharacteristic
390C2×C4#409611yescharacteristic
391C2×C4#409611yescharacteristic
392C8—81no—
393C8—102no—
394C8—201no—
395C8—202no—
396C8—202no—
397C5#922211yescharacteristic, complemented, Sylow
398C22—402no—
399C22—402no—
400C22—402no—
401C22—801no—
402C22—801no—
403C22—801no—
404C22—801no—
405C22#6524711yescharacteristic
406C22#6532711yescharacteristic
407C22#6533711yescharacteristic
408C22#6545211yescharacteristic
409C22#6547411yescharacteristic
410C22#6548811yescharacteristic
411C22#6549211yescharacteristic
412C4—24no—
413C4—21no—
414C4—21no—
415C4—42no—
416C4—161no—
417C4#6507711yescharacteristic
418C4#6509511yescharacteristic
419C4#6510011yescharacteristic
420C4#6510611yescharacteristic
421C4C2×#394111yescharacteristic
422C4#6529111yescharacteristic
423C4#6532711yescharacteristic
424C4#6533711yescharacteristic
425C2—802no—
426C2#1060030811yescharacteristic
427C2#1060103311yescharacteristic
428C2#1060109611yescharacteristic
429C2#1060181411yescharacteristic
430C2#1060184811yescharacteristic
431C2#1060190911yescharacteristic
432C2#1060194311yescharacteristic
subgroupG/H
centerC23#4085
commutatorC42×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#1803C2
socleC23×C5#121
prime radicalC2×#4020C22
cosocleC2×C42×C5C23
hypercenter#1803D5
hypocenterC5#9222
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1803

Complements

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

NH ≅ G/Ntype
2. C2×Q8×#168C2semidirect
3. C5×#1803C2semidirect
6. #10598194C2semidirect
7. #10598125C2semidirect
15. #65316C4semidirect
73. #1803D5semidirect
136. C2×#168SD16semidirect
168. C5×Q8#102semidirect
356. Q8#3941semidirect
397. C5#9222semidirect

Maximal subgroups

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

subgroupindex
C2×#653162
C2×Q8×#1682
C5×#18032
C2×#647052
#106003732
#105981942
#105981252
#92225