Finite Group Databasebeta

← C4×#66045 #12261990

Subgroups — C4×#66045 #12261990

Order 1280.

2568 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66045C211yesmaximal, characteristic
2C4×C5×#126C211yesmaximal, characteristic, complemented
3#10614807C211yesmaximal, characteristic, complemented
4#10607571C213yesmaximal, complemented
5#10607221C213yesmaximal, complemented
6#10607044C213yesmaximal, complemented
7#10607043C213yesmaximal, complemented
8#10606030C211yesmaximal, characteristic, complemented
9#10606029C211yesmaximal, characteristic, complemented
10C4×#4040C213yesmaximal, complemented
11C4×#4041C213yesmaximal, complemented
12C4×#4030C213yesmaximal, complemented
13C4×#4028C213yesmaximal, complemented
14C4×#4020C211yesmaximal, characteristic, complemented
15C4×#4022C211yesmaximal, characteristic, complemented
16C23×C4×D5C2211yescharacteristic
17C2×C5×#126C2211yescharacteristic
18C2×C4×C22⋊D5C2213yes—
19#66045C4116yesdirect product factor
20C2×#4041C2213yes—
21C2×#4040C2213yes—
22C2×#4030C2213yes—
23C2×#4028C2213yes—
24C2×#4022C2211yescharacteristic
25C2×#4020C2211yescharacteristic
26C2×C4×D20C2213yes—
27C2×C4×D20C2213yes—
28C2×C4×D20C2213yescomplemented
29C2×C42×D5C2213yescomplemented
30C5×#388C2213yes—
31C5×#387C2213yescomplemented
32C5×#383C2211yescharacteristic, complemented
33C4×C5×C4⋊C4C2213yescomplemented
34C4×C5×C22⋊C4C2213yes—
35C43×C5C2211yescharacteristic, complemented
36#65279C2213yes—
37#65278C2213yescomplemented
38#65277C2213yes—
39#65276C2213yescomplemented
40#65274C2213yescomplemented
41#65270C2213yescomplemented
42#65247C2213yes—
43#65246C2213yes—
44#65245C2213yes—
45#65244C2213yes—
46#65240C2213yes—
47#65239C2213yes—
48#65229C2213yes—
49#65228C2213yes—
50#65228C2213yescomplemented
51C4×#685C2213yes—
52C4×#685C2213yes—
53C4×#685C2213yescomplemented
54#65226C2211yescharacteristic, complemented
55#65224C2211yescharacteristic, complemented
56#65222C2213yescomplemented
57C4×#683C2213yescomplemented
58#64959C2213yes—
59#64959C2213yescomplemented
60#64958C2213yes—
61#64958C2213yescomplemented
62#64957C2213yes—
63#64957C2213yes—
64#64956C2213yescomplemented
65#64954C2213yes—
66#64954C2213yes—
67#64954C2213yes—
68#64954C2213yes—
69#64954C2213yescomplemented
70#64954C2213yescomplemented
71#64953C2213yescomplemented
72#64944C2213yescomplemented
73#64936C2213yescomplemented
74C4×#560—51nomaximal, Sylow
75C24×D5C2311yescharacteristic
76C23×C4×C5C2311yescharacteristic
77C22×C22⋊D5C2313yes—
78C23×Dic5C2311yescharacteristic
79C22×D20C2313yes—
80C22×D20C2313yes—
81C22×D20C2313yes—
82C22×C4×D5—46no—
83C22×C4×D5C2313yes—
84C22×C4×D5C2311yescharacteristic
85C22×C4×D5C2311yescharacteristic
86C22×C4×D5C2313yes—
87C22×C4×D5C2311yescharacteristic
88C22×C4×D5C2311yescharacteristic
89C22×C4×D5C2313yes—
90C5×#126C2×C418yescomplemented
91C2×C5×C4⋊C4C2313yes—
92C2×C5×C4⋊C4C2313yes—
93C2×C5×C22⋊C4C2313yes—
94C2×C5×C22⋊C4C2313yes—
95C2×C42×C5C2313yes—
96C2×C42×C5C2313yes—
97C2×C42×C5C2313yes—
98C2×C42×C5C2311yescharacteristic
99C2×C22⋊Dic5C2313yes—
100C4×C22⋊D5—46no—
101C2×#685C2313yes—
102C2×#685C2313yes—
103C2×#685C2313yes—
104C2×#685C2313yes—
105C2×#685C2313yes—
106C2×#685C2313yes—
107C2×#685C2313yes—
108C2×#685C2313yes—
109C2×#685C2313yes—
110C2×#685C2313yes—
111C2×#685C2313yes—
112C2×#685C2313yes—
113C2×#685C2313yes—
114C2×C4⋊Dic5C2313yes—
115C2×C4⋊Dic5C2313yes—
116C2×C4⋊Dic5C2313yes—
117C2×#683C2313yes—
118C2×#683C2313yes—
119C2×#683C2313yes—
120C2×C4×Dic5C2313yes—
121C2×C4×Dic5C2313yes—
122C2×C4×Dic5C2313yes—
123#4041C2×C4124yescomplemented
124#4040C2×C4124yescomplemented
125#4030C2×C4124yescomplemented
126#4028C2×C4124yescomplemented
127#4022C2×C418yescomplemented
128#4020C2×C418yescomplemented
129C4×D20—46no—
130C4×D20—46no—
131C4×D20—46no—
132C42×D5—46no—
133C5×#95C2313yes—
134C5×#95C2313yes—
135C5×#95C2313yes—
136C5×#95C2313yes—
137#3963C2313yes—
138#3963C2313yes—
139#3963C2313yes—
140#3963C2313yes—
141#3963C2313yes—
142#3963C2313yes—
143#3963C2313yes—
144#3963C2313yes—
145C2×#560—51no—
146#2383—51no—
147#2383—51no—
148#2380—51no—
149#2377—53no—
150#2377—53no—
151#2376—53no—
152#2375—53no—
153C4×#127—51no—
154C4×#126—51no—
155C4×#126D511yescharacteristic, complemented
156C4×#123—53no—
157C4×#121—53no—
158C4×#121—53no—
159C4×#120—53no—
160C24×C5C2411yescharacteristic
161C23×D5—43no—
162C23×D5—43no—
163C23×D5C22×C414yes—
164C23×D5C2413yes—
165C23×D5C2411yescharacteristic
166C23×D5C2411yescharacteristic
167C22×C4×C5—26no—
168C22×C4×C5C2413yes—
169C22×C4×C5C2413yes—
170C22×C4×C5C2411yescharacteristic
171C22×C4×C5C2413yes—
172C22×C4×C5C2413yes—
173C22×C4×C5C2411yescharacteristic
174C2×C22⋊D5—43no—
175C2×C22⋊D5—43no—
176C2×C22⋊D5C22×C4112yes—
177C22×Dic5—43no—
178C22×Dic5C2413yes—
179C22×Dic5C2413yes—
180C22×Dic5C2411yescharacteristic
181C22×Dic5C2411yescharacteristic
182C22×Dic5C2413yes—
183C2×D20—43no—
184C2×D20—43no—
185C2×D20—43no—
186C2×D20—43no—
187C2×D20—43no—
188C2×D20—43no—
189C2×D20C22×C4112yes—
190C2×D20C22×C4112yes—
191C2×D20C22×C4112yescomplemented
192C2×C4×D5—26no—
193C2×C4×D5—26no—
194C2×C4×D5—26no—
195C2×C4×D5—26no—
196C2×C4×D5—26no—
197C2×C4×D5—43no—
198C2×C4×D5—43no—
199C2×C4×D5—43no—
200C2×C4×D5—43no—
201C2×C4×D5—43no—
202C2×C4×D5—43no—
203C2×C4×D5—43no—
204C2×C4×D5—416no—
205C2×C4×D5C22×C4112yescomplemented
206C5×C4⋊C4—43no—
207C5×C4⋊C4C22×C4112yescomplemented
208C5×C22⋊C4—43no—
209C5×C22⋊C4C22×C4112yes—
210C42×C5—26no—
211C42×C5—26no—
212C42×C5—43no—
213C42×C5C22×C414yescomplemented
214C22⋊Dic5—43no—
215#685—43no—
216#685—43no—
217#685—43no—
218#685—43no—
219#685—43no—
220#685—43no—
221#685—43no—
222#685—43no—
223#685—43no—
224#685—43no—
225#685C22×C4112yes—
226#685C22×C4112yes—
227#685C22×C4112yescomplemented
228C4⋊Dic5—43no—
229C4⋊Dic5—43no—
230C4⋊Dic5—43no—
231#683—43no—
232#683—43no—
233#683C22×C4112yescomplemented
234C4×Dic5—26no—
235C4×Dic5—43no—
236C4×Dic5—43no—
237C24×C4—51no—
238#560—516no—
239C2×#127—51no—
240C2×#126—51no—
241C2×#126C2×D511yescharacteristic
242C2×#123—53no—
243C2×#121—53no—
244C2×#121—53no—
245C2×#120—53no—
246C2×C4×D4—53no—
247C2×C4×D4—53no—
248C2×C4×D4—53no—
249C2×C4×D4—53no—
250C22×C42—53no—
251#390—53no—
252#390—53no—
253#390—53no—
254#390—53no—
255#389—53no—
256#389—53no—
257#388—53no—
258#388—53no—
259#388—53no—
260#388—53no—
261#388—53no—
262#388—53no—
263#388—53no—
264#388C2×D513yes—
265#387—53no—
266#387—53no—
267#387—53no—
268#387C2×D513yescomplemented
269#386—53no—
270#386—53no—
271#386—53no—
272#386—53no—
273#386—53no—
274#386—53no—
275#386—53no—
276#386—53no—
277#385—53no—
278#385—53no—
279#385—53no—
280#385—53no—
281#384—51no—
282#383—51no—
283#383C2×D511yescharacteristic, complemented
284#381—53no—
285#380—53no—
286#380—53no—
287#379—53no—
288C4×C4⋊C4—53no—
289C4×C4⋊C4C2×D513yescomplemented
290C4×C22⋊C4—53no—
291C4×C22⋊C4—53no—
292C4×C22⋊C4—53no—
293C4×C22⋊C4C2×D513yes—
294C43C2×D511yescharacteristic, complemented
295C23×C5—23no—
296C23×C5—23no—
297C23×C5C23×C412yes—
298C23×C5C2511yescharacteristic
299C22×D5—23no—
300C22×D5—23no—
301C22×D5—23no—
302C22×D5—23no—
303C22×D5—23no—
304C22×D5—23no—
305C22×D5—23no—
306C22×D5—23no—
307C22×D5—23no—
308C22×D5—23no—
309C22×D5—412no—
310C22×D5—44no—
311C22×D5—412no—
312C22×D5C23×C412yes—
313C22×D5C23×C412yes—
314C22×D5C23×C416yes—
315C2×C4×C5—23no—
316C2×C4×C5—23no—
317C2×C4×C5—23no—
318C2×C4×C5—23no—
319C2×C4×C5—23no—
320C2×C4×C5—23no—
321C2×C4×C5—23no—
322C2×C4×C5—23no—
323C2×C4×C5—23no—
324C2×C4×C5—23no—
325C2×C4×C5—23no—
326C2×C4×C5—44no—
327C2×C4×C5C23×C416yes—
328C2×C4×C5C23×C416yes—
329C2×C4×C5H(5,𝔽2)16yes—
330C22⋊D5—412no—
331C2×Dic5—23no—
332C2×Dic5—23no—
333C2×Dic5—23no—
334C2×Dic5—23no—
335C2×Dic5—23no—
336C2×Dic5—23no—
337C2×Dic5—23no—
338C2×Dic5—23no—
339C2×Dic5—23no—
340C2×Dic5—23no—
341C2×Dic5—44no—
342C2×Dic5C23×C416yes—
343D20—412no—
344D20—412no—
345D20—412no—
346C4×D5—412no—
347C4×D5—412no—
348C4×D5—44no—
349C4×D5—44no—
350C4×D5—412no—
351C4×D5—44no—
352C4×D5—44no—
353C25—51no—
354C22×D4—53no—
355C22×D4—53no—
356C22×D4—53no—
357C22×D4—53no—
358C23×C4—53no—
359C23×C4—51no—
360C23×C4—53no—
361C23×C4—51no—
362C23×C4—51no—
363C23×C4—51no—
364C23×C4—51no—
365C23×C4—53no—
366C23×C4—206no—
367C23×C4C22×D511yescharacteristic
368#127—58no—
369#126—58no—
370#126C4×D518yescomplemented
371#123—524no—
372#121—524no—
373#121—524no—
374#120—524no—
375C4×D4—206no—
376C4×D4—206no—
377C4×D4—206no—
378C4×D4—206no—
379C2×C4⋊C4—53no—
380C2×C4⋊C4—53no—
381C2×C4⋊C4—53no—
382C2×C4⋊C4—53no—
383C2×C4⋊C4—53no—
384C2×C4⋊C4—53no—
385C2×C4⋊C4C22×D513yes—
386C2×C4⋊C4C22×D513yes—
387C2×C22⋊C4—53no—
388C2×C22⋊C4—53no—
389C2×C22⋊C4—53no—
390C2×C22⋊C4—53no—
391C2×C22⋊C4—53no—
392C2×C22⋊C4—53no—
393C2×C22⋊C4—53no—
394C2×C22⋊C4—53no—
395C2×C22⋊C4—53no—
396C2×C22⋊C4—53no—
397C2×C22⋊C4—53no—
398C2×C22⋊C4—53no—
399C2×C22⋊C4—53no—
400C2×C22⋊C4—53no—
401C2×C22⋊C4C22×D513yes—
402C2×C22⋊C4C22×D513yes—
403C2×C42—53no—
404C2×C42—53no—
405C2×C42—53no—
406C2×C42—206no—
407C2×C42C22×D513yes—
408C2×C42C22×D513yes—
409C2×C42C22×D513yes—
410C2×C42C22×D511yescharacteristic
411#95—53no—
412#95—53no—
413#95—53no—
414#95—53no—
415#95—53no—
416#95—53no—
417#95—53no—
418#95—53no—
419#95C22×D513yes—
420#95C22×D513yes—
421#95C22×D513yes—
422#95C22×D513yes—
423C22×C5—26no—
424C22×C5—41no—
425C22×C5—43no—
426C22×C5C24×C411yescharacteristic
427C22×C5C2×H(5,𝔽2)13yes—
428C22×C5#58513yes—
429C2×D5—26no—
430C2×D5—26no—
431C2×D5—26no—
432C2×D5—26no—
433C2×D5—26no—
434C2×D5—416no—
435C2×D5—41no—
436C2×D5—41no—
437C2×D5—43no—
438C2×D5—43no—
439C2×D5—43no—
440C2×D5—43no—
441C2×D5—43no—
442C2×D5—43no—
443C4×C5—26no—
444C4×C5—26no—
445C4×C5—41no—
446C4×C5—43no—
447C4×C5—43no—
448C4×C5#56014yescomplemented
449Dic5—26no—
450Dic5—41no—
451Dic5—41no—
452Dic5—43no—
453Dic5—43no—
454C24—51no—
455C24—51no—
456C24—53no—
457C24—54no—
458C24—203no—
459C24—203no—
460C24C23×D511yescharacteristic
461C2×D4—512no—
462C2×D4—512no—
463C2×D4—512no—
464C2×D4—512no—
465C2×D4—203no—
466C2×D4—203no—
467C2×D4—203no—
468C2×D4—203no—
469C2×D4—203no—
470C2×D4—203no—
471C2×D4—203no—
472C2×D4—203no—
473C22×C4—26no—
474C22×C4—53no—
475C22×C4—512no—
476C22×C4—53no—
477C22×C4—51no—
478C22×C4—51no—
479C22×C4—53no—
480C22×C4—106no—
481C22×C4—106no—
482C22×C4—106no—
483C22×C4—106no—
484C22×C4—106no—
485C22×C4—203no—
486C22×C4—203no—
487C22×C4—203no—
488C22×C4—203no—
489C22×C4—203no—
490C22×C4—203no—
491C22×C4—203no—
492C22×C4—2016no—
493C22×C4—203no—
494C22×C4C23×D513yes—
495C22×C4C23×D513yes—
496C22×C4C23×D511yescharacteristic
497C22×C4C23×D513yes—
498C22×C4C23×D513yes—
499C22×C4C23×D511yescharacteristic
500C4⋊C4—43no—
501C4⋊C4—512no—
502C4⋊C4—203no—
503C4⋊C4—203no—
504C4⋊C4—203no—
505C4⋊C4—203no—
506C4⋊C4—203no—
507C4⋊C4C2×C4×D5112yescomplemented
508C22⋊C4—43no—
509C22⋊C4—512no—
510C22⋊C4—512no—
511C22⋊C4—512no—
512C22⋊C4—203no—
513C22⋊C4—203no—
514C22⋊C4—203no—
515C22⋊C4—203no—
516C22⋊C4—203no—
517C22⋊C4—203no—
518C22⋊C4—203no—
519C22⋊C4—203no—
520C22⋊C4—203no—
521C22⋊C4—203no—
522C22⋊C4—203no—
523C22⋊C4C2×C4×D5112yes—
524C42—26no—
525C42—26no—
526C42—43no—
527C42—106no—
528C42—203no—
529C42—203no—
530C42C2×C4×D514yescomplemented
531C2×C5—42no—
532C2×C5C4×H(5,𝔽2)13yes—
533C2×C5C2×#56011yescharacteristic
534C2×C5#352913yes—
535D5—46no—
536D5—42no—
537D5—42no—
538C23—23no—
539C23—23no—
540C23—52no—
541C23—52no—
542C23—56no—
543C23—103no—
544C23—103no—
545C23—103no—
546C23—103no—
547C23—103no—
548C23—103no—
549C23—103no—
550C23—103no—
551C23—103no—
552C23—103no—
553C23—2012no—
554C23—204no—
555C23—2012no—
556C23C22×C4×D512yes—
557C23C24×D511yescharacteristic
558D4—2012no—
559D4—2012no—
560D4—2012no—
561D4—2012no—
562C2×C4—23no—
563C2×C4—23no—
564C2×C4—23no—
565C2×C4—23no—
566C2×C4—23no—
567C2×C4—23no—
568C2×C4—23no—
569C2×C4—23no—
570C2×C4—23no—
571C2×C4—23no—
572C2×C4—23no—
573C2×C4—44no—
574C2×C4—56no—
575C2×C4—103no—
576C2×C4—103no—
577C2×C4—103no—
578C2×C4—103no—
579C2×C4—103no—
580C2×C4—103no—
581C2×C4—103no—
582C2×C4—103no—
583C2×C4—103no—
584C2×C4—103no—
585C2×C4—2012no—
586C2×C4—204no—
587C2×C4—204no—
588C2×C4—2012no—
589C2×C4—204no—
590C2×C4—204no—
591C2×C4—204no—
592C2×C4—2012no—
593C2×C4C22×C4×D516yes—
594C2×C4C22×C4×D516yes—
595C2×C4#414916yes—
596C5C4×#56011yescharacteristic, complemented, Sylow
597C22—26no—
598C22—41no—
599C22—43no—
600C22—106no—
601C22—106no—
602C22—106no—
603C22—106no—
604C22—106no—
605C22—2016no—
606C22—201no—
607C22—201no—
608C22—203no—
609C22—203no—
610C22—203no—
611C22—203no—
612C22—203no—
613C22—203no—
614C22C23×C4×D511yescharacteristic
615C22C2×#414913yes—
616C22#6628313yes—
617C4—26no—
618C4—26no—
619C4—41no—
620C4—43no—
621C4—43no—
622C4—106no—
623C4—201no—
624C4—201no—
625C4—203no—
626C4—203no—
627C4#6604514yesdirect product factor
628C2—42no—
629C2—202no—
630C2—202no—
631C2—206no—
632C2C4×#414913yes—
633C2C2×#6604511yescharacteristic
634C2#1061807213yes—
subgroupG/H
centerC22×C4C23×D5
commutatorC22×C5C24×C4
FrattiniC23C24×D5
FittingC4×C5×#126C2
socle, cosocleC23×C5C25
prime radicalC2×#66045C2
hypercenterC4×#126D5
hypocenterC5C4×#560
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C4×#126

Complements

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

NH ≅ G/Ntype
2. C4×C5×#126C2semidirect
3. #10614807C2semidirect
4. #10607571C2semidirect
5. #10607221C2semidirect
6. #10607044C2semidirect
7. #10607043C2semidirect
8. #10606030C2semidirect
9. #10606029C2semidirect
10. C4×#4040C2semidirect
11. C4×#4041C2semidirect
12. C4×#4030C2semidirect
13. C4×#4028C2semidirect
14. C4×#4020C2semidirect
15. C4×#4022C2semidirect
19. #66045C4direct (N × H)
28. C2×C4×D20C22semidirect
29. C2×C42×D5C22semidirect
31. C5×#387C22semidirect
32. C5×#383C22semidirect
33. C4×C5×C4⋊C4C22semidirect
35. C43×C5C22semidirect
37. #65278C22semidirect
39. #65276C22semidirect
40. #65274C22semidirect
41. #65270C22semidirect
50. #65228C22semidirect
53. C4×#685C22semidirect
54. #65226C22semidirect
55. #65224C22semidirect
56. #65222C22semidirect
57. C4×#683C22semidirect
59. #64959C22semidirect
61. #64958C22semidirect
64. #64956C22semidirect
69. #64954C22semidirect
70. #64954C22semidirect
71. #64953C22semidirect
72. #64944C22semidirect
73. #64936C22semidirect
90. C5×#126C2×C4semidirect
123. #4041C2×C4semidirect
124. #4040C2×C4semidirect
125. #4030C2×C4semidirect
126. #4028C2×C4semidirect
127. #4022C2×C4semidirect
128. #4020C2×C4semidirect
155. C4×#126D5semidirect
191. C2×D20C22×C4semidirect
205. C2×C4×D5C22×C4semidirect
207. C5×C4⋊C4C22×C4semidirect
213. C42×C5C22×C4semidirect
227. #685C22×C4semidirect
233. #683C22×C4semidirect
268. #387C2×D5semidirect
283. #383C2×D5semidirect
289. C4×C4⋊C4C2×D5semidirect
294. C43C2×D5semidirect
370. #126C4×D5semidirect
448. C4×C5#560semidirect
507. C4⋊C4C2×C4×D5semidirect
530. C42C2×C4×D5semidirect
596. C5C4×#560semidirect
627. C4#66045direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#660452
C4×C5×#1262
#106148072
#106075712
#106072212
#106070442
#106070432
#106060302
#106060292
C4×#40402
C4×#40412
C4×#40302
C4×#40282
C4×#40202
C4×#40222
C4×#5605