Finite Group Databasebeta

← #12109821

Subgroups — #12109821

Order 1280.

966 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65122C211yesmaximal, characteristic
2D5×#384C211yesmaximal, characteristic
3#10605484C211yesmaximal, characteristic
4C5×#1947C211yesmaximal, characteristic, complemented
5#10601425C212yesmaximal
6#10601399C212yesmaximal, complemented
7#10601246C211yesmaximal, characteristic, complemented
8#10600360C211yesmaximal, characteristic, complemented
9#10600259C211yesmaximal, characteristic, complemented
10#10599667C212yesmaximal
11#10599640C212yesmaximal, complemented
12C2×D5×C4⋊C4—21no—
13C2×D5×C4⋊C4—21no—
14C2×D5×C4⋊C4C2212yes—
15C2×#4018—21no—
16C2×C42×D5C2211yescharacteristic
17C2×C5×#107C2212yes—
18C2×C5×C4⋊C8C2211yescharacteristic
19C5×#384C2211yescharacteristic
20C4×C5×C4⋊C4C2211yescharacteristic
21C2×#3952C2212yes—
22C2×#3950C2212yes—
23C2×C8×Dic5C2212yes—
24#65276C2211yescharacteristic
25#65276C2211yescharacteristic
26#65265—21no—
27#65265—21no—
28#65265C2212yes—
29#65265C2211yescharacteristic
30#65265C2211yescharacteristic
31C2×#3939C2212yes—
32C2×#3939C2212yes—
33#65224C2211yescharacteristic
34C4×C4⋊Dic5C2211yescharacteristic
35C4×#683—21no—
36C2×C4⋊#168C2211yescharacteristic
37#65122C418yescomplemented
38#64956—21no—
39#64939—21no—
40C5×#340C2212yes—
41#64771C2212yes—
42#64749C2212yes—
43#64749C2212yes—
44#21982—51nomaximal, Sylow
45C22×C4×D5—22no—
46C22×C4×D5D411yescharacteristic
47C22×C4×D5D411yescharacteristic
48C22×C4×D5C2311yescharacteristic
49C22×C5×C8C2312yes—
50C2×C5×C4⋊C4—21no—
51C2×C5×C4⋊C4—21no—
52C2×C5×C4⋊C4C2311yescharacteristic
53C2×C5×C4⋊C4C2311yescharacteristic
54C2×C5×C4⋊C4C2312yes—
55C2×C42×C5—21no—
56C2×C42×C5C2311yescharacteristic
57C2×#685—21no—
58C2×#685—21no—
59C2×C4⋊Dic5—21no—
60C2×C4⋊Dic5—21no—
61C2×C4⋊Dic5C2311yescharacteristic
62C2×C4⋊Dic5C2312yes—
63C2×C4⋊Dic5C2311yescharacteristic
64C2×#683—21no—
65C2×#683—21no—
66C2×#683—22no—
67C2×#683—22no—
68C2×#683—22no—
69C2×#683—21no—
70C2×#683—21no—
71C2×C4×Dic5—21no—
72C2×C4×Dic5D411yescharacteristic
73C2×C4×Dic5D411yescharacteristic
74C2×C4×Dic5C2311yescharacteristic
75C22×#168C2312yes—
76D5×C4⋊C4—42no—
77D5×C4⋊C4—42no—
78D5×C4⋊C4—44no—
79D5×C4⋊C4—44no—
80#4018—44no—
81C42×D5C2×C414yes—
82C42×D5Q814yes—
83C5×#107—42no—
84C5×C4⋊C8C2×C414yescomplemented
85C5×#95—21no—
86#3963—21no—
87#3963—21no—
88#3963—21no—
89#3952C2×C418yes—
90#3950—42no—
91C8×Dic5C2×C418yescomplemented
92#3939—42no—
93#3939—42no—
94C4⋊#168C2×C414yescomplemented
95C2×#431—51no—
96#2285—51no—
97C2×#384—51no—
98#1947—51no—
99#1947—51no—
100#1947—51no—
101#1947D511yescharacteristic, complemented
102#1852—52no—
103#1852—52no—
104#1845—52no—
105#1834—52no—
106C23×D5C2×D411yescharacteristic
107C22×C4×C5—21no—
108C22×C4×C5—21no—
109C22×C4×C5—22no—
110C22×C4×C5C2×D411yescharacteristic
111C22×C4×C5C2×D411yescharacteristic
112C22×C4×C5C2411yescharacteristic
113C22×Dic5—22no—
114C22×Dic5—21no—
115C22×Dic5—21no—
116C22×Dic5C2×D411yescharacteristic
117C22×Dic5C2×D411yescharacteristic
118C22×Dic5C2×D411yescharacteristic
119C2×C4×D5—21no—
120C2×C4×D5—21no—
121C2×C4×D5—21no—
122C2×C4×D5—21no—
123C2×C4×D5—22no—
124C2×C4×D5—22no—
125C2×C4×D5—44no—
126C2×C4×D5—44no—
127C2×C4×D5—44no—
128C2×C4×D5C4⋊C414yes—
129C2×C4×D5C4⋊C414yes—
130C2×C4×D5D814yes—
131C2×C4×D5Q1614yes—
132C2×C4×D5C22×C412yes—
133C2×C4×D5C2×Q812yes—
134C2×C5×C8—22no—
135C2×C5×C8—22no—
136C2×C5×C8C22×C414yes—
137C5×C4⋊C4—21no—
138C5×C4⋊C4—22no—
139C5×C4⋊C4—21no—
140C5×C4⋊C4—22no—
141C5×C4⋊C4—21no—
142C5×C4⋊C4—21no—
143C5×C4⋊C4—42no—
144C5×C4⋊C4—42no—
145C42×C5—42no—
146C42×C5C22×C412yes—
147C42×C5C2×Q812yes—
148#685—42no—
149#685—42no—
150C4⋊Dic5—21no—
151C4⋊Dic5—22no—
152C4⋊Dic5—21no—
153C4⋊Dic5—22no—
154C4⋊Dic5—21no—
155C4⋊Dic5—21no—
156C4⋊Dic5—42no—
157C4⋊Dic5—42no—
158#683—44no—
159#683—42no—
160#683—42no—
161#683—44no—
162#683—44no—
163#683—42no—
164#683—42no—
165C4×Dic5—42no—
166C4×Dic5C4⋊C414yes—
167C4×Dic5C4⋊C414yes—
168C4×Dic5C22×C412yes—
169C4×Dic5C2×Q812yes—
170C2×#168—22no—
171C2×#168—22no—
172C2×#168C22×C414yes—
173C2×#117—101no—
174C22×C4⋊C4—52no—
175C22×C4⋊C4—101no—
176C22×C4⋊C4—101no—
177C22×C42—51no—
178#431—58no—
179C2×#107—52no—
180C2×#107—52no—
181C2×#107—52no—
182C2×#107C2×D512yes—
183C2×C4⋊C8—51no—
184C2×C4⋊C8C2×D511yescharacteristic
185C2×C22⋊C8—52no—
186C2×C4×C8—52no—
187#384—51no—
188#384—52no—
189#384—51no—
190#384—51no—
191#384—101no—
192#384—101no—
193#384C2×D511yescharacteristic
194#382—101no—
195#380—51no—
196#380—51no—
197#380—101no—
198C4×C4⋊C4—51no—
199C4×C4⋊C4—101no—
200C4×C4⋊C4C2×D511yescharacteristic
201#340—52no—
202#340—52no—
203#340—52no—
204#340C2×D512yes—
205C23×C5C22×D411yescharacteristic
206C22×D5—21no—
207C22×D5—21no—
208C22×D5—21no—
209C22×D5—21no—
210C22×D5C2×C4⋊C412yes—
211C22×D5C2×D812yes—
212C22×D5C2×Q1612yes—
213C2×C4×C5—21no—
214C2×C4×C5—21no—
215C2×C4×C5—42no—
216C2×C4×C5—41no—
217C2×C4×C5—41no—
218C2×C4×C5—41no—
219C2×C4×C5—41no—
220C2×C4×C5—42no—
221C2×C4×C5—42no—
222C2×C4×C5—41no—
223C2×C4×C5—41no—
224C2×C4×C5C2×C4⋊C412yes—
225C2×C4×C5C2×C4⋊C412yes—
226C2×C4×C5C2×D812yes—
227C2×C4×C5C2×Q1612yes—
228C2×C4×C5C23×C411yescharacteristic
229C2×C4×C5C22×Q811yescharacteristic
230C2×C4×C5H(5,𝔽2)11yescharacteristic
231C2×C4×C5H(5,𝔽2)11yescharacteristic
232C2×C4×C52−1+411yescharacteristic
233C2×C4×C52−1+411yescharacteristic
234C2×Dic5—21no—
235C2×Dic5—21no—
236C2×Dic5—42no—
237C2×Dic5—41no—
238C2×Dic5—41no—
239C2×Dic5—41no—
240C2×Dic5—41no—
241C2×Dic5—42no—
242C2×Dic5—42no—
243C2×Dic5—41no—
244C2×Dic5—41no—
245C2×Dic5C2×C4⋊C412yes—
246C2×Dic5C2×C4⋊C412yes—
247C2×Dic5C2×C4⋊C412yes—
248C2×Dic5C2×D812yes—
249C2×Dic5C2×Q1612yes—
250C2×Dic5AGL(1,ℤ/8)12yes—
251C2×Dic5#13712yes—
252C4×D5—22no—
253C4×D5—22no—
254C4×D5—22no—
255C4×D5—22no—
256C4×D5—28no—
257C4×D5—88no—
258C4×D5#107116yescomplemented
259C5×C8—24no—
260#168—24no—
261C23×C4—51no—
262C23×C4—51no—
263C23×C4—51no—
264C23×C4—102no—
265C22×C8—52no—
266C22×C8C22×D512yes—
267#117—204no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—52no—
271C2×C4⋊C4—51no—
272C2×C4⋊C4—51no—
273C2×C4⋊C4—102no—
274C2×C4⋊C4—102no—
275C2×C4⋊C4—102no—
276C2×C4⋊C4—101no—
277C2×C4⋊C4—101no—
278C2×C4⋊C4—101no—
279C2×C4⋊C4—101no—
280C2×C4⋊C4—101no—
281C2×C4⋊C4—101no—
282C2×C4⋊C4—202no—
283C2×C4⋊C4—202no—
284C2×C4⋊C4—204no—
285C2×C4⋊C4—204no—
286C2×C4⋊C4C22×D512yes—
287C2×C4⋊C4C22×D511yescharacteristic
288C2×C4⋊C4C22×D511yescharacteristic
289C2×C22⋊C4—101no—
290C2×C22⋊C4—101no—
291C2×C42—21no—
292C2×C42—51no—
293C2×C42—51no—
294C2×C42—51no—
295C2×C42—54no—
296C2×C42—54no—
297C2×C42—101no—
298C2×C42C22×D511yescharacteristic
299#107—42no—
300#107—202no—
301#107—202no—
302#107—202no—
303C4⋊C8—54no—
304C4⋊C8C4×D514yescomplemented
305C22⋊C8—58no—
306C4×C8—58no—
307#95—21no—
308#95—101no—
309#95—101no—
310#95—101no—
311C22×C5C22×C4⋊C411yescharacteristic
312C22×C5#53511yescharacteristic
313C22×C5#53611yescharacteristic
314C22×C5C22×D811yescharacteristic
315C22×C5C22×Q1611yescharacteristic
316C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
317C22×C5C2×#13711yescharacteristic
318C2×D5—22no—
319C2×D5—22no—
320C2×D5—22no—
321C2×D5—22no—
322C2×D5—22no—
323C2×D5—22no—
324C2×D5C2×#10714yes—
325C4×C5—22no—
326C4×C5—82no—
327C4×C5—81no—
328C4×C5—81no—
329C4×C5C2×#10714yes—
330C4×C5#52011yescharacteristic
331C4×C5#52011yescharacteristic
332C4×C5#54411yescharacteristic
333C4×C5#54411yescharacteristic
334Dic5—22no—
335Dic5—82no—
336Dic5—81no—
337Dic5—81no—
338Dic5C2×#10714yes—
339Dic5#42814yes—
340C24—51no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—22no—
344C22×C4—51no—
345C22×C4—51no—
346C22×C4—54no—
347C22×C4—54no—
348C22×C4—54no—
349C22×C4—51no—
350C22×C4—52no—
351C22×C4—52no—
352C22×C4—54no—
353C22×C4—102no—
354C22×C4—102no—
355C22×C4—101no—
356C22×C4—101no—
357C22×C4—101no—
358C22×C4—101no—
359C22×C4—101no—
360C22×C4—101no—
361C22×C4—102no—
362C22×C4—204no—
363C22×C4—204no—
364C22×C4—204no—
365C22×C4D4×D511yescharacteristic
366C22×C4D4×D511yescharacteristic
367C22×C4C23×D511yescharacteristic
368C2×C8—22no—
369C2×C8—22no—
370C2×C8—54no—
371C2×C8—102no—
372C2×C8—102no—
373C2×C8C2×C4×D514yes—
374C4⋊C4—21no—
375C4⋊C4—22no—
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—22no—
379C4⋊C4—21no—
380C4⋊C4—42no—
381C4⋊C4—42no—
382C4⋊C4—101no—
383C4⋊C4—102no—
384C4⋊C4—101no—
385C4⋊C4—101no—
386C4⋊C4—102no—
387C4⋊C4—101no—
388C4⋊C4—202no—
389C4⋊C4—204no—
390C4⋊C4—204no—
391C4⋊C4—202no—
392C4⋊C4—202no—
393C4⋊C4—202no—
394C4⋊C4—202no—
395C4⋊C4—204no—
396C4⋊C4—202no—
397C22⋊C4—202no—
398C22⋊C4—202no—
399C42—42no—
400C42—52no—
401C42—52no—
402C42—54no—
403C42—54no—
404C42—202no—
405C42C2×C4×D512yes—
406C42Q8×D512yes—
407C2×C5#231711yescharacteristic
408C2×C5C22×#10711yescharacteristic
409C2×C5C2×#42811yescharacteristic
410C2×C5#320511yescharacteristic
411C2×C5#320911yescharacteristic
412C2×C5#322611yescharacteristic
413C2×C5#323011yescharacteristic
414D5—24no—
415C23—52no—
416C23—52no—
417C23—52no—
418C23—101no—
419C23—101no—
420C23—101no—
421C23—101no—
422C23C2×D4×D511yescharacteristic
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—42no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—52no—
435C2×C4—52no—
436C2×C4—52no—
437C2×C4—52no—
438C2×C4—52no—
439C2×C4—52no—
440C2×C4—516no—
441C2×C4—52no—
442C2×C4—108no—
443C2×C4—101no—
444C2×C4—101no—
445C2×C4—102no—
446C2×C4—102no—
447C2×C4—102no—
448C2×C4—102no—
449C2×C4—201no—
450C2×C4—201no—
451C2×C4—202no—
452C2×C4—202no—
453C2×C4—201no—
454C2×C4—201no—
455C2×C4—202no—
456C2×C4—201no—
457C2×C4—201no—
458C2×C4—408no—
459C2×C4D5×C4⋊C412yes—
460C2×C4D5×C4⋊C412yes—
461C2×C4D5×D812yes—
462C2×C4D5×Q1612yes—
463C2×C4C22×C4×D511yescharacteristic
464C2×C4#414411yescharacteristic
465C2×C4C2×Q8×D511yescharacteristic
466C2×C4#414711yescharacteristic
467C2×C4#414911yescharacteristic
468C2×C4#415011yescharacteristic
469C8—24no—
470C8—104no—
471C5#2198211yescharacteristic, complemented, Sylow
472C22—54no—
473C22—102no—
474C22—102no—
475C22—102no—
476C22—102no—
477C22—102no—
478C22—102no—
479C22C2×D5×C4⋊C411yescharacteristic
480C22#6594111yescharacteristic
481C22#6596211yescharacteristic
482C22C2×D5×D811yescharacteristic
483C22C2×D5×Q1611yescharacteristic
484C22D5×AGL(1,ℤ/8)11yescharacteristic
485C22D5×#13711yescharacteristic
486C4—22no—
487C4—54no—
488C4—54no—
489C4—82no—
490C4—81no—
491C4—81no—
492C4—102no—
493C4—402no—
494C4—401no—
495C4—401no—
496C4D5×#10714yes—
497C4#6588011yescharacteristic
498C4#6590811yescharacteristic
499C4#6602311yescharacteristic
500C4#6606311yescharacteristic
501C2—104no—
502C2#1060769911yescharacteristic
503C2C2×D5×#10711yescharacteristic
504C2D5×#42811yescharacteristic
505C2#1061206711yescharacteristic
506C2#1061221111yescharacteristic
507C2#1061270011yescharacteristic
508C2#1061284311yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC5×#1947C2
socleC23×C5C22×D4
prime radicalC23×D5C2×D4
cosocleC22×C4×C5C24
hypercenter#1947D5
hypocenterC5#21982
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1947

Complements

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

NH ≅ G/Ntype
4. C5×#1947C2semidirect
6. #10601399C2semidirect
7. #10601246C2semidirect
8. #10600360C2semidirect
9. #10600259C2semidirect
11. #10599640C2semidirect
37. #65122C4semidirect
84. C5×C4⋊C8C2×C4semidirect
91. C8×Dic5C2×C4semidirect
94. C4⋊#168C2×C4semidirect
101. #1947D5semidirect
258. C4×D5#107semidirect
304. C4⋊C8C4×D5semidirect
471. C5#21982semidirect

Maximal subgroups

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

subgroupindex
C2×#651222
D5×#3842
#106054842
C5×#19472
#106014252
#106013992
#106012462
#106003602
#106002592
#105996672
#105996402
#219825