Finite Group Databasebeta

← #13007694

Subgroups — #13007694

Order 1280.

7856 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C5×#41C211yesmaximal, characteristic, complemented
2#10619176C212yesmaximal, complemented
3#10617754C212yesmaximal, complemented
4#10617753C216yesmaximal, complemented
5#10617751C213yesmaximal, complemented
6#10617749C213yesmaximal, complemented
7#10617747C211yesmaximal, characteristic, complemented
8#10617746C212yesmaximal, complemented
9#10617744C216yesmaximal, complemented
10#10617739C216yesmaximal, complemented
11C4×#4149C212yesmaximal, complemented
12#10617729C211yesmaximal, characteristic, complemented
13#10617722C212yesmaximal, complemented
14#10617703C212yesmaximal, complemented
15#10617691C216yesmaximal, complemented
16D4×#709C216yesmaximal, complemented
17#10617648C216yesmaximal, complemented
18#10617581C213yesmaximal, complemented
19C2×#65811C213yesmaximal, complemented
20C22×C5×#41C2211yescharacteristic
21C2×#4149C2212yes—
22C22×#709C2216yescomplemented
23C4×C5×#41C2211yescharacteristic
24C4×C5×#41C2211yescharacteristic
25C4×C5×#41C2213yescomplemented
26C4×C5×#41C2213yescomplemented
27C4×C5×#41C2211yescharacteristic, complemented
28C4×C5×#41C2213yescomplemented
29C4×C5×#41C2213yescomplemented
30C4×C5×#41C2211yescharacteristic, complemented
31C2×C4×C5×Q8C2211yescharacteristic, complemented
32C2×C4×C5×Q8C2211yescharacteristic, complemented
33C2×C4×C5×D4C2213yescomplemented
34C2×C4×C5×D4C2213yescomplemented
35C2×C5×#117C2213yescomplemented
36C22×C42×C5C2213yescomplemented
37#66168C2214yescomplemented
38#66167C2216yescomplemented
39#66164C2216yescomplemented
40#66163C22112yescomplemented
41#66161C2212yes—
42#66151C2214yescomplemented
43D4×C22⋊D5C22112yescomplemented
44#66125C2216yescomplemented
45#66125C2216yescomplemented
46#66125C2216yescomplemented
47C2×#4076C2216yescomplemented
48C2×#4076C2216yescomplemented
49#65919C2216yescomplemented
50#65919C2216yescomplemented
51#65918C2216yescomplemented
52#65916C22112yescomplemented
53#65914C22112yescomplemented
54#65913C2216yescomplemented
55#65911C2212yescomplemented
56#65911C2212yescomplemented
57#65908C2214yescomplemented
58C4×#713C2214yescomplemented
59#65904C2212yescomplemented
60Q8×Dic10C2212yescomplemented
61#65899C22112yescomplemented
62#65897C2216yescomplemented
63#65896C22112yescomplemented
64#65894C22124yescomplemented
65#65887C2216yescomplemented
66#65887C2216yescomplemented
67#65886C22112yescomplemented
68#65885C2216yescomplemented
69#65884C22112yescomplemented
70#65884C22112yescomplemented
71D4×D20C2216yescomplemented
72D4×D20C2216yescomplemented
73#65882C22112yescomplemented
74#65881C22124yescomplemented
75#65879C22112yescomplemented
76C4×D4×D5C22112yescomplemented
77#65877C2216yescomplemented
78D4×Dic10C2216yescomplemented
79#65869C22112yescomplemented
80#65868C22112yescomplemented
81#65866C22112yescomplemented
82#65864C22112yescomplemented
83#65861C22124yescomplemented
84#65859C2216yescomplemented
85#65857C2216yescomplemented
86#65855C2216yescomplemented
87#65853C2216yescomplemented
88#65848C22112yescomplemented
89#65841C22112yescomplemented
90#65824C22124yescomplemented
91#65813C2216yescomplemented
92#65813C2216yescomplemented
93#65813C2216yescomplemented
94#65813C2216yescomplemented
95#65813C2216yescomplemented
96#65813C2216yescomplemented
97#65811C2216yescomplemented
98#65811C2216yescomplemented
99#65811C2216yescomplemented
100#65811C2216yescomplemented
101#65811C2216yescomplemented
102#65811C2213yescomplemented
103#65811C2213yescomplemented
104#65811C2216yescomplemented
105#65811C2216yescomplemented
106#65811C2213yescomplemented
107C2×#4021C2216yescomplemented
108C2×#4020C2213yescomplemented
109C4×#709C2216yescomplemented
110C4×#709C2216yescomplemented
111C4×#709C2216yescomplemented
112C2×C4×D20C2216yescomplemented
113C2×C4×D20C2216yescomplemented
114#65804C2213yescomplemented
115#65804C2213yescomplemented
116#65804C2211yescharacteristic, complemented
117C2×#4015C2213yescomplemented
118#62800—51nomaximal, Sylow
119C2×C5×#41—28no—
120C2×C5×#41C2313yes—
121C2×C5×#41C2313yes—
122C2×C5×#41C2311yescharacteristic
123C2×C5×#41C2311yescharacteristic
124C22×C5×Q8C2311yescharacteristic
125C22×C5×D4C2313yes—
126C23×C4×C5C2313yes—
127C23×C4×C5C2313yes—
128C23×C4×C5C2313yes—
129C22×C22⋊D5C23112yes—
130#4149—216no—
131C2×#713C2314yes—
132C2×D4×D5C23112yes—
133C2×#709—424no—
134C2×#709C2316yes—
135C2×#709C2316yes—
136C2×#709C2316yes—
137C2×#709C23112yes—
138C2×#709C23112yes—
139C2×#709C23112yes—
140C22×D20C2316yes—
141C22×D20C2316yes—
142C22×D20C2316yes—
143C22×C4×D5C23112yes—
144C22×Dic10C2316yes—
145C4×C5×Q8C2311yescharacteristic
146C4×C5×Q8C2311yescharacteristic
147C4×C5×Q8C2311yescharacteristic
148C4×C5×Q8C2311yescharacteristic
149C4×C5×Q8C2313yes—
150C4×C5×Q8C2313yes—
151C4×C5×Q8C2313yes—
152C4×C5×Q8C2313yes—
153C4×C5×D4C2313yes—
154C4×C5×D4C2313yes—
155C4×C5×D4C2313yes—
156C4×C5×D4C2313yes—
157C4×C5×D4C2316yes—
158C4×C5×D4C2313yes—
159C4×C5×D4C2316yes—
160C4×C5×D4C2316yes—
161C4×C5×D4C2313yes—
162C4×C5×D4C2313yes—
163C4×C5×D4C2316yes—
164C4×C5×D4C2313yes—
165C5×#117C2313yes—
166C5×#117C2313yes—
167C5×#117C2316yes—
168C5×#117C2313yes—
169C5×#117C2313yes—
170C5×#117C2316yes—
171C2×C5×C4⋊C4C2313yes—
172C2×C5×C4⋊C4C2313yes—
173C2×C5×C22⋊C4C2316yes—
174C2×C42×C5C2313yes—
175C2×C42×C5C2311yescharacteristic
176C2×C42×C5C2313yes—
177C2×C42×C5C2313yes—
178C2×C42×C5C2313yes—
179C2×C42×C5C2313yes—
180C2×C42×C5C2313yes—
181C2×C42×C5C2313yes—
182C2×C42×C5C2313yes—
183C2×C42×C5C2313yes—
184C2×C42×C5C2313yes—
185C2×C42×C5C2313yes—
186#4099C23112yes—
187#4093C23112yes—
188#4092C23112yes—
189Q8×Dic5C2314yes—
190#4086C23112yes—
191#4085C23124yes—
192#4084C23112yes—
193#4083C23124yes—
194D4×Dic5C23112yes—
195#4076C2316yes—
196#4076C2316yes—
197#4076C23112yes—
198#4076C23112yes—
199#4076C23112yes—
200#4076C23112yes—
201#4076C23112yes—
202#4076C23112yes—
203#4076C2316yes—
204#4076C2316yes—
205#4076C2316yes—
206#4076C2316yes—
207#4075C23112yes—
208#4075C23112yes—
209#4075C23112yes—
210C4×C22⋊D5C23112yes—
211C4×C22⋊D5C23112yes—
212C4×C22⋊D5C23112yes—
213C4×C22⋊D5C23112yes—
214C4×C22⋊D5C23112yes—
215C4×C22⋊D5C23112yes—
216C2×#685C23112yes—
217C2×#685C23112yes—
218#4072C2312yes—
219#4072C2316yes—
220#4072C2316yes—
221C2×C4⋊Dic5C2316yes—
222C2×C4⋊Dic5C2316yes—
223#4070C2312yes—
224#4070C2312yes—
225#4070C2316yes—
226#4070C2316yes—
227#4070C2316yes—
228#4070C2316yes—
229#4044C23124yes—
230#4042C23124yes—
231#4041C23112yes—
232#4041C23112yes—
233#4040C23124yes—
234#4040C23124yes—
235#4039C23112yes—
236#4039C23112yes—
237#4038C23112yes—
238D5×C4⋊C4C23112yes—
239#4036C23112yes—
240#4034C23112yes—
241#4031C23124yes—
242#4030C23124yes—
243#4030C23124yes—
244#4029C23124yes—
245#4028C23124yes—
246#4027C23124yes—
247D5×C22⋊C4C23124yes—
248#4024C23124yes—
249#4022C23112yes—
250#4022C23112yes—
251#4021C2316yes—
252#4021C23112yes—
253#4021C23112yes—
254#4021C23112yes—
255#4021C2316yes—
256#4021C2316yes—
257#4020C2313yes—
258#4020C2316yes—
259#4020C2316yes—
260#4020C2316yes—
261C4×D20C2316yes—
262C4×D20C2316yes—
263C4×D20C23112yes—
264C4×D20C23112yes—
265C4×D20C23112yes—
266C4×D20C23112yes—
267C4×D20C23112yes—
268C4×D20C23112yes—
269C4×D20C2316yes—
270C4×D20C2316yes—
271C4×D20C2316yes—
272C4×D20C2316yes—
273#4018C23112yes—
274#4018C23112yes—
275#4018C23112yes—
276C42×D5C23112yes—
277#4016C2312yes—
278#4016C2316yes—
279#4016C2316yes—
280#4015C2313yes—
281#4015C2316yes—
282#4015C2316yes—
283#4015C2316yes—
284#4015C2311yescharacteristic
285#4015C2311yescharacteristic
286C4×Dic10C2312yes—
287C4×Dic10C2312yes—
288C4×Dic10C2316yes—
289C4×Dic10C2316yes—
290C4×Dic10C2316yes—
291C4×Dic10C2316yes—
292#3522—52no—
293#3519—56no—
294#3517—52no—
295#3514—56no—
296#3511—53no—
297#3508—53no—
298#3503—51no—
299#3498—51no—
300#3494—56no—
301#3488—52no—
302#3483—52no—
303#3481—56no—
304#3480—52no—
305D4×#41—56no—
306#3460—56no—
307#3444—53no—
308C2×#532—53no—
309C4×H(5,𝔽2)—52no—
310C2×C4×#41D511yescharacteristic, complemented
311C24×C5C2413yes—
312C23×D5C24112yes—
313C5×#41—24no—
314C5×#41—212no—
315C5×#41—212no—
316C5×#41#4118yescomplemented
317C2×C5×Q8—24no—
318C2×C5×Q8C2413yes—
319C2×C5×Q8C2411yescharacteristic
320C2×C5×D4—212no—
321C2×C5×D4C2416yes—
322C2×C5×D4C2413yes—
323C2×C5×D4C2413yes—
324C22×C4×C5—212no—
325C22×C4×C5—212no—
326C22×C4×C5—46no—
327C22×C4×C5C2411yescharacteristic
328C22×C4×C5C2411yescharacteristic
329C22×C4×C5C2413yes—
330C22×C4×C5C2413yes—
331C22×C4×C5C2413yes—
332C22×C4×C5C2413yes—
333C22×C4×C5C2413yes—
334C22×C4×C5C2413yes—
335C22×C4×C5C2413yes—
336C22×C4×C5C2413yes—
337C22×C4×C5C2413yes—
338C22×C4×C5C2413yes—
339C22×C4×C5C2413yes—
340C22×C4×C5C2413yes—
341C22×C4×C5C2413yes—
342C22×C4×C5C2413yes—
343C22×C4×C5C2413yes—
344C22×C4×C5C2411yescharacteristic
345C2×C22⋊D5—424no—
346C2×C22⋊D5C24112yes—
347C2×C22⋊D5C24112yes—
348C2×C22⋊D5C24112yes—
349C2×C22⋊D5C24124yes—
350C22×Dic5C24112yes—
351#713—216no—
352D4×D5—248no—
353#709—224no—
354#709—224no—
355#709—424no—
356#709—412no—
357#709—424no—
358#709—424no—
359C2×D20—224no—
360C2×D20—412no—
361C2×D20—412no—
362C2×D20C2416yes—
363C2×D20C2416yes—
364C2×D20C2416yes—
365C2×D20C24112yes—
366C2×D20C24112yes—
367C2×D20C24112yes—
368C2×C4×D5—424no—
369C2×C4×D5C24112yes—
370C2×C4×D5C24112yes—
371C2×C4×D5C24124yes—
372C2×C4×D5C24112yes—
373C2×Dic10—412no—
374C2×Dic10C2416yes—
375C2×Dic10C2412yes—
376C2×Dic10C2412yes—
377C2×Dic10C24112yes—
378C5×C4⋊C4C2413yes—
379C5×C4⋊C4C2413yes—
380C5×C4⋊C4C2413yes—
381C5×C4⋊C4C2413yes—
382C5×C4⋊C4C2416yes—
383C5×C4⋊C4C2416yes—
384C5×C22⋊C4C2416yes—
385C5×C22⋊C4C2416yes—
386C5×C22⋊C4C2416yes—
387C5×C22⋊C4C2416yes—
388C42×C5C2411yescharacteristic
389C42×C5C2411yescharacteristic
390C42×C5C2411yescharacteristic
391C42×C5C2411yescharacteristic
392C42×C5C2413yes—
393C42×C5C2413yes—
394C42×C5C2413yes—
395C42×C5C2413yes—
396C42×C5C2413yes—
397C42×C5C2413yes—
398C42×C5C2413yes—
399C42×C5C2413yes—
400C42×C5C2413yes—
401C42×C5C2413yes—
402C42×C5C2413yes—
403C42×C5C2413yes—
404C22⋊Dic5C2414yes—
405C22⋊Dic5C24112yes—
406C22⋊Dic5C24112yes—
407#685C24112yes—
408#685C24112yes—
409#685C24112yes—
410#685C24112yes—
411#685C24112yes—
412#685C24112yes—
413#685C24124yes—
414#685C24124yes—
415C4⋊Dic5C2412yes—
416C4⋊Dic5C2412yes—
417C4⋊Dic5C2416yes—
418C4⋊Dic5C2416yes—
419C4⋊Dic5C2412yes—
420C4⋊Dic5C2412yes—
421C4⋊Dic5C24112yes—
422C4⋊Dic5C24112yes—
423#683C2414yes—
424#683C2414yes—
425#683C24112yes—
426#683C24112yes—
427#683C24112yes—
428#683C24112yes—
429C4×Dic5C2414yes—
430C4×Dic5C24112yes—
431C4×Dic5C24112yes—
432C2×H(5,𝔽2)—52no—
433C22×#41—56no—
434C22×#41C2×D511yescharacteristic
435#559—56no—
436#559—56no—
437Q82—52no—
438#557—52no—
439#556—56no—
440#555—56no—
441#555—512no—
442#554—56no—
443#554—56no—
444#553—512no—
445#553—512no—
446#553—512no—
447#551—524no—
448#550—54no—
449#550—52no—
450#550—52no—
451#550—56no—
452#550—56no—
453D4×Q8—56no—
454#548—54no—
455#548—512no—
456#547—56no—
457#547—512no—
458#546—512no—
459#546—512no—
460#546—512no—
461#546—524no—
462D42—512no—
463D42—56no—
464D42—56no—
465#544—56no—
466#542—512no—
467#542—512no—
468#540—512no—
469#540—512no—
470#538—524no—
471#537—56no—
472#535—56no—
473#535—56no—
474#533—51no—
475#533—53no—
476#533—53no—
477#532—512no—
478#532—53no—
479#532—56no—
480#532—56no—
481#532—56no—
482#532—56no—
483#532—56no—
484#532—56no—
485#532—56no—
486#532—53no—
487#532—53no—
488C2×C4⋊Q8—53no—
489C2×#127—53no—
490#529—512no—
491#529—56no—
492#529—56no—
493#529—56no—
494#529—56no—
495#529—56no—
496#529—56no—
497C2×#124—56no—
498#525—56no—
499#525—56no—
500#525—56no—
501#525—524no—
502C2×#121—56no—
503C2×#121—56no—
504#520—52no—
505#520—54no—
506#520—56no—
507#518—512no—
508#518—56no—
509C4×#41—54no—
510C4×#41—56no—
511C4×#41—56no—
512C4×#41—56no—
513C4×#41C2×D511yescharacteristic
514C4×#41C2×D511yescharacteristic
515C4×#41C2×D513yescomplemented
516C4×#41C2×D513yescomplemented
517C4×#41C2×D511yescharacteristic, complemented
518C4×#41C2×D513yescomplemented
519C4×#41C2×D513yescomplemented
520C4×#41C2×D511yescharacteristic, complemented
521C2×C4×Q8C2×D511yescharacteristic, complemented
522C2×C4×Q8C2×D511yescharacteristic, complemented
523C2×C4×D4—512no—
524C2×C4×D4—56no—
525C2×C4×D4—56no—
526C2×C4×D4C2×D513yescomplemented
527C2×C4×D4C2×D513yescomplemented
528C2×#117C2×D513yescomplemented
529C22×C42C2×D513yescomplemented
530C23×C5—26no—
531C23×C5—26no—
532C23×C5—43no—
533C23×C5C2513yes—
534C23×C5C2513yes—
535C23×C5C2511yescharacteristic
536C22×D5—224no—
537C22×D5—412no—
538C22×D5—412no—
539C22×D5C25112yes—
540C5×Q8—26no—
541C5×Q8C2×#4114yescomplemented
542C5×D4—212no—
543C5×D4—26no—
544C5×D4C2×#41112yescomplemented
545C2×C4×C5—26no—
546C2×C4×C5—26no—
547C2×C4×C5—22no—
548C2×C4×C5—26no—
549C2×C4×C5—26no—
550C2×C4×C5—26no—
551C2×C4×C5—26no—
552C2×C4×C5—26no—
553C2×C4×C5—26no—
554C2×C4×C5—26no—
555C2×C4×C5—26no—
556C2×C4×C5—26no—
557C2×C4×C5—22no—
558C2×C4×C5—43no—
559C2×C4×C5—43no—
560C2×C4×C5—43no—
561C2×C4×C5C2×#41112yescomplemented
562C2×C4×C5H(5,𝔽2)14yescomplemented
563C2×C4×C5C2513yes—
564C2×C4×C5C2513yes—
565C2×C4×C5C2511yescharacteristic
566C2×C4×C5C2511yescharacteristic
567C2×C4×C5C2513yes—
568C2×C4×C5C2513yes—
569C2×C4×C5C2513yes—
570C2×C4×C5C2513yes—
571C2×C4×C5C2511yescharacteristic
572C2×C4×C5C2511yescharacteristic
573C2×C4×C5C2511yescharacteristic
574C2×C4×C5C2511yescharacteristic
575C22⋊D5—224no—
576C22⋊D5—224no—
577C22⋊D5—424no—
578C22⋊D5—412no—
579C2×Dic5—412no—
580C2×Dic5C2514yes—
581C2×Dic5C2514yes—
582C2×Dic5C25112yes—
583D20—212no—
584D20—224no—
585D20—212no—
586D20—212no—
587D20—412no—
588D20—412no—
589C4×D5—224no—
590C4×D5—224no—
591C4×D5—424no—
592C4×D5—412no—
593Dic10—24no—
594Dic10—212no—
595Dic10—24no—
596Dic10—412no—
597H(5,𝔽2)—1016no—
598C2×#41—28no—
599C2×#41—54no—
600C2×#41—56no—
601C2×#41—56no—
602C2×#41—56no—
603C2×#41—512no—
604C2×#41—512no—
605C2×#41—512no—
606C2×#41—2024no—
607C2×#41C22×D513yes—
608C2×#41C22×D513yes—
609C2×#41C22×D511yescharacteristic
610C2×#41C22×D511yescharacteristic
611C22×Q8—56no—
612C22×Q8C22×D511yescharacteristic
613C22×D4—512no—
614C22×D4—512no—
615C22×D4—56no—
616C22×D4—56no—
617C22×D4—56no—
618C22×D4C22×D513yes—
619C23×C4—512no—
620C23×C4C22×D513yes—
621C23×C4C22×D513yes—
622C23×C4C22×D513yes—
623C4⋊Q8—512no—
624C4⋊Q8—53no—
625C4⋊Q8—56no—
626C4⋊Q8—56no—
627C4⋊Q8—56no—
628C4⋊Q8—51no—
629C4⋊Q8—51no—
630#127—512no—
631#127—53no—
632#127—56no—
633#127—56no—
634#127—56no—
635#126—524no—
636#126—512no—
637#126—512no—
638#125—512no—
639#125—52no—
640#125—56no—
641#125—56no—
642#124—512no—
643#124—524no—
644#124—56no—
645#124—512no—
646#124—512no—
647#124—512no—
648#124—56no—
649#124—56no—
650#123—512no—
651#123—512no—
652#123—512no—
653#123—524no—
654#123—524no—
655#123—524no—
656C22⋊Q8—512no—
657C22⋊Q8—52no—
658C22⋊Q8—52no—
659C22⋊Q8—56no—
660C22⋊Q8—56no—
661C22⋊Q8—56no—
662C22⋊Q8—56no—
663C22⋊Q8—524no—
664C22⋊Q8—524no—
665#121—524no—
666#121—512no—
667#121—56no—
668#121—56no—
669#121—512no—
670#121—512no—
671#121—512no—
672#121—512no—
673#121—512no—
674#121—512no—
675#121—56no—
676#121—56no—
677#121—56no—
678#121—56no—
679#121—512no—
680#121—512no—
681#121—524no—
682#121—524no—
683#120—512no—
684#120—524no—
685#120—524no—
686C4×Q8—54no—
687C4×Q8—52no—
688C4×Q8—52no—
689C4×Q8—56no—
690C4×Q8—56no—
691C4×Q8—56no—
692C4×Q8—56no—
693C4×Q8C22×D511yescharacteristic
694C4×Q8C22×D511yescharacteristic
695C4×Q8C22×D511yescharacteristic
696C4×Q8C22×D511yescharacteristic
697C4×Q8C22×D513yes—
698C4×Q8C22×D513yes—
699C4×Q8C22×D513yes—
700C4×Q8C22×D513yes—
701C4×D4—512no—
702C4×D4—512no—
703C4×D4—512no—
704C4×D4—512no—
705C4×D4—512no—
706C4×D4—512no—
707C4×D4—512no—
708C4×D4—512no—
709C4×D4—512no—
710C4×D4—524no—
711C4×D4—512no—
712C4×D4—56no—
713C4×D4—56no—
714C4×D4—512no—
715C4×D4—512no—
716C4×D4—512no—
717C4×D4—512no—
718C4×D4—512no—
719C4×D4—56no—
720C4×D4—56no—
721C4×D4—56no—
722C4×D4—56no—
723C4×D4C22×D513yes—
724C4×D4C22×D513yes—
725C4×D4C22×D513yes—
726C4×D4C22×D513yes—
727C4×D4C22×D516yes—
728C4×D4C22×D513yes—
729C4×D4C22×D516yes—
730C4×D4C22×D513yes—
731C4×D4C22×D516yes—
732C4×D4C22×D516yes—
733C4×D4C22×D513yes—
734C4×D4C22×D513yes—
735#117—52no—
736#117—56no—
737#117—56no—
738#117—512no—
739#117—512no—
740#117—512no—
741#117—512no—
742#117C22×D513yes—
743#117C22×D513yes—
744#117C22×D516yes—
745#117C22×D516yes—
746#117C22×D513yes—
747#117C22×D513yes—
748C2×C4⋊C4—56no—
749C2×C4⋊C4—56no—
750C2×C4⋊C4—512no—
751C2×C4⋊C4C22×D513yes—
752C2×C4⋊C4C22×D513yes—
753C2×C22⋊C4—512no—
754C2×C22⋊C4—512no—
755C2×C22⋊C4—524no—
756C2×C22⋊C4C22×D516yes—
757C2×C42—512no—
758C2×C42C22×D513yes—
759C2×C42C22×D513yes—
760C2×C42C22×D513yes—
761C2×C42C22×D513yes—
762C2×C42C22×D513yes—
763C2×C42C22×D513yes—
764C2×C42C22×D513yes—
765C2×C42C22×D513yes—
766C2×C42C22×D513yes—
767C2×C42C22×D513yes—
768C2×C42C22×D513yes—
769C2×C42C22×D511yescharacteristic
770C22×C5—21no—
771C22×C5—23no—
772C22×C5—21no—
773C22×C5—23no—
774C22×C5—23no—
775C22×C5—23no—
776C22×C5—23no—
777C22×C5—412no—
778C22×C5C22×#4116yes—
779C22×C5C2×H(5,𝔽2)12yes—
780C22×C5C2611yescharacteristic
781C2×D5—212no—
782C2×D5—212no—
783C2×D5—212no—
784C2×D5—824no—
785C4×C5—21no—
786C4×C5—23no—
787C4×C5—23no—
788C4×C5—23no—
789C4×C5—23no—
790C4×C5—23no—
791C4×C5—21no—
792C4×C5C22×#4112yes—
793C4×C5C22×#4116yes—
794C4×C5C2×H(5,𝔽2)12yes—
795C4×C5C2×H(5,𝔽2)12yes—
796C4×C5#58512yes—
797Dic5—24no—
798Dic5—212no—
799Dic5—24no—
800C24—512no—
801C24C23×D513yes—
802#41—24no—
803#41—212no—
804#41—212no—
805#41—1016no—
806#41—1024no—
807#41—1024no—
808#41—2024no—
809#41—2024no—
810#41—2024no—
811#41—2012no—
812#41#70918yescomplemented
813C2×Q8—24no—
814C2×Q8—52no—
815C2×Q8—52no—
816C2×Q8—56no—
817C2×Q8—512no—
818C2×Q8—2012no—
819C2×Q8C23×D513yes—
820C2×Q8C23×D511yescharacteristic
821C2×D4—212no—
822C2×D4—512no—
823C2×D4—512no—
824C2×D4—512no—
825C2×D4—524no—
826C2×D4—512no—
827C2×D4—56no—
828C2×D4—56no—
829C2×D4—56no—
830C2×D4—512no—
831C2×D4—512no—
832C2×D4—1048no—
833C2×D4—1024no—
834C2×D4—2012no—
835C2×D4—2012no—
836C2×D4—2024no—
837C2×D4C23×D516yes—
838C2×D4C23×D513yes—
839C2×D4C23×D513yes—
840C22×C4—212no—
841C22×C4—212no—
842C22×C4—46no—
843C22×C4—512no—
844C22×C4—512no—
845C22×C4—512no—
846C22×C4—512no—
847C22×C4—524no—
848C22×C4—2024no—
849C22×C4C23×D511yescharacteristic
850C22×C4C23×D511yescharacteristic
851C22×C4C23×D513yes—
852C22×C4C23×D513yes—
853C22×C4C23×D513yes—
854C22×C4C23×D513yes—
855C22×C4C23×D513yes—
856C22×C4C23×D513yes—
857C22×C4C23×D513yes—
858C22×C4C23×D513yes—
859C22×C4C23×D513yes—
860C22×C4C23×D513yes—
861C22×C4C23×D513yes—
862C22×C4C23×D513yes—
863C22×C4C23×D513yes—
864C22×C4C23×D513yes—
865C22×C4C23×D513yes—
866C22×C4C23×D511yescharacteristic
867C4⋊C4—512no—
868C4⋊C4—56no—
869C4⋊C4—56no—
870C4⋊C4—512no—
871C4⋊C4—512no—
872C4⋊C4—52no—
873C4⋊C4—52no—
874C4⋊C4—54no—
875C4⋊C4—54no—
876C4⋊C4—52no—
877C4⋊C4—52no—
878C4⋊C4—512no—
879C4⋊C4—512no—
880C4⋊C4—512no—
881C4⋊C4C23×D513yes—
882C4⋊C4C23×D513yes—
883C4⋊C4C23×D513yes—
884C4⋊C4C23×D513yes—
885C4⋊C4C23×D516yes—
886C4⋊C4C23×D516yes—
887C22⋊C4—512no—
888C22⋊C4—54no—
889C22⋊C4—512no—
890C22⋊C4—512no—
891C22⋊C4—524no—
892C22⋊C4—512no—
893C22⋊C4—512no—
894C22⋊C4—524no—
895C22⋊C4—512no—
896C22⋊C4—512no—
897C22⋊C4—512no—
898C22⋊C4C23×D516yes—
899C22⋊C4C23×D516yes—
900C22⋊C4C23×D516yes—
901C22⋊C4C23×D516yes—
902C42—512no—
903C42—512no—
904C42—54no—
905C42C23×D511yescharacteristic
906C42C23×D511yescharacteristic
907C42C23×D513yes—
908C42C23×D513yes—
909C42C23×D513yes—
910C42C23×D513yes—
911C42C23×D513yes—
912C42C23×D513yes—
913C42C23×D513yes—
914C42C23×D513yes—
915C42C23×D513yes—
916C42C23×D513yes—
917C42C23×D513yes—
918C42C23×D511yescharacteristic
919C42C23×D511yescharacteristic
920C42C23×D513yes—
921C2×C5—26no—
922C2×C5—22no—
923C2×C5—43no—
924C2×C5C23×#4111yescharacteristic
925C2×C5C22×H(5,𝔽2)11yescharacteristic
926C2×C5C2×#58511yescharacteristic
927D5—412no—
928C23—26no—
929C23—26no—
930C23—43no—
931C23—512no—
932C23—1024no—
933C23—2012no—
934C23—2012no—
935C23C24×D513yes—
936C23C24×D513yes—
937C23C24×D511yescharacteristic
938Q8—26no—
939Q8—104no—
940Q8—1012no—
941Q8—104no—
942Q8—2012no—
943Q8C2×#70914yescomplemented
944D4—212no—
945D4—26no—
946D4—1024no—
947D4—1024no—
948D4—1012no—
949D4—1024no—
950D4—1012no—
951D4—1012no—
952D4—2012no—
953D4—2012no—
954D4—2024no—
955D4—2012no—
956D4C2×#709112yescomplemented
957C2×C4—26no—
958C2×C4—26no—
959C2×C4—22no—
960C2×C4—26no—
961C2×C4—26no—
962C2×C4—26no—
963C2×C4—26no—
964C2×C4—26no—
965C2×C4—26no—
966C2×C4—26no—
967C2×C4—22no—
968C2×C4—26no—
969C2×C4—26no—
970C2×C4—43no—
971C2×C4—43no—
972C2×C4—43no—
973C2×C4—54no—
974C2×C4—54no—
975C2×C4—512no—
976C2×C4—1024no—
977C2×C4—1024no—
978C2×C4—2024no—
979C2×C4—2012no—
980C2×C4—2012no—
981C2×C4C2×#709112yescomplemented
982C2×C4#414914yescomplemented
983C2×C4C24×D513yes—
984C2×C4C24×D511yescharacteristic
985C2×C4C24×D511yescharacteristic
986C2×C4C24×D513yes—
987C2×C4C24×D513yes—
988C2×C4C24×D513yes—
989C2×C4C24×D513yes—
990C2×C4C24×D513yes—
991C2×C4C24×D511yescharacteristic
992C2×C4C24×D511yescharacteristic
993C2×C4C24×D511yescharacteristic
994C2×C4C24×D511yescharacteristic
995C5#6280011yescharacteristic, complemented, Sylow
996C22—21no—
997C22—23no—
998C22—21no—
999C22—23no—
1000C22—23no—
1001C22—23no—
1002C22—23no—
1003C22—412no—
1004C22—1012no—
1005C22—1012no—
1006C22—1012no—
1007C22—4024no—
1008C22C22×#70916yes—
1009C22C2×#414912yes—
1010C22C25×D511yescharacteristic
1011C4—21no—
1012C4—23no—
1013C4—23no—
1014C4—23no—
1015C4—21no—
1016C4—23no—
1017C4—23no—
1018C4—104no—
1019C4—1012no—
1020C4—104no—
1021C4C22×#70912yes—
1022C4C22×#70916yes—
1023C4C2×#414912yes—
1024C4C2×#414912yes—
1025C4#6628312yes—
1026C2—22no—
1027C2—26no—
1028C2—43no—
1029C2—2012no—
1030C2C23×#70911yescharacteristic
1031C2C22×#414911yescharacteristic
1032C2C2×#6628311yescharacteristic
subgroupG/H
centerC2×C4C24×D5
commutator, socle, cosocleC22×C5C26
FrattiniC22C25×D5
FittingC2×C4×C5×#41C2
hypercenterC2×C4×#41D5
hypocenterC5#62800
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
1. C2×C4×C5×#41C2semidirect
2. #10619176C2semidirect
3. #10617754C2semidirect
4. #10617753C2semidirect
5. #10617751C2semidirect
6. #10617749C2semidirect
7. #10617747C2semidirect
8. #10617746C2semidirect
9. #10617744C2semidirect
10. #10617739C2semidirect
11. C4×#4149C2semidirect
12. #10617729C2semidirect
13. #10617722C2semidirect
14. #10617703C2semidirect
15. #10617691C2semidirect
16. D4×#709C2semidirect
17. #10617648C2semidirect
18. #10617581C2semidirect
19. C2×#65811C2semidirect
22. C22×#709C22semidirect
25. C4×C5×#41C22semidirect
26. C4×C5×#41C22semidirect
27. C4×C5×#41C22semidirect
28. C4×C5×#41C22semidirect
29. C4×C5×#41C22semidirect
30. C4×C5×#41C22semidirect
31. C2×C4×C5×Q8C22semidirect
32. C2×C4×C5×Q8C22semidirect
33. C2×C4×C5×D4C22semidirect
34. C2×C4×C5×D4C22semidirect
35. C2×C5×#117C22semidirect
36. C22×C42×C5C22semidirect
37. #66168C22semidirect
38. #66167C22semidirect
39. #66164C22semidirect
40. #66163C22semidirect
42. #66151C22semidirect
43. D4×C22⋊D5C22semidirect
44. #66125C22semidirect
45. #66125C22semidirect
46. #66125C22semidirect
47. C2×#4076C22semidirect
48. C2×#4076C22semidirect
49. #65919C22semidirect
50. #65919C22semidirect
51. #65918C22semidirect
52. #65916C22semidirect
53. #65914C22semidirect
54. #65913C22semidirect
55. #65911C22semidirect
56. #65911C22semidirect
57. #65908C22semidirect
58. C4×#713C22semidirect
59. #65904C22semidirect
60. Q8×Dic10C22semidirect
61. #65899C22semidirect
62. #65897C22semidirect
63. #65896C22semidirect
64. #65894C22semidirect
65. #65887C22semidirect
66. #65887C22semidirect
67. #65886C22semidirect
68. #65885C22semidirect
69. #65884C22semidirect
70. #65884C22semidirect
71. D4×D20C22semidirect
72. D4×D20C22semidirect
73. #65882C22semidirect
74. #65881C22semidirect
75. #65879C22semidirect
76. C4×D4×D5C22semidirect
77. #65877C22semidirect
78. D4×Dic10C22semidirect
79. #65869C22semidirect
80. #65868C22semidirect
81. #65866C22semidirect
82. #65864C22semidirect
83. #65861C22semidirect
84. #65859C22semidirect
85. #65857C22semidirect
86. #65855C22semidirect
87. #65853C22semidirect
88. #65848C22semidirect
89. #65841C22semidirect
90. #65824C22semidirect
91. #65813C22semidirect
92. #65813C22semidirect
93. #65813C22semidirect
94. #65813C22semidirect
95. #65813C22semidirect
96. #65813C22semidirect
97. #65811C22semidirect
98. #65811C22semidirect
99. #65811C22semidirect
100. #65811C22semidirect
101. #65811C22semidirect
102. #65811C22semidirect
103. #65811C22semidirect
104. #65811C22semidirect
105. #65811C22semidirect
106. #65811C22semidirect
107. C2×#4021C22semidirect
108. C2×#4020C22semidirect
109. C4×#709C22semidirect
110. C4×#709C22semidirect
111. C4×#709C22semidirect
112. C2×C4×D20C22semidirect
113. C2×C4×D20C22semidirect
114. #65804C22semidirect
115. #65804C22semidirect
116. #65804C22semidirect
117. C2×#4015C22semidirect
310. C2×C4×#41D5semidirect
316. C5×#41#41semidirect
515. C4×#41C2×D5semidirect
516. C4×#41C2×D5semidirect
517. C4×#41C2×D5semidirect
518. C4×#41C2×D5semidirect
519. C4×#41C2×D5semidirect
520. C4×#41C2×D5semidirect
521. C2×C4×Q8C2×D5semidirect
522. C2×C4×Q8C2×D5semidirect
526. C2×C4×D4C2×D5semidirect
527. C2×C4×D4C2×D5semidirect
528. C2×#117C2×D5semidirect
529. C22×C42C2×D5semidirect
541. C5×Q8C2×#41semidirect
544. C5×D4C2×#41semidirect
561. C2×C4×C5C2×#41semidirect
562. C2×C4×C5H(5,𝔽2)semidirect
812. #41#709semidirect
943. Q8C2×#709semidirect
956. D4C2×#709semidirect
981. C2×C4C2×#709semidirect
982. C2×C4#4149semidirect
995. C5#62800semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C5×#412
#106191762
#106177542
#106177532
#106177512
#106177492
#106177472
#106177462
#106177442
#106177392
C4×#41492
#106177292
#106177222
#106177032
#106176912
D4×#7092
#106176482
#106175812
C2×#658112
#628005