Finite Group Databasebeta

← #12018002

Subgroups — #12018002

Order 1280.

618 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#466C211yesmaximal, characteristic
2C22×#3959C211yesmaximal, characteristic, complemented
3C2×#65405C211yesmaximal, characteristic, complemented
4C2×#64782C211yesmaximal, characteristic, complemented
5C2×C22⋊#672C211yesmaximal, characteristic, complemented
6C2×#64712C211yesmaximal, characteristic, complemented
7#10598213C211yesmaximal, characteristic, complemented
8C22×C5×D8C2211yescharacteristic
9C23×C5×C8C2211yescharacteristic
10C2×C5×#121—21no—
11C2×#4070—21no—
12C22×Dic20C2211yescharacteristic
13C5×#466—22no—
14C5×#466—22no—
15C2×C5×#107C2211yescharacteristic
16C2×C5×#102—21no—
17C2×#3959—22no—
18C2×#3959—22no—
19C2×#3959—22no—
20#65405—22no—
21#65405—22no—
22C2×#3950C2211yescharacteristic
23C2×#3948—21no—
24C22×#672C2211yescharacteristic
25C22×#672C2211yescharacteristic
26#64782—22no—
27C22⋊#672—22no—
28#64712—22no—
29#13305—51nomaximal, Sylow
30C22×C5×D4—21no—
31C22×C5×D4—41no—
32C23×C4×C5D411yescharacteristic
33C22×Dic10—21no—
34C2×C5×D8—21no—
35C2×C5×D8—21no—
36C2×C5×D8—21no—
37C2×C5×D8—21no—
38C2×C5×D8—21no—
39C2×C5×D8D412yes—
40C22×C5×C8—21no—
41C22×C5×C8—21no—
42C22×C5×C8—21no—
43C22×C5×C8—21no—
44C22×C5×C8—21no—
45C22×C5×C8—21no—
46C22×C5×C8D411yescharacteristic
47C22×C5×C8C2311yescharacteristic
48C5×#121—24no—
49C5×#121—42no—
50C2×C5×C4⋊C4—21no—
51C2×C5×C22⋊C4—41no—
52C2×C22⋊Dic5—41no—
53C2×C4⋊Dic5—21no—
54#4070—24no—
55#4070—42no—
56C2×#683—41no—
57C2×Dic20—21no—
58C2×Dic20—21no—
59C2×Dic20—21no—
60C2×Dic20—21no—
61C2×Dic20—21no—
62C2×Dic20D412yescomplemented
63C5×#107—21no—
64C5×#107D412yes—
65C5×#102—24no—
66#3959—28no—
67#3950—21no—
68#3950D412yescomplemented
69#3948—24no—
70C2×#672—21no—
71C2×#672—21no—
72C2×#672—21no—
73C2×#672—21no—
74C2×#672—21no—
75C2×#672D412yescomplemented
76C22×SD32—51no—
77C2×#467—51no—
78C2×#466D511yescharacteristic
79C2×#358—51no—
80C2×#357—51no—
81C2×C22⋊C16—51no—
82#1380—51no—
83C24×C5—41no—
84C24×C5D811yescharacteristic
85C2×C5×D4—22no—
86C2×C5×D4—44no—
87C2×C5×D4—41no—
88C2×C5×D4—41no—
89C2×C5×D4—41no—
90C2×C5×D4—41no—
91C2×C5×D4—41no—
92C2×C5×D4—82no—
93C2×C5×D4—82no—
94C22×C4×C5—21no—
95C22×C4×C5—21no—
96C22×C4×C5—21no—
97C22×C4×C5—21no—
98C22×C4×C5—21no—
99C22×C4×C5—21no—
100C22×C4×C5—41no—
101C22×C4×C5D811yescharacteristic
102C22×C4×C5C2×D411yescharacteristic
103C22×Dic5—41no—
104C22×Dic5—41no—
105C2×Dic10—22no—
106C2×Dic10—41no—
107C2×Dic10—41no—
108C2×Dic10—41no—
109C2×Dic10—41no—
110C2×Dic10—41no—
111C5×D8—22no—
112C5×D8—22no—
113C5×D8—41no—
114C5×D8—41no—
115C2×C5×C8—21no—
116C2×C5×C8—21no—
117C2×C5×C8—21no—
118C2×C5×C8—41no—
119C2×C5×C8—41no—
120C2×C5×C8—41no—
121C2×C5×C8—41no—
122C2×C5×C8C2×D411yescharacteristic
123C2×C5×C8C2×D411yescharacteristic
124C2×C5×C8C2×D411yescharacteristic
125C2×C5×C8C2×D411yescharacteristic
126C2×C5×C8C2×D411yescharacteristic
127C2×C5×C8#4111yescharacteristic
128C5×C4⋊C4—22no—
129C5×C4⋊C4—41no—
130C5×C22⋊C4—44no—
131C22⋊Dic5—44no—
132C4⋊Dic5—22no—
133C4⋊Dic5—41no—
134#683—44no—
135Dic20—22no—
136Dic20—22no—
137Dic20—41no—
138Dic20—41no—
139#672—22no—
140#672—41no—
141C22×Q16—51no—
142C22×D8C2×D511yescharacteristic
143C23×C8C2×D511yescharacteristic
144C2×C22⋊Q8—101no—
145C2×#121—21no—
146C2×SD32—102no—
147C2×SD32—102no—
148C2×SD32—102no—
149C22×C16—51no—
150C22×C16—51no—
151#467—102no—
152#467—102no—
153#466—22no—
154#466—22no—
155C2×#107—51no—
156C2×#107C2×D511yescharacteristic
157C2×#103—101no—
158C2×#102—21no—
159#358—102no—
160#357—102no—
161C22⋊C16—102no—
162C23×C5—21no—
163C23×C5—21no—
164C23×C5—21no—
165C23×C5—21no—
166C23×C5—21no—
167C23×C5—21no—
168C23×C5—42no—
169C23×C5—81no—
170C23×C5—81no—
171C23×C5—81no—
172C23×C5—81no—
173C23×C5—81no—
174C23×C5—81no—
175C23×C5SD3212yescomplemented
176C23×C5C2×D811yescharacteristic
177C5×D4—42no—
178C5×D4—42no—
179C5×D4—88no—
180C5×D4—81no—
181C5×D4—81no—
182C2×C4×C5—21no—
183C2×C4×C5—21no—
184C2×C4×C5—21no—
185C2×C4×C5—41no—
186C2×C4×C5—41no—
187C2×C4×C5—41no—
188C2×C4×C5—41no—
189C2×C4×C5—42no—
190C2×C4×C5—81no—
191C2×C4×C5—81no—
192C2×C4×C5#12011yescharacteristic
193C2×C4×C5#12011yescharacteristic
194C2×C4×C5#12111yescharacteristic
195C2×C4×C5#13511yescharacteristic
196C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
197C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
198C2×Dic5—42no—
199C2×Dic5—42no—
200C2×Dic5—81no—
201C2×Dic5—81no—
202C2×Dic5—81no—
203C2×Dic5—81no—
204Dic10—42no—
205Dic10—42no—
206Dic10—81no—
207Dic10—81no—
208C5×C8—41no—
209C5×C8#12011yescharacteristic
210C5×C8#12111yescharacteristic
211C5×C8#12111yescharacteristic
212C5×C8#12711yescharacteristic
213C22×Q8—101no—
214C22×D4—21no—
215C22×D4—41no—
216C23×C4C22⋊D511yescharacteristic
217C2×Q16—52no—
218C2×Q16—101no—
219C2×Q16—101no—
220C2×Q16—101no—
221C2×Q16—101no—
222C2×Q16—101no—
223C2×D8—21no—
224C2×D8—21no—
225C2×D8—21no—
226C2×D8—21no—
227C2×D8—21no—
228C2×D8C22⋊D512yes—
229C22×C8—21no—
230C22×C8—21no—
231C22×C8—21no—
232C22×C8—21no—
233C22×C8—21no—
234C22×C8—21no—
235C22×C8C22⋊D511yescharacteristic
236C22×C8C22×D511yescharacteristic
237C22⋊Q8—104no—
238C22⋊Q8—202no—
239#121—24no—
240#121—42no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—101no—
243C2×C4⋊C4—201no—
244C2×C22⋊C4—41no—
245C2×C22⋊C4—201no—
246SD32—108no—
247C2×C16—52no—
248C2×C16—101no—
249C2×C16—101no—
250C2×C16—101no—
251C2×C16—101no—
252C2×C16—101no—
253#107—21no—
254#107—52no—
255#107—101no—
256#107C22⋊D512yes—
257#103—104no—
258#102—24no—
259C22×C5—22no—
260C22×C5—22no—
261C22×C5—22no—
262C22×C5—41no—
263C22×C5—41no—
264C22×C5—41no—
265C22×C5—41no—
266C22×C5—82no—
267C22×C5—82no—
268C22×C5—82no—
269C22×C5—161no—
270C22×C5—161no—
271C22×C5—161no—
272C22×C5—161no—
273C22×C5#44711yescharacteristic
274C22×C5#44711yescharacteristic
275C22×C5#46611yescharacteristic
276C22×C5C2×SD3211yescharacteristic
277C22×C5#50811yescharacteristic
278C22×C5#50911yescharacteristic
279C22×C5#51011yescharacteristic
280C4×C5—41no—
281C4×C5—82no—
282C4×C5#39211yescharacteristic
283C4×C5#44911yescharacteristic
284C4×C5#44911yescharacteristic
285C4×C5#46911yescharacteristic
286Dic5—82no—
287Dic5—82no—
288C24—41no—
289C24#68611yescharacteristic
290C2×Q8—102no—
291C2×Q8—201no—
292C2×Q8—201no—
293C2×Q8—201no—
294C2×Q8—201no—
295C2×Q8—201no—
296C2×D4—22no—
297C2×D4—44no—
298C2×D4—41no—
299C2×D4—41no—
300C2×D4—41no—
301C2×D4—41no—
302C2×D4—41no—
303C2×D4—82no—
304C2×D4—82no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—41no—
312C22×C4—201no—
313C22×C4—201no—
314C22×C4#68611yescharacteristic
315C22×C4C2×C22⋊D511yescharacteristic
316Q16—102no—
317Q16—102no—
318Q16—201no—
319Q16—201no—
320D8—22no—
321D8—22no—
322D8—41no—
323D8—41no—
324C2×C8—21no—
325C2×C8—21no—
326C2×C8—21no—
327C2×C8—41no—
328C2×C8—41no—
329C2×C8—41no—
330C2×C8—41no—
331C2×C8D4×D511yescharacteristic
332C2×C8D4×D511yescharacteristic
333C2×C8D4×D511yescharacteristic
334C2×C8#71111yescharacteristic
335C2×C8C2×C22⋊D511yescharacteristic
336C2×C8C2×C22⋊D511yescharacteristic
337C4⋊C4—22no—
338C4⋊C4—41no—
339C4⋊C4—102no—
340C4⋊C4—204no—
341C4⋊C4—201no—
342C22⋊C4—44no—
343C22⋊C4—204no—
344C16—102no—
345C16—201no—
346C2×C5—42no—
347C2×C5—162no—
348C2×C5#199911yescharacteristic
349C2×C5#218511yescharacteristic
350C2×C5#218611yescharacteristic
351C2×C5#218711yescharacteristic
352C2×C5#218911yescharacteristic
353C2×C5#221711yescharacteristic
354C2×C5#222011yescharacteristic
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—42no—
362C23—81no—
363C23—81no—
364C23—81no—
365C23—81no—
366C23—81no—
367C23—81no—
368C23#395912yescomplemented
369C23C2×#68611yescharacteristic
370Q8—202no—
371Q8—202no—
372Q8—401no—
373Q8—401no—
374D4—42no—
375D4—42no—
376D4—88no—
377D4—81no—
378D4—81no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—42no—
387C2×C4—81no—
388C2×C4—81no—
389C2×C4—202no—
390C2×C4—202no—
391C2×C4—401no—
392C2×C4—401no—
393C2×C4—401no—
394C2×C4—401no—
395C2×C4#407811yescharacteristic
396C2×C4#408311yescharacteristic
397C2×C4#408511yescharacteristic
398C2×C4#409511yescharacteristic
399C2×C4#409611yescharacteristic
400C2×C4#409911yescharacteristic
401C8—41no—
402C8#408311yescharacteristic
403C8#408411yescharacteristic
404C8#408511yescharacteristic
405C8#408611yescharacteristic
406C5#1330511yescharacteristic, complemented, Sylow
407C22—22no—
408C22—22no—
409C22—22no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—82no—
415C22—82no—
416C22—82no—
417C22—161no—
418C22—161no—
419C22—161no—
420C22—161no—
421C22#6532511yescharacteristic
422C22#6532711yescharacteristic
423C22#6543611yescharacteristic
424C22C2×#395911yescharacteristic
425C22#6548311yescharacteristic
426C22#6548411yescharacteristic
427C22#6550611yescharacteristic
428C4—41no—
429C4—82no—
430C4—402no—
431C4—402no—
432C4#6532611yescharacteristic
433C4#6532811yescharacteristic
434C4#6551211yescharacteristic
435C4#6552711yescharacteristic
436C2—42no—
437C2—162no—
438C2#1060186511yescharacteristic
439C2#1060186711yescharacteristic
440C2#1060186911yescharacteristic
441C2#1060187011yescharacteristic
442C2#1060247711yescharacteristic
443C2#1060282911yescharacteristic
444C2#1060287611yescharacteristic
subgroupG/H
centerC23C2×#686
commutator, cosocleC22×C5×C8C23
FrattiniC22×C8C22×D5
Fitting, prime radicalC2×C5×#466C2
socleC23×C5C2×D8
hypercenterC2×#466D5
hypocenterC5#13305
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
2. C22×#3959C2semidirect
3. C2×#65405C2semidirect
4. C2×#64782C2semidirect
5. C2×C22⋊#672C2semidirect
6. C2×#64712C2semidirect
7. #10598213C2semidirect
62. C2×Dic20D4semidirect
68. #3950D4semidirect
75. C2×#672D4semidirect
175. C23×C5SD32semidirect
368. C23#3959semidirect
406. C5#13305semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#4662
C22×#39592
C2×#654052
C2×#647822
C2×C22⋊#6722
C2×#647122
#105982132
#133055