Finite Group Databasebeta

← #12017995

Subgroups — #12017995

Order 1280.

670 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#466C211yesmaximal, characteristic, complemented
2C22×#3958C211yesmaximal, characteristic, complemented
3C2×#65404C211yesmaximal, characteristic, complemented
4C2×#64782C211yesmaximal, characteristic, complemented
5C2×C22⋊#672C211yesmaximal, characteristic, complemented
6C2×#64711C211yesmaximal, characteristic, complemented
7#10598213C211yesmaximal, characteristic, complemented
8C22×C5×D8C2211yescharacteristic
9C23×C5×C8C2211yescharacteristic
10C2×C5×#121—21no—
11C2×#4076—21no—
12C22×D40C2211yescharacteristic
13C5×#466—22no—
14C5×#466—22no—
15C2×C5×#107C2211yescharacteristic
16C2×C5×#102—21no—
17C2×#3958—22no—
18C2×#3958—22no—
19C2×#3958—22no—
20#65404—22no—
21#65404—22no—
22C2×#3953—21no—
23C2×#3950C2211yescharacteristic
24C22×#672C2211yescharacteristic
25C22×#672C2211yescharacteristic
26#64782—22no—
27C22⋊#672—22no—
28#64711—22no—
29#13304—51nomaximal, Sylow
30C22×C5×D4—21no—
31C22×C5×D4—41no—
32C23×C4×C5D411yescharacteristic
33C22×C22⋊D5—41no—
34C22×D20—21no—
35C2×C5×D8—21no—
36C2×C5×D8—21no—
37C2×C5×D8—21no—
38C2×C5×D8—21no—
39C2×C5×D8—21no—
40C2×C5×D8D412yescomplemented
41C22×C5×C8—21no—
42C22×C5×C8—21no—
43C22×C5×C8—21no—
44C22×C5×C8—21no—
45C22×C5×C8—21no—
46C22×C5×C8—21no—
47C22×C5×C8D411yescharacteristic
48C22×C5×C8C2311yescharacteristic
49C5×#121—24no—
50C5×#121—42no—
51C2×C5×C4⋊C4—21no—
52C2×C5×C22⋊C4—41no—
53#4076—24no—
54#4076—42no—
55C2×#685—41no—
56C2×C4⋊Dic5—21no—
57C2×D40—21no—
58C2×D40—21no—
59C2×D40—21no—
60C2×D40—21no—
61C2×D40—21no—
62C2×D40D412yescomplemented
63C5×#107—21no—
64C5×#107D412yescomplemented
65C5×#102—24no—
66#3958—28no—
67#3953—24no—
68#3950—21no—
69#3950D412yescomplemented
70C2×#672—21no—
71C2×#672—21no—
72C2×#672—21no—
73C2×#672—21no—
74C2×#672—21no—
75C2×#672D412yescomplemented
76C22×D16—51no—
77C2×#466—51no—
78C2×#466D511yescharacteristic, complemented
79C2×#357—51no—
80C2×#357—51no—
81C2×C22⋊C16—51no—
82#1380—51no—
83C24×C5—41no—
84C24×C5D811yescharacteristic
85C23×D5—41no—
86C2×C5×D4—22no—
87C2×C5×D4—44no—
88C2×C5×D4—41no—
89C2×C5×D4—41no—
90C2×C5×D4—41no—
91C2×C5×D4—41no—
92C2×C5×D4—41no—
93C2×C5×D4—82no—
94C2×C5×D4—82no—
95C22×C4×C5—21no—
96C22×C4×C5—21no—
97C22×C4×C5—21no—
98C22×C4×C5—21no—
99C22×C4×C5—21no—
100C22×C4×C5—21no—
101C22×C4×C5—41no—
102C22×C4×C5D811yescharacteristic
103C22×C4×C5C2×D411yescharacteristic
104C2×C22⋊D5—44no—
105C2×C22⋊D5—82no—
106C2×C22⋊D5—82no—
107C22×Dic5—41no—
108C2×D20—22no—
109C2×D20—41no—
110C2×D20—41no—
111C2×D20—41no—
112C2×D20—41no—
113C2×D20—41no—
114C5×D8—22no—
115C5×D8—22no—
116C5×D8—41no—
117C5×D8—41no—
118C2×C5×C8—21no—
119C2×C5×C8—21no—
120C2×C5×C8—21no—
121C2×C5×C8—41no—
122C2×C5×C8—41no—
123C2×C5×C8—41no—
124C2×C5×C8—41no—
125C2×C5×C8C2×D411yescharacteristic
126C2×C5×C8C2×D411yescharacteristic
127C2×C5×C8C2×D411yescharacteristic
128C2×C5×C8C2×D411yescharacteristic
129C2×C5×C8C2×D411yescharacteristic
130C2×C5×C8#4111yescharacteristic
131C5×C4⋊C4—22no—
132C5×C4⋊C4—41no—
133C5×C22⋊C4—44no—
134#685—44no—
135C4⋊Dic5—22no—
136C4⋊Dic5—41no—
137D40—22no—
138D40—22no—
139D40—41no—
140D40—41no—
141#672—22no—
142#672—41no—
143C22×D8—51no—
144C22×D8C2×D511yescharacteristic
145C23×C8C2×D511yescharacteristic
146C2×#121—21no—
147C2×#121—101no—
148C2×D16—102no—
149C2×D16—102no—
150C2×D16—102no—
151C22×C16—51no—
152C22×C16—51no—
153#466—22no—
154#466—22no—
155#466—102no—
156#466—102no—
157C2×#107—51no—
158C2×#107C2×D511yescharacteristic
159C2×#102—21no—
160C2×#102—101no—
161#357—102no—
162#357—102no—
163C22⋊C16—102no—
164C23×C5—21no—
165C23×C5—21no—
166C23×C5—21no—
167C23×C5—21no—
168C23×C5—21no—
169C23×C5—21no—
170C23×C5—42no—
171C23×C5—81no—
172C23×C5—81no—
173C23×C5—81no—
174C23×C5—81no—
175C23×C5—81no—
176C23×C5—81no—
177C23×C5D1612yescomplemented
178C23×C5C2×D811yescharacteristic
179C22×D5—42no—
180C22×D5—81no—
181C22×D5—81no—
182C22×D5—81no—
183C22×D5—81no—
184C22×D5—81no—
185C22×D5—81no—
186C5×D4—42no—
187C5×D4—42no—
188C5×D4—88no—
189C5×D4—81no—
190C5×D4—81no—
191C2×C4×C5—21no—
192C2×C4×C5—21no—
193C2×C4×C5—21no—
194C2×C4×C5—41no—
195C2×C4×C5—41no—
196C2×C4×C5—41no—
197C2×C4×C5—41no—
198C2×C4×C5—42no—
199C2×C4×C5—81no—
200C2×C4×C5—81no—
201C2×C4×C5#12011yescharacteristic
202C2×C4×C5#12011yescharacteristic
203C2×C4×C5#12111yescharacteristic
204C2×C4×C5#13511yescharacteristic
205C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
206C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
207C22⋊D5—88no—
208C2×Dic5—42no—
209C2×Dic5—81no—
210C2×Dic5—81no—
211D20—42no—
212D20—42no—
213D20—81no—
214D20—81no—
215C5×C8—41no—
216C5×C8#12011yescharacteristic
217C5×C8#12111yescharacteristic
218C5×C8#12111yescharacteristic
219C5×C8#12711yescharacteristic
220C22×D4—21no—
221C22×D4—41no—
222C22×D4—101no—
223C22×D4—201no—
224C23×C4C22⋊D511yescharacteristic
225C2×D8—21no—
226C2×D8—21no—
227C2×D8—21no—
228C2×D8—21no—
229C2×D8—21no—
230C2×D8—52no—
231C2×D8—101no—
232C2×D8—101no—
233C2×D8—101no—
234C2×D8—101no—
235C2×D8—101no—
236C2×D8C22⋊D512yescomplemented
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—21no—
240C22×C8—21no—
241C22×C8—21no—
242C22×C8—21no—
243C22×C8C22⋊D511yescharacteristic
244C22×C8C22×D511yescharacteristic
245#121—24no—
246#121—42no—
247#121—104no—
248#121—202no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—101no—
251C2×C22⋊C4—41no—
252C2×C22⋊C4—201no—
253D16—108no—
254C2×C16—52no—
255C2×C16—101no—
256C2×C16—101no—
257C2×C16—101no—
258C2×C16—101no—
259C2×C16—101no—
260#107—21no—
261#107—52no—
262#107—101no—
263#107C22⋊D512yescomplemented
264#102—24no—
265#102—104no—
266C22×C5—22no—
267C22×C5—22no—
268C22×C5—22no—
269C22×C5—41no—
270C22×C5—41no—
271C22×C5—41no—
272C22×C5—41no—
273C22×C5—82no—
274C22×C5—82no—
275C22×C5—82no—
276C22×C5—161no—
277C22×C5—161no—
278C22×C5—161no—
279C22×C5—161no—
280C22×C5#44711yescharacteristic
281C22×C5#44711yescharacteristic
282C22×C5#46611yescharacteristic
283C22×C5C2×D1611yescharacteristic
284C22×C5#50811yescharacteristic
285C22×C5#50911yescharacteristic
286C22×C5#50911yescharacteristic
287C2×D5—82no—
288C2×D5—82no—
289C2×D5—82no—
290C2×D5—161no—
291C2×D5—161no—
292C2×D5—161no—
293C2×D5—161no—
294C4×C5—41no—
295C4×C5—82no—
296C4×C5#39211yescharacteristic
297C4×C5#44911yescharacteristic
298C4×C5#44911yescharacteristic
299C4×C5#46911yescharacteristic
300Dic5—82no—
301C24—41no—
302C24—201no—
303C24#68611yescharacteristic
304C2×D4—22no—
305C2×D4—44no—
306C2×D4—41no—
307C2×D4—41no—
308C2×D4—41no—
309C2×D4—41no—
310C2×D4—41no—
311C2×D4—82no—
312C2×D4—82no—
313C2×D4—102no—
314C2×D4—204no—
315C2×D4—201no—
316C2×D4—201no—
317C2×D4—201no—
318C2×D4—201no—
319C2×D4—201no—
320C2×D4—402no—
321C2×D4—402no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—41no—
329C22×C4—201no—
330C22×C4#68611yescharacteristic
331C22×C4C2×C22⋊D511yescharacteristic
332D8—22no—
333D8—22no—
334D8—41no—
335D8—41no—
336D8—102no—
337D8—102no—
338D8—201no—
339D8—201no—
340C2×C8—21no—
341C2×C8—21no—
342C2×C8—21no—
343C2×C8—41no—
344C2×C8—41no—
345C2×C8—41no—
346C2×C8—41no—
347C2×C8D4×D511yescharacteristic
348C2×C8D4×D511yescharacteristic
349C2×C8D4×D511yescharacteristic
350C2×C8#71111yescharacteristic
351C2×C8C2×C22⋊D511yescharacteristic
352C2×C8C2×C22⋊D511yescharacteristic
353C4⋊C4—22no—
354C4⋊C4—41no—
355C4⋊C4—102no—
356C4⋊C4—201no—
357C22⋊C4—44no—
358C22⋊C4—204no—
359C16—102no—
360C16—201no—
361C2×C5—42no—
362C2×C5—162no—
363C2×C5#199911yescharacteristic
364C2×C5#218411yescharacteristic
365C2×C5#218411yescharacteristic
366C2×C5#218611yescharacteristic
367C2×C5#218611yescharacteristic
368C2×C5#221511yescharacteristic
369C2×C5#221811yescharacteristic
370D5—162no—
371C23—21no—
372C23—21no—
373C23—21no—
374C23—21no—
375C23—21no—
376C23—21no—
377C23—42no—
378C23—81no—
379C23—81no—
380C23—81no—
381C23—81no—
382C23—81no—
383C23—81no—
384C23—202no—
385C23—401no—
386C23—401no—
387C23—401no—
388C23—401no—
389C23—401no—
390C23—401no—
391C23#395812yescomplemented
392C23C2×#68611yescharacteristic
393D4—42no—
394D4—42no—
395D4—88no—
396D4—81no—
397D4—81no—
398D4—202no—
399D4—202no—
400D4—408no—
401D4—401no—
402D4—401no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—42no—
411C2×C4—81no—
412C2×C4—81no—
413C2×C4—202no—
414C2×C4—401no—
415C2×C4—401no—
416C2×C4#407811yescharacteristic
417C2×C4#408311yescharacteristic
418C2×C4#408511yescharacteristic
419C2×C4#409511yescharacteristic
420C2×C4#409611yescharacteristic
421C2×C4#409911yescharacteristic
422C8—41no—
423C8#408311yescharacteristic
424C8#408411yescharacteristic
425C8#408511yescharacteristic
426C8#408611yescharacteristic
427C5#1330411yescharacteristic, complemented, Sylow
428C22—22no—
429C22—22no—
430C22—22no—
431C22—41no—
432C22—41no—
433C22—41no—
434C22—41no—
435C22—82no—
436C22—82no—
437C22—82no—
438C22—161no—
439C22—161no—
440C22—161no—
441C22—161no—
442C22—402no—
443C22—402no—
444C22—402no—
445C22—801no—
446C22—801no—
447C22—801no—
448C22—801no—
449C22#6532511yescharacteristic
450C22#6532711yescharacteristic
451C22C2×#395811yescharacteristic
452C22#6543611yescharacteristic
453C22#6548211yescharacteristic
454C22#6548311yescharacteristic
455C22#6550611yescharacteristic
456C4—41no—
457C4—82no—
458C4—402no—
459C4#6532611yescharacteristic
460C4#6532811yescharacteristic
461C4#6551211yescharacteristic
462C4#6552711yescharacteristic
463C2—42no—
464C2—162no—
465C2—802no—
466C2#1060186411yescharacteristic
467C2#1060186611yescharacteristic
468C2#1060186811yescharacteristic
469C2#1060186911yescharacteristic
470C2#1060247711yescharacteristic
471C2#1060282811yescharacteristic
472C2#1060287511yescharacteristic
subgroupG/H
centerC23C2×#686
commutator, cosocleC22×C5×C8C23
FrattiniC22×C8C22×D5
FittingC2×C5×#466C2
socleC23×C5C2×D8
hypercenterC2×#466D5
hypocenterC5#13304
LCSG ▷ C22×C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C2×#466

Complements

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

NH ≅ G/Ntype
1. C2×C5×#466C2semidirect
2. C22×#3958C2semidirect
3. C2×#65404C2semidirect
4. C2×#64782C2semidirect
5. C2×C22⋊#672C2semidirect
6. C2×#64711C2semidirect
7. #10598213C2semidirect
40. C2×C5×D8D4semidirect
62. C2×D40D4semidirect
64. C5×#107D4semidirect
69. #3950D4semidirect
75. C2×#672D4semidirect
78. C2×#466D5semidirect
177. C23×C5D16semidirect
236. C2×D8C22⋊D5semidirect
263. #107C22⋊D5semidirect
391. C23#3958semidirect
427. C5#13304semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#4662
C22×#39582
C2×#654042
C2×#647822
C2×C22⋊#6722
C2×#647112
#105982132
#133045