Finite Group Databasebeta

← #12109678

Subgroups — #12109678

Order 1280.

906 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×C4⋊C8C211yesmaximal, characteristic
2#10606049C211yesmaximal, characteristic
3#10605484C211yesmaximal, characteristic
4C5×#1947C211yesmaximal, characteristic, complemented
5#10601423C212yesmaximal
6#10601408C212yesmaximal, complemented
7#10601246C211yesmaximal, characteristic, complemented
8#10600360C211yesmaximal, characteristic, complemented
9#10600259C211yesmaximal, characteristic, complemented
10#10599662C212yesmaximal
11#10599588C212yesmaximal, complemented
12C22×C8×D5C2212yes—
13C2×#4038—21no—
14C2×#4018—21no—
15C2×C42×D5C2211yescharacteristic
16C2×C5×#107C2212yes—
17C2×C5×C4⋊C8C2211yescharacteristic
18C5×#384C2211yescharacteristic
19C4×C5×C4⋊C4C2211yescharacteristic
20C2×#3950C2212yes—
21C2×#3946C2212yes—
22#65276—21no—
23#65276C2211yescharacteristic
24#65276C2211yescharacteristic
25#65276C2212yes—
26#65266—21no—
27#65265C2211yescharacteristic
28#65265C2211yescharacteristic
29C4⋊C4×Dic5—21no—
30C4⋊C4×Dic5C2212yes—
31C2×#3939C2212yes—
32C2×#3939C2212yes—
33#65224C2211yescharacteristic
34C4×C4⋊Dic5C2211yescharacteristic
35C4×#683—21no—
36C2×C4⋊#168C2211yescharacteristic
37D5×C4⋊C8C418yescomplemented
38#64956—21no—
39#64939—21no—
40C5×#340C2212yes—
41#64771C2212yes—
42#64749C2212yes—
43#64749C2212yes—
44#21961—51nomaximal, Sylow
45C22×C4×D5D411yescharacteristic
46C22×C4×D5D411yescharacteristic
47C22×C4×D5C2311yescharacteristic
48C22×C5×C8C2312yes—
49C2×C5×C4⋊C4—21no—
50C2×C5×C4⋊C4—21no—
51C2×C5×C4⋊C4C2311yescharacteristic
52C2×C5×C4⋊C4C2311yescharacteristic
53C2×C5×C4⋊C4C2312yes—
54C2×C42×C5—21no—
55C2×C42×C5C2311yescharacteristic
56C2×#685—21no—
57C2×#685—21no—
58C2×#685—22no—
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—21no—
67C2×#683—21no—
68C2×C4×Dic5—21no—
69C2×C4×Dic5—22no—
70C2×C4×Dic5D411yescharacteristic
71C2×C4×Dic5D411yescharacteristic
72C2×C4×Dic5C2311yescharacteristic
73C22×#168C2312yes—
74C2×C8×D5—42no—
75C2×C8×D5—42no—
76C2×C8×D5C2×C418yes—
77#4038—44no—
78#4018—44no—
79C42×D5C2×C414yes—
80C42×D5Q814yes—
81C5×#107—42no—
82C5×C4⋊C8C2×C414yes—
83C5×#95—21no—
84#3963—21no—
85#3963—21no—
86#3963—21no—
87#3963—22no—
88#3963—22no—
89#3950—42no—
90#3946C2×C418yes—
91#3939—42no—
92#3939—42no—
93C4⋊#168C2×C414yes—
94C22×C4⋊C8—51no—
95#2285—51no—
96#2285—51no—
97#1947—52no—
98#1947—51no—
99#1947—51no—
100#1947—51no—
101#1947—52no—
102#1947D511yescharacteristic, complemented
103#1808—52no—
104#1808—52no—
105C23×D5C2×D411yescharacteristic
106C22×C4×C5—21no—
107C22×C4×C5—21no—
108C22×C4×C5—22no—
109C22×C4×C5C2×D411yescharacteristic
110C22×C4×C5C2×D411yescharacteristic
111C22×C4×C5C2411yescharacteristic
112C22×Dic5—21no—
113C22×Dic5—21no—
114C22×Dic5—22no—
115C22×Dic5C2×D411yescharacteristic
116C22×Dic5C2×D411yescharacteristic
117C22×Dic5C2×D411yescharacteristic
118C2×C4×D5—21no—
119C2×C4×D5—21no—
120C2×C4×D5—21no—
121C2×C4×D5—21no—
122C2×C4×D5—41no—
123C2×C4×D5—41no—
124C2×C4×D5C4⋊C414yes—
125C2×C4×D5C4⋊C414yes—
126C2×C4×D5D814yes—
127C2×C4×D5Q1614yes—
128C2×C4×D5C22×C412yes—
129C2×C4×D5C2×Q812yes—
130C2×C5×C8—22no—
131C2×C5×C8—22no—
132C2×C5×C8C22×C414yes—
133C5×C4⋊C4—21no—
134C5×C4⋊C4—22no—
135C5×C4⋊C4—21no—
136C5×C4⋊C4—21no—
137C5×C4⋊C4—21no—
138C5×C4⋊C4—22no—
139C5×C4⋊C4—42no—
140C5×C4⋊C4—42no—
141C42×C5—42no—
142C42×C5C22×C412yes—
143C42×C5C2×Q812yes—
144#685—42no—
145#685—42no—
146#685—44no—
147C4⋊Dic5—21no—
148C4⋊Dic5—22no—
149C4⋊Dic5—21no—
150C4⋊Dic5—22no—
151C4⋊Dic5—21no—
152C4⋊Dic5—21no—
153C4⋊Dic5—42no—
154C4⋊Dic5—42no—
155#683—42no—
156#683—42no—
157#683—42no—
158#683—42no—
159C4×Dic5—42no—
160C4×Dic5—44no—
161C4×Dic5C4⋊C414yes—
162C4×Dic5C4⋊C414yes—
163C4×Dic5C22×C412yes—
164C4×Dic5C2×Q812yes—
165C2×#168—22no—
166C2×#168—22no—
167C2×#168C22×C414yes—
168C8×D5—48no—
169C23×C8—52no—
170C2×#117—101no—
171C2×#117—101no—
172C22×C42—51no—
173C2×#107—52no—
174C2×#107—52no—
175C2×#107—52no—
176C2×#107C2×D512yes—
177C2×C4⋊C8—52no—
178C2×C4⋊C8—51no—
179C2×C4⋊C8—58no—
180C2×C4⋊C8C2×D511yescharacteristic
181#384—51no—
182#384—51no—
183#384—51no—
184#384C2×D511yescharacteristic
185#382—101no—
186#382—101no—
187#380—51no—
188#380—52no—
189#380—51no—
190#380—101no—
191#380—101no—
192C4×C4⋊C4—52no—
193C4×C4⋊C4—51no—
194C4×C4⋊C4—101no—
195C4×C4⋊C4—101no—
196C4×C4⋊C4C2×D511yescharacteristic
197#340—52no—
198#340—52no—
199#340—52no—
200#340C2×D512yes—
201C23×C5C22×D411yescharacteristic
202C22×D5—21no—
203C22×D5—21no—
204C22×D5—21no—
205C22×D5—21no—
206C22×D5C2×C4⋊C412yes—
207C22×D5C2×D812yes—
208C22×D5C2×Q1612yes—
209C2×C4×C5—21no—
210C2×C4×C5—21no—
211C2×C4×C5—42no—
212C2×C4×C5—41no—
213C2×C4×C5—41no—
214C2×C4×C5—42no—
215C2×C4×C5—41no—
216C2×C4×C5—41no—
217C2×C4×C5—41no—
218C2×C4×C5—41no—
219C2×C4×C5—42no—
220C2×C4×C5C2×C4⋊C412yes—
221C2×C4×C5C2×C4⋊C412yes—
222C2×C4×C5C2×D812yes—
223C2×C4×C5C2×Q1612yes—
224C2×C4×C5C23×C411yescharacteristic
225C2×C4×C5C22×Q811yescharacteristic
226C2×C4×C5H(5,𝔽2)11yescharacteristic
227C2×C4×C5H(5,𝔽2)11yescharacteristic
228C2×C4×C52−1+411yescharacteristic
229C2×C4×C52−1+411yescharacteristic
230C2×Dic5—21no—
231C2×Dic5—21no—
232C2×Dic5—21no—
233C2×Dic5—21no—
234C2×Dic5—41no—
235C2×Dic5—42no—
236C2×Dic5—41no—
237C2×Dic5—41no—
238C2×Dic5—41no—
239C2×Dic5—42no—
240C2×Dic5—41no—
241C2×Dic5—41no—
242C2×Dic5—42no—
243C2×Dic5C2×C4⋊C412yes—
244C2×Dic5C2×C4⋊C412yes—
245C2×Dic5C2×C4⋊C412yes—
246C2×Dic5C2×D812yes—
247C2×Dic5C2×Q1612yes—
248C4×D5—22no—
249C4×D5—22no—
250C4×D5—22no—
251C4×D5—22no—
252C4×D5—44no—
253C4×D5#107116yescomplemented
254C5×C8—24no—
255#168—24no—
256C23×C4—51no—
257C23×C4—51no—
258C23×C4—51no—
259C22×C8—52no—
260C22×C8—58no—
261C22×C8—202no—
262C22×C8—202no—
263C22×C8C22×D512yes—
264#117—204no—
265#117—204no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—51no—
269C2×C4⋊C4—52no—
270C2×C4⋊C4—51no—
271C2×C4⋊C4—101no—
272C2×C4⋊C4—101no—
273C2×C4⋊C4—101no—
274C2×C4⋊C4—101no—
275C2×C4⋊C4—101no—
276C2×C4⋊C4—101no—
277C2×C4⋊C4C22×D511yescharacteristic
278C2×C4⋊C4C22×D512yes—
279C2×C4⋊C4C22×D511yescharacteristic
280C2×C22⋊C4—101no—
281C2×C22⋊C4—101no—
282C2×C22⋊C4—102no—
283C2×C42—21no—
284C2×C42—51no—
285C2×C42—51no—
286C2×C42—51no—
287C2×C42—54no—
288C2×C42—54no—
289C2×C42—102no—
290C2×C42—101no—
291C2×C42C22×D511yescharacteristic
292#107—42no—
293#107—202no—
294#107—202no—
295#107—202no—
296C4⋊C8—58no—
297C4⋊C8—54no—
298C4⋊C8C4×D514yes—
299#95—21no—
300#95—102no—
301#95—101no—
302#95—101no—
303#95—102no—
304#95—101no—
305C22×C5C22×C4⋊C411yescharacteristic
306C22×C5#53711yescharacteristic
307C22×C5#53711yescharacteristic
308C22×C5C22×D811yescharacteristic
309C22×C5C22×Q1611yescharacteristic
310C22×C5#57511yescharacteristic
311C22×C5#57511yescharacteristic
312C2×D5—22no—
313C2×D5—22no—
314C2×D5—22no—
315C2×D5—22no—
316C2×D5—22no—
317C2×D5—22no—
318C2×D5C2×#10714yes—
319C4×C5—22no—
320C4×C5—82no—
321C4×C5—81no—
322C4×C5—81no—
323C4×C5C2×#10714yes—
324C4×C5#51811yescharacteristic
325C4×C5#51911yescharacteristic
326C4×C5#54411yescharacteristic
327C4×C5#54411yescharacteristic
328Dic5—22no—
329Dic5—22no—
330Dic5—81no—
331Dic5—81no—
332Dic5—82no—
333Dic5C2×#10714yes—
334C24—51no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—22no—
338C22×C4—51no—
339C22×C4—54no—
340C22×C4—54no—
341C22×C4—54no—
342C22×C4—51no—
343C22×C4—51no—
344C22×C4—52no—
345C22×C4—52no—
346C22×C4—54no—
347C22×C4—101no—
348C22×C4—101no—
349C22×C4—101no—
350C22×C4—101no—
351C22×C4—101no—
352C22×C4—102no—
353C22×C4—101no—
354C22×C4—201no—
355C22×C4—201no—
356C22×C4D4×D511yescharacteristic
357C22×C4D4×D511yescharacteristic
358C22×C4C23×D511yescharacteristic
359C2×C8—22no—
360C2×C8—22no—
361C2×C8—54no—
362C2×C8—102no—
363C2×C8—102no—
364C2×C8—208no—
365C2×C8C2×C4×D514yes—
366C4⋊C4—21no—
367C4⋊C4—22no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—22no—
372C4⋊C4—42no—
373C4⋊C4—42no—
374C4⋊C4—101no—
375C4⋊C4—102no—
376C4⋊C4—101no—
377C4⋊C4—102no—
378C4⋊C4—101no—
379C4⋊C4—101no—
380C4⋊C4—202no—
381C4⋊C4—202no—
382C4⋊C4—202no—
383C4⋊C4—202no—
384C4⋊C4—202no—
385C4⋊C4—202no—
386C22⋊C4—202no—
387C22⋊C4—202no—
388C22⋊C4—204no—
389C42—42no—
390C42—52no—
391C42—52no—
392C42—54no—
393C42—54no—
394C42—204no—
395C42—202no—
396C42C2×C4×D512yes—
397C42Q8×D512yes—
398C2×C5#231611yescharacteristic
399C2×C5C22×#10711yescharacteristic
400C2×C5#291111yescharacteristic
401C2×C5#324511yescharacteristic
402C2×C5#324511yescharacteristic
403C2×C5#324911yescharacteristic
404C2×C5#324911yescharacteristic
405D5—24no—
406C23—52no—
407C23—52no—
408C23—52no—
409C23—101no—
410C23—101no—
411C23—101no—
412C23—101no—
413C23C2×D4×D511yescharacteristic
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—42no—
424C2×C4—41no—
425C2×C4—52no—
426C2×C4—52no—
427C2×C4—52no—
428C2×C4—516no—
429C2×C4—52no—
430C2×C4—52no—
431C2×C4—101no—
432C2×C4—101no—
433C2×C4—101no—
434C2×C4—101no—
435C2×C4—102no—
436C2×C4—102no—
437C2×C4—102no—
438C2×C4—102no—
439C2×C4—204no—
440C2×C4—201no—
441C2×C4—202no—
442C2×C4—201no—
443C2×C4—201no—
444C2×C4—202no—
445C2×C4—201no—
446C2×C4—201no—
447C2×C4—202no—
448C2×C4—201no—
449C2×C4D5×C4⋊C412yes—
450C2×C4D5×C4⋊C412yes—
451C2×C4D5×D812yes—
452C2×C4D5×Q1612yes—
453C2×C4C22×C4×D511yescharacteristic
454C2×C4#414411yescharacteristic
455C2×C4C2×Q8×D511yescharacteristic
456C2×C4#414711yescharacteristic
457C2×C4#414911yescharacteristic
458C2×C4#415011yescharacteristic
459C8—24no—
460C8—104no—
461C5#2196111yescharacteristic, complemented, Sylow
462C22—54no—
463C22—102no—
464C22—102no—
465C22—102no—
466C22—102no—
467C22—102no—
468C22—102no—
469C22C2×D5×C4⋊C411yescharacteristic
470C22#6594211yescharacteristic
471C22#6596311yescharacteristic
472C22C2×D5×D811yescharacteristic
473C22C2×D5×Q1611yescharacteristic
474C22#6610711yescharacteristic
475C22#6611111yescharacteristic
476C4—22no—
477C4—54no—
478C4—81no—
479C4—82no—
480C4—81no—
481C4—102no—
482C4—102no—
483C4—401no—
484C4—402no—
485C4—401no—
486C4D5×#10714yes—
487C4#6587911yescharacteristic
488C4#6590611yescharacteristic
489C4#6602311yescharacteristic
490C4#6606311yescharacteristic
491C2—104no—
492C2#1060792611yescharacteristic
493C2C2×D5×#10711yescharacteristic
494C2#1061093911yescharacteristic
495C2#1061207311yescharacteristic
496C2#1061221711yescharacteristic
497C2#1061270611yescharacteristic
498C2#1061284911yescharacteristic
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#21961
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. #10601408C2semidirect
7. #10601246C2semidirect
8. #10600360C2semidirect
9. #10600259C2semidirect
11. #10599588C2semidirect
37. D5×C4⋊C8C4semidirect
102. #1947D5semidirect
253. C4×D5#107semidirect
461. C5#21961semidirect

Maximal subgroups

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

subgroupindex
C2×D5×C4⋊C82
#106060492
#106054842
C5×#19472
#106014232
#106014082
#106012462
#106003602
#106002592
#105996622
#105995882
#219615