Finite Group Databasebeta

← #13007849

Subgroups — #13007849

Order 1280.

11346 conjugacy classes of subgroups.

The subgroup lattice has 1212 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66287C211yesmaximal, characteristic, complemented
2C2×#66285C211yesmaximal, characteristic, complemented
3C5×#3500C211yesmaximal, characteristic, complemented
4#10619193C211yesmaximal, characteristic, complemented
5#10619183C211yesmaximal, characteristic, complemented
6#10618638C214yesmaximal, complemented
7#10618611C214yesmaximal, complemented
8#10618566C2112yesmaximal, complemented
9#10618527C2112yesmaximal, complemented
10#10618241C213yesmaximal, complemented
11#10618239C213yesmaximal, complemented
12#10618217C213yesmaximal, complemented
13#10618214C213yesmaximal, complemented
14#10618145C213yesmaximal, complemented
15D5×#532C213yesmaximal, complemented
16#10617977C213yesmaximal, complemented
17C2×#66002C213yesmaximal, complemented
18#10617748C211yesmaximal, characteristic, complemented
19C4×D5×#41C211yesmaximal, characteristic, complemented
20C2×C5×2−1+4C2211yescharacteristic, complemented
21C2×C5×H(5,𝔽2)C2211yescharacteristic, complemented
22#66287—216no—
23#66285—216no—
24C2×#4150C2212yescomplemented
25C2×#4150C2213yescomplemented
26C2×#4150C2211yescharacteristic, complemented
27C2×#4149C2213yescomplemented
28C2×#4149C2211yescharacteristic, complemented
29C2×#4149C2216yescomplemented
30C2×D5×#41C2211yescharacteristic
31C2×D5×#41C2213yescomplemented
32C2×D5×#41C2213yescomplemented
33C2×D5×#41C2212yescomplemented
34C2×D5×#41C2216yescomplemented
35C2×#4147C2212yescomplemented
36C2×#4147C2213yescomplemented
37C22×#713C2213yescomplemented
38C22×#713C2212yescomplemented
39C2×#4144C2213yescomplemented
40C2×#4144C2216yescomplemented
41C22×#711C2213yescomplemented
42C22×#711C2216yescomplemented
43C5×#548C2214yescomplemented
44C5×#546C22112yescomplemented
45C5×#536C2213yescomplemented
46C5×#535C2213yescomplemented
47C5×#532C2213yescomplemented
48C2×C5×#124C2213yescomplemented
49C4×C5×#41C2211yescharacteristic, complemented
50#66168C2214yescomplemented
51#66166C2213yescomplemented
52#66166C2213yescomplemented
53#66164C2213yescomplemented
54#41×Dic5C2211yescharacteristic, complemented
55#66159C2213yescomplemented
56#66158C22112yescomplemented
57#66150C2213yescomplemented
58Q8×C22⋊D5C2214yescomplemented
59C2×#4090C2213yescomplemented
60#66139C2213yescomplemented
61C2×#4086C2213yescomplemented
62D4×C22⋊D5C22112yescomplemented
63#66059C2213yescomplemented
64#66058C2216yescomplemented
65D5×C4⋊Q8C2213yescomplemented
66#66050C2213yescomplemented
67#66049C2216yescomplemented
68D5×#127C2213yescomplemented
69#66011C22112yescomplemented
70#66010C22112yescomplemented
71#66009C2216yescomplemented
72#66008C2216yescomplemented
73D5×#124C2213yescomplemented
74D5×#124C2213yescomplemented
75#66002C22112yescomplemented
76#66002C2211yescharacteristic, complemented
77#66002C2213yescomplemented
78#66002C2216yescomplemented
79#66002C2216yescomplemented
80#66002C2216yescomplemented
81#66002C22112yescomplemented
82#65990C22112yescomplemented
83#65989C22124yescomplemented
84#65987C22112yescomplemented
85#65966C22112yescomplemented
86#65965C22112yescomplemented
87#65963C22112yescomplemented
88#65961C22112yescomplemented
89#65944C22124yescomplemented
90#65943C22112yescomplemented
91#65942C22112yescomplemented
92#65940C22112yescomplemented
93D5×#121C22112yescomplemented
94#65933C22112yescomplemented
95#65930C22112yescomplemented
96#65924C22124yescomplemented
97#65923C22112yescomplemented
98#65920C22112yescomplemented
99#65910C2214yescomplemented
100C4×#713C2212yescomplemented
101C4×Q8×D5C2212yescomplemented
102#65888C22112yescomplemented
103#65886C22112yescomplemented
104#65884C22112yescomplemented
105#65882C22112yescomplemented
106C4×D4×D5C22112yescomplemented
107C4×D4×D5C2216yescomplemented
108C4×#711C2216yescomplemented
109#65860C2213yescomplemented
110#65859C2213yescomplemented
111#65856C2213yescomplemented
112D5×#117C2213yescomplemented
113#65824C22124yescomplemented
114C2×#4030C22112yescomplemented
115C2×#4027C22112yescomplemented
116#65811C2213yescomplemented
117C2×#4021C2213yescomplemented
118C4×#709C2213yescomplemented
119C2×C42×D5C2213yescomplemented
120#62812—51nomaximal, Sylow
121C5×2−1+4—28no—
122C5×H(5,𝔽2)—28no—
123C2×C5×#41C2316yes—
124C2×C5×#41C2313yes—
125C2×C5×#41C2313yes—
126C2×C5×#41C2312yes—
127C2×C5×#41C2311yescharacteristic
128C22×C5×Q8C2313yes—
129C22×C5×Q8C2312yes—
130C22×C5×D4C2316yes—
131C22×C5×D4C2313yes—
132C22×C22⋊D5C2316yes—
133C22×C22⋊D5C23112yes—
134C22×C22⋊D5C23112yes—
135C23×Dic5C2316yes—
136#4150—28no—
137#4150—216no—
138#4150—224no—
139#4149—28no—
140#4149—248no—
141#4149—224no—
142D5×#41—216no—
143D5×#41—248no—
144D5×#41—224no—
145D5×#41—224no—
146D5×#41D4116yescomplemented
147#4147—216no—
148#4147—224no—
149C2×#713—216no—
150C2×#713—224no—
151C2×#713C2316yes—
152C2×#713C2311yescharacteristic
153C2×#713C2313yes—
154C2×#713C2312yes—
155C2×#713C2316yes—
156C2×#713C2316yes—
157C2×#713C2316yes—
158C2×#713C2311yescharacteristic
159C2×Q8×D5C2313yes—
160C2×Q8×D5C2313yes—
161C2×Q8×D5C2312yes—
162C2×Q8×D5C2316yes—
163C2×Q8×D5C2311yescharacteristic
164#4144—248no—
165#4144—224no—
166C2×#711—248no—
167C2×#711—224no—
168C2×#711C2316yes—
169C2×#711C2311yescharacteristic
170C2×#711C2313yes—
171C2×#711C2316yes—
172C2×#711C2316yes—
173C2×#711C2316yes—
174C2×#711C2316yes—
175C2×#711C2316yes—
176C2×#711C2316yes—
177C2×#711C23112yes—
178C2×#711C2313yes—
179C2×D4×D5C2313yes—
180C2×D4×D5C2313yes—
181C2×D4×D5C2316yes—
182C2×D4×D5C2316yes—
183C2×D4×D5C23112yes—
184C2×D4×D5C2316yes—
185C2×D4×D5C2316yes—
186C2×D4×D5C23112yes—
187C2×D4×D5C2313yes—
188C2×#709C2313yes—
189C2×#709C2313yes—
190C2×#709C23112yes—
191C2×#709C2316yes—
192C2×#709C2316yes—
193C2×#709C2316yes—
194C2×#709C2316yes—
195C2×#709C2313yes—
196C22×D20C2313yes—
197C22×D20C2316yes—
198C22×D20C2316yes—
199C22×C4×D5C2316yes—
200C22×C4×D5C2316yes—
201C22×C4×D5C2316yes—
202C22×C4×D5C2316yes—
203C22×C4×D5C2313yes—
204C22×Dic10C2313yes—
205C22×Dic10C2316yes—
206C5×C4⋊Q8C2313yes—
207C5×#127C2313yes—
208C5×#124C2313yes—
209C5×#124C2316yes—
210C5×#124C23112yes—
211C5×#124C2311yescharacteristic
212C5×#123C23112yes—
213C5×C22⋊Q8C23112yes—
214C5×#121C23112yes—
215C5×#121C23112yes—
216C5×#120C23112yes—
217C4×C5×Q8C2312yes—
218C4×C5×D4C2316yes—
219C4×C5×D4C23112yes—
220C5×#117C2313yes—
221C2×C5×C22⋊C4C23112yes—
222C2×C42×C5C2313yes—
223#4099C23112yes—
224#4093C2313yes—
225#4093C2313yes—
226#4092C23112yes—
227Q8×Dic5C2312yes—
228#4090C2311yescharacteristic
229#4090C2313yes—
230#4090C2316yes—
231#4090C23112yes—
232#4086C2311yescharacteristic
233#4086C2313yes—
234#4086C23112yes—
235#4086C2316yes—
236#4086C23112yes—
237#4085C23124yes—
238#4085C23112yes—
239#4085C23112yes—
240#4084C23112yes—
241#4084C23112yes—
242#4083C23124yes—
243#4083C23112yes—
244#4082C2313yes—
245#4082C2313yes—
246#4081C23112yes—
247D4×Dic5C23112yes—
248D4×Dic5C2316yes—
249#4076C23112yes—
250#4076C23112yes—
251#4075C23112yes—
252C4×C22⋊D5C23112yes—
253C4×C22⋊D5C23112yes—
254C4×C22⋊D5C23112yes—
255C2×#685C23112yes—
256#4072C2313yes—
257#4070C23112yes—
258C2×#683C23112yes—
259C2×C4×Dic5C2316yes—
260C2×C4×Dic5C2313yes—
261#4043C23112yes—
262#4042C23124yes—
263#4041C23112yes—
264#4041C23112yes—
265#4040C23124yes—
266#4039C23112yes—
267#4039C2316yes—
268#4038C2316yes—
269D5×C4⋊C4C23112yes—
270D5×C4⋊C4C2316yes—
271#4034C23112yes—
272#4033C2316yes—
273#4032C23112yes—
274#4031C23112yes—
275#4031C23112yes—
276#4030C23112yes—
277#4030C23124yes—
278#4030C23124yes—
279#4030C23124yes—
280#4030C23124yes—
281#4030C2314yes—
282#4029C23124yes—
283#4028C23124yes—
284#4028C23112yes—
285#4027C23112yes—
286#4027C23124yes—
287#4027C23124yes—
288#4027C23124yes—
289#4027C23112yes—
290#4027C2314yes—
291D5×C22⋊C4C23112yes—
292D5×C22⋊C4C2316yes—
293D5×C22⋊C4C23112yes—
294#4024C23124yes—
295#4023C2316yes—
296#4021C2316yes—
297#4021C2313yes—
298#4021C23112yes—
299#4021C2311yescharacteristic
300#4020C2313yes—
301C4×D20C2316yes—
302C4×D20C23112yes—
303#4018C2316yes—
304C42×D5C2313yes—
305C42×D5C2313yes—
306C42×D5C2311yescharacteristic
307C42×D5C2313yes—
308C42×D5C2316yes—
309C42×D5C2316yes—
310#4015C2313yes—
311C4×Dic10C2316yes—
312C2×#585—51no—
313C2×#585—51no—
314#3500—53no—
315#3500—53no—
316#3500—51no—
317#3500D511yescharacteristic, complemented
318#3499—51no—
319#3499—53no—
320#3498—51no—
321#3498—53no—
322#3497—54no—
323#3496—512no—
324D4×#41—54no—
325D4×#41—512no—
326#3449—53no—
327#3449—53no—
328C2×#532—53no—
329C2×#532—53no—
330C2×C4×#41—51no—
331C24×C5C2416yes—
332C23×D5C2416yes—
333C23×D5C2416yes—
334C23×D5C2416yes—
335C23×D5C2413yes—
336C5×#41—28no—
337C5×#41—224no—
338C5×#41—212no—
339C5×#41—212no—
340C5×#41C2×D418yescomplemented
341C2×C5×Q8—28no—
342C2×C5×Q8—212no—
343C2×C5×Q8C2416yes—
344C2×C5×Q8C2413yes—
345C2×C5×Q8C2411yescharacteristic
346C2×C5×Q8C2411yescharacteristic
347C2×C5×D4—224no—
348C2×C5×D4—212no—
349C2×C5×D4C2416yes—
350C2×C5×D4C2416yes—
351C2×C5×D4C2416yes—
352C2×C5×D4C2413yes—
353C2×C5×D4C2411yescharacteristic
354C2×C5×D4C24112yes—
355C2×C5×D4C2413yes—
356C22×C4×C5C2416yes—
357C22×C4×C5C2416yes—
358C22×C4×C5C2416yes—
359C22×C4×C5C2416yes—
360C22×C4×C5C2413yes—
361C2×C22⋊D5—224no—
362C2×C22⋊D5—248no—
363C2×C22⋊D5—424no—
364C2×C22⋊D5C2416yes—
365C2×C22⋊D5C2412yes—
366C2×C22⋊D5C2416yes—
367C2×C22⋊D5C2416yes—
368C2×C22⋊D5C24112yes—
369C2×C22⋊D5C2416yes—
370C2×C22⋊D5C2416yes—
371C2×C22⋊D5C2414yes—
372C2×C22⋊D5C24112yes—
373C2×C22⋊D5C24124yes—
374C2×C22⋊D5C2416yes—
375C22×Dic5—224no—
376C22×Dic5C24112yes—
377C22×Dic5C2416yes—
378C22×Dic5C2412yes—
379C22×Dic5C2416yes—
380C22×Dic5C2416yes—
381C22×Dic5C2413yes—
382#713—28no—
383#713—224no—
384#713—224no—
385#713—212no—
386#713—224no—
387#713—224no—
388#713—24no—
389#713C2×D418yescomplemented
390Q8×D5—28no—
391Q8×D5—212no—
392Q8×D5—212no—
393Q8×D5—224no—
394Q8×D5C2×D418yescomplemented
395#711—224no—
396#711—248no—
397#711—224no—
398#711—224no—
399#711—224no—
400#711—212no—
401#711—224no—
402#711—224no—
403#711—24no—
404#711—224no—
405#711C2×D4124yescomplemented
406D4×D5—224no—
407D4×D5—224no—
408D4×D5—224no—
409D4×D5—248no—
410D4×D5—224no—
411D4×D5—212no—
412D4×D5—212no—
413D4×D5—424no—
414D4×D5C2×D4124yescomplemented
415#709—212no—
416#709—212no—
417#709—248no—
418#709—224no—
419#709—224no—
420#709—224no—
421#709—224no—
422#709C2×D4124yescomplemented
423C2×D20—224no—
424C2×D20—212no—
425C2×D20—224no—
426C2×D20C2413yes—
427C2×D20C2416yes—
428C2×D20C24112yes—
429C2×D20C2416yes—
430C2×D20C2411yescharacteristic
431C2×D20C2412yes—
432C2×D20C24112yes—
433C2×D20C2413yes—
434C2×C4×D5—224no—
435C2×C4×D5—224no—
436C2×C4×D5—224no—
437C2×C4×D5—412no—
438C2×C4×D5C2×D4124yescomplemented
439C2×C4×D5C2412yes—
440C2×C4×D5C2416yes—
441C2×C4×D5C2412yes—
442C2×C4×D5C2416yes—
443C2×C4×D5C2416yes—
444C2×C4×D5C2416yes—
445C2×C4×D5C2416yes—
446C2×C4×D5C24112yes—
447C2×C4×D5C2416yes—
448C2×C4×D5C2416yes—
449C2×C4×D5C2416yes—
450C2×C4×D5C2413yes—
451C2×C4×D5C2411yescharacteristic
452C2×C4×D5C2413yes—
453C2×C4×D5C2413yes—
454C2×Dic10—212no—
455C2×Dic10—224no—
456C2×Dic10C2413yes—
457C2×Dic10C2416yes—
458C2×Dic10C2416yes—
459C2×Dic10C2411yescharacteristic
460C2×Dic10C2416yes—
461C2×Dic10C2413yes—
462C5×C4⋊C4C2416yes—
463C5×C4⋊C4C24112yes—
464C5×C22⋊C4C24112yes—
465C5×C22⋊C4C24124yes—
466C5×C22⋊C4C2416yes—
467C5×C22⋊C4C2414yes—
468C42×C5C2411yescharacteristic
469C42×C5C2413yes—
470C42×C5C2416yes—
471C22⋊Dic5C2416yes—
472C22⋊Dic5C24112yes—
473C22⋊Dic5C24112yes—
474#685C24112yes—
475#685C2414yes—
476#685C24112yes—
477#685C24124yes—
478#685C24112yes—
479#685C24112yes—
480C4⋊Dic5C2416yes—
481C4⋊Dic5C24112yes—
482#683C24112yes—
483#683C24124yes—
484#683C24112yes—
485#683C2414yes—
486C4×Dic5C2416yes—
487C4×Dic5C2412yes—
488C4×Dic5C2411yescharacteristic
489C4×Dic5C2413yes—
490C4×Dic5C2416yes—
491C4×Dic5C2416yes—
492C4×Dic5C2416yes—
493#585—1016no—
494#585—1016no—
495C2×2−1+4—52no—
496C2×2−1+4—53no—
497C2×2−1+4—51no—
498C2×2−1+4—52no—
499C2×2−1+4—53no—
500C2×2−1+4C2×D511yescharacteristic, complemented
501C2×H(5,𝔽2)—56no—
502C2×H(5,𝔽2)—53no—
503C2×H(5,𝔽2)—51no—
504C2×H(5,𝔽2)—56no—
505C2×H(5,𝔽2)—53no—
506C2×H(5,𝔽2)C2×D511yescharacteristic, complemented
507C22×#41—51no—
508C22×#41—53no—
509C22×#41—53no—
510C22×#41—52no—
511C22×#41—56no—
512C22×#41—53no—
513C22×#41—52no—
514C22×#41—53no—
515C22×#41—56no—
516#550—54no—
517#550—512no—
518D4×Q8—54no—
519D4×Q8—512no—
520#548—512no—
521#548—54no—
522#548—512no—
523#548C2×D514yescomplemented
524#547—512no—
525#547—524no—
526#547—512no—
527#546—512no—
528#546—524no—
529#546—512no—
530#546—512no—
531#546—524no—
532#546C2×D5112yescomplemented
533D42—512no—
534D42—512no—
535D42—524no—
536#537—512no—
537#537—512no—
538#536—53no—
539#536—53no—
540#536—56no—
541#536—56no—
542#536—53no—
543#536C2×D513yescomplemented
544#535—53no—
545#535—53no—
546#535—56no—
547#535—56no—
548#535—53no—
549#535C2×D513yescomplemented
550#534—512no—
551#534—512no—
552#532—53no—
553#532—53no—
554#532—53no—
555#532—53no—
556#532—51no—
557#532—53no—
558#532—56no—
559#532—512no—
560#532—512no—
561#532—56no—
562#532—56no—
563#532—512no—
564#532—512no—
565#532—53no—
566#532C2×D513yescomplemented
567C2×C4⋊Q8—53no—
568C2×C4⋊Q8—53no—
569C2×#127—53no—
570C2×#127—53no—
571C2×#124—53no—
572C2×#124—53no—
573C2×#124—53no—
574C2×#124C2×D513yescomplemented
575#525—512no—
576#525—512no—
577#525—512no—
578#525—512no—
579C2×#121—512no—
580C2×#121—512no—
581C4×#41—51no—
582C4×#41—52no—
583C4×#41—56no—
584C4×#41—53no—
585C4×#41—53no—
586C4×#41C2×D511yescharacteristic, complemented
587C2×C4×Q8—52no—
588C2×C4×D4—56no—
589C2×C4×D4—512no—
590C2×C4×D4—512no—
591C2×#117—53no—
592C22×C42—53no—
593C23×C5—212no—
594C23×C5—412no—
595C23×C5C2512yes—
596C23×C5C2516yes—
597C23×C5C2513yes—
598C22×D5—212no—
599C22×D5—212no—
600C22×D5—212no—
601C22×D5—46no—
602C22×D5—412no—
603C22×D5—412no—
604C22×D5—412no—
605C22×D5C22×D4112yes—
606C22×D5C2516yes—
607C22×D5C2512yes—
608C22×D5C2513yes—
609C22×D5C2511yescharacteristic
610C5×Q8—22no—
611C5×Q8—26no—
612C5×Q8—212no—
613C5×Q8C22×D414yes—
614C5×D4—212no—
615C5×D4—212no—
616C5×D4—22no—
617C5×D4—26no—
618C5×D4—212no—
619C5×D4—412no—
620C5×D4C22×D4112yes—
621C2×C4×C5—212no—
622C2×C4×C5—212no—
623C2×C4×C5—212no—
624C2×C4×C5—46no—
625C2×C4×C5C22×D4112yes—
626C2×C4×C5C2512yes—
627C2×C4×C5C2516yes—
628C2×C4×C5C2516yes—
629C2×C4×C5C2512yes—
630C2×C4×C5C2511yescharacteristic
631C2×C4×C5C2513yes—
632C22⋊D5—212no—
633C22⋊D5—212no—
634C22⋊D5—24no—
635C22⋊D5—224no—
636C22⋊D5—212no—
637C22⋊D5—212no—
638C22⋊D5—212no—
639C22⋊D5—28no—
640C22⋊D5—224no—
641C22⋊D5—424no—
642C22⋊D5C22×D4124yes—
643C2×Dic5—212no—
644C2×Dic5—224no—
645C2×Dic5—24no—
646C2×Dic5—212no—
647C2×Dic5—212no—
648C2×Dic5C22×D4112yes—
649C2×Dic5C2516yes—
650C2×Dic5C2516yes—
651C2×Dic5C2512yes—
652C2×Dic5C2511yescharacteristic
653C2×Dic5C2513yes—
654C2×Dic5C2512yes—
655D20—224no—
656D20—212no—
657D20—24no—
658D20—26no—
659D20—212no—
660D20—22no—
661D20—412no—
662D20C22×D4112yes—
663C4×D5—212no—
664C4×D5—212no—
665C4×D5—212no—
666C4×D5—212no—
667C4×D5—24no—
668C4×D5—212no—
669C4×D5—224no—
670C4×D5—24no—
671C4×D5—212no—
672C4×D5—46no—
673C4×D5—46no—
674C4×D5C22×D4112yes—
675C4×D5C22×D414yes—
676C4×D5C22×D4112yes—
677C4×D5C22×D4112yes—
678Dic10—26no—
679Dic10—212no—
680Dic10—22no—
681Dic10—212no—
682Dic10—212no—
683Dic10C22×D4112yes—
6842−1+4—28no—
6852−1+4—1016no—
6862−1+4—1024no—
6872−1+4—1016no—
6882−1+4—1024no—
6892−1+4—108no—
690H(5,𝔽2)—28no—
691H(5,𝔽2)—1048no—
692H(5,𝔽2)—1024no—
693H(5,𝔽2)—1048no—
694H(5,𝔽2)—1024no—
695H(5,𝔽2)—108no—
696C2×#41—516no—
697C2×#41—51no—
698C2×#41—56no—
699C2×#41—51no—
700C2×#41—53no—
701C2×#41—56no—
702C2×#41—56no—
703C2×#41—56no—
704C2×#41—52no—
705C2×#41—53no—
706C2×#41—56no—
707C2×#41—56no—
708C2×#41—56no—
709C2×#41—51no—
710C2×#41—53no—
711C2×#41—56no—
712C2×#41—56no—
713C2×#41—56no—
714C2×#41—512no—
715C2×#41—56no—
716C2×#41—53no—
717C2×#41—53no—
718C2×#41—53no—
719C2×#41—56no—
720C2×#41—56no—
721C2×#41—56no—
722C2×#41—512no—
723C2×#41—56no—
724C2×#41—1024no—
725C2×#41—1024no—
726C2×#41—1024no—
727C2×#41—1024no—
728C2×#41—1048no—
729C2×#41—1016no—
730C2×#41—1016no—
731C2×#41—1048no—
732C2×#41C22×D513yes—
733C2×#41C22×D513yes—
734C2×#41C22×D516yes—
735C2×#41C22×D512yes—
736C2×#41C22×D511yescharacteristic
737C22×Q8—51no—
738C22×Q8—53no—
739C22×Q8—53no—
740C22×Q8—56no—
741C22×Q8—52no—
742C22×Q8—53no—
743C22×Q8—56no—
744C22×Q8C22×D513yes—
745C22×Q8C22×D512yes—
746C22×D4—53no—
747C22×D4—56no—
748C22×D4—512no—
749C22×D4—512no—
750C22×D4—56no—
751C22×D4—56no—
752C22×D4—53no—
753C22×D4—53no—
754C22×D4—512no—
755C22×D4—56no—
756C22×D4—56no—
757C22×D4—512no—
758C22×D4—56no—
759C22×D4—53no—
760C22×D4—56no—
761C22×D4C22×D513yes—
762C22×D4C22×D516yes—
763C23×C4—53no—
764C23×C4—56no—
765C23×C4—56no—
766C23×C4—56no—
767C23×C4—56no—
768C23×C4—56no—
769C4⋊Q8—51no—
770C4⋊Q8—53no—
771C4⋊Q8—56no—
772C4⋊Q8—512no—
773C4⋊Q8—512no—
774C4⋊Q8—53no—
775C4⋊Q8C22×D513yes—
776#127—51no—
777#127—53no—
778#127—56no—
779#127—512no—
780#127—512no—
781#127—53no—
782#127C22×D513yes—
783#124—53no—
784#124—53no—
785#124—53no—
786#124—53no—
787#124—512no—
788#124—512no—
789#124—51no—
790#124—53no—
791#124—56no—
792#124—512no—
793#124C22×D511yescharacteristic
794#124C22×D513yes—
795#124C22×D516yes—
796#124C22×D5112yes—
797#123—512no—
798#123—512no—
799#123—524no—
800#123—524no—
801#123—512no—
802#123C22×D5112yes—
803C22⋊Q8—512no—
804C22⋊Q8—512no—
805C22⋊Q8—524no—
806C22⋊Q8—512no—
807C22⋊Q8—524no—
808C22⋊Q8C22×D5112yes—
809#121—512no—
810#121—512no—
811#121—512no—
812#121—512no—
813#121—524no—
814#121—512no—
815#121—512no—
816#121—512no—
817#121—512no—
818#121—54no—
819#121—512no—
820#121—524no—
821#121—524no—
822#121—524no—
823#121—524no—
824#121C22×D5112yes—
825#121C22×D5112yes—
826#120—512no—
827#120—512no—
828#120—524no—
829#120—524no—
830#120—512no—
831#120C22×D5112yes—
832C4×Q8—52no—
833C4×Q8—56no—
834C4×Q8—56no—
835C4×Q8C22×D512yes—
836C4×D4—56no—
837C4×D4—512no—
838C4×D4—512no—
839C4×D4—512no—
840C4×D4—512no—
841C4×D4—56no—
842C4×D4—512no—
843C4×D4—54no—
844C4×D4—512no—
845C4×D4—512no—
846C4×D4—524no—
847C4×D4—524no—
848C4×D4—524no—
849C4×D4—56no—
850C4×D4—512no—
851C4×D4C22×D516yes—
852C4×D4C22×D5112yes—
853#117—53no—
854#117—56no—
855#117—56no—
856#117—56no—
857#117C22×D513yes—
858C2×C4⋊C4—512no—
859C2×C4⋊C4—56no—
860C2×C4⋊C4—512no—
861C2×C22⋊C4—512no—
862C2×C22⋊C4—56no—
863C2×C22⋊C4—512no—
864C2×C22⋊C4—512no—
865C2×C22⋊C4C22×D5112yes—
866C2×C42—56no—
867C2×C42—53no—
868C2×C42—53no—
869C2×C42—56no—
870C2×C42—56no—
871C2×C42—53no—
872C2×C42—53no—
873C2×C42—51no—
874C2×C42C22×D513yes—
875C22×C5—26no—
876C22×C5—26no—
877C22×C5—22no—
878C22×C5—212no—
879C22×C5—24no—
880C22×C5—812no—
881C22×C5C23×D416yes—
882C22×C5C2611yescharacteristic
883C2×D5—22no—
884C2×D5—26no—
885C2×D5—26no—
886C2×D5—22no—
887C2×D5—24no—
888C2×D5—212no—
889C2×D5—412no—
890C2×D5—812no—
891C2×D5—812no—
892C2×D5—812no—
893C2×D5C23×D416yes—
894C2×D5C23×D412yes—
895C4×C5—22no—
896C4×C5—26no—
897C4×C5—22no—
898C4×C5—26no—
899C4×C5C23×D412yes—
900C4×C5C23×D416yes—
901Dic5—22no—
902Dic5—26no—
903Dic5—26no—
904Dic5C23×D416yes—
905Dic5C23×D412yes—
906Dic5#58514yescomplemented
907C24—53no—
908C24—56no—
909C24—56no—
910C24—56no—
911C24C23×D516yes—
912#41—28no—
913#41—224no—
914#41—212no—
915#41—212no—
916#41—58no—
917#41—524no—
918#41—524no—
919#41—1024no—
920#41—1024no—
921#41—1048no—
922#41—1024no—
923#41—1024no—
924#41—1024no—
925#41—1024no—
926#41—1012no—
927#41—104no—
928#41—1024no—
929#41—1024no—
930#41—1024no—
931#41—1012no—
932#41—104no—
933#41—1024no—
934#41—1024no—
935#41—1024no—
936#41—1048no—
937#41—1024no—
938#41—1024no—
939#41—108no—
940#41—1024no—
941#41—1012no—
942#41—1012no—
943#41D4×D518yescomplemented
944C2×Q8—28no—
945C2×Q8—212no—
946C2×Q8—58no—
947C2×Q8—53no—
948C2×Q8—56no—
949C2×Q8—56no—
950C2×Q8—56no—
951C2×Q8—51no—
952C2×Q8—53no—
953C2×Q8—1024no—
954C2×Q8—1012no—
955C2×Q8—1012no—
956C2×Q8—1024no—
957C2×Q8—108no—
958C2×Q8—1012no—
959C2×Q8C23×D516yes—
960C2×Q8C23×D511yescharacteristic
961C2×Q8C23×D513yes—
962C2×Q8C23×D511yescharacteristic
963C2×D4—224no—
964C2×D4—212no—
965C2×D4—56no—
966C2×D4—524no—
967C2×D4—54no—
968C2×D4—512no—
969C2×D4—512no—
970C2×D4—56no—
971C2×D4—56no—
972C2×D4—52no—
973C2×D4—56no—
974C2×D4—56no—
975C2×D4—56no—
976C2×D4—524no—
977C2×D4—53no—
978C2×D4—512no—
979C2×D4—52no—
980C2×D4—56no—
981C2×D4—56no—
982C2×D4—51no—
983C2×D4—53no—
984C2×D4—512no—
985C2×D4—1024no—
986C2×D4—1024no—
987C2×D4—1012no—
988C2×D4—1012no—
989C2×D4—1048no—
990C2×D4—1024no—
991C2×D4—1024no—
992C2×D4—1024no—
993C2×D4—1048no—
994C2×D4—1024no—
995C2×D4—1024no—
996C2×D4—1012no—
997C2×D4—2024no—
998C2×D4—2024no—
999C2×D4C23×D516yes—
1000C2×D4C23×D516yes—
1001C2×D4C23×D516yes—
1002C2×D4C23×D511yescharacteristic
1003C2×D4C23×D513yes—
1004C2×D4C23×D5112yes—
1005C2×D4C23×D513yes—
1006C22×C4—53no—
1007C22×C4—524no—
1008C22×C4—51no—
1009C22×C4—53no—
1010C22×C4—53no—
1011C22×C4—53no—
1012C22×C4—56no—
1013C22×C4—56no—
1014C22×C4—52no—
1015C22×C4—56no—
1016C22×C4—512no—
1017C22×C4—52no—
1018C22×C4—56no—
1019C22×C4—56no—
1020C22×C4—56no—
1021C22×C4—52no—
1022C22×C4—56no—
1023C22×C4—512no—
1024C22×C4—56no—
1025C22×C4—56no—
1026C22×C4—56no—
1027C22×C4—56no—
1028C22×C4—1024no—
1029C22×C4—1024no—
1030C22×C4—1024no—
1031C22×C4—1024no—
1032C22×C4—2012no—
1033C22×C4C23×D516yes—
1034C22×C4C23×D516yes—
1035C22×C4C23×D516yes—
1036C22×C4C23×D516yes—
1037C22×C4C23×D513yes—
1038C4⋊C4—54no—
1039C4⋊C4—512no—
1040C4⋊C4—512no—
1041C4⋊C4—56no—
1042C4⋊C4—524no—
1043C4⋊C4—512no—
1044C4⋊C4C23×D516yes—
1045C4⋊C4C23×D5112yes—
1046C22⋊C4—56no—
1047C22⋊C4—512no—
1048C22⋊C4—512no—
1049C22⋊C4—512no—
1050C22⋊C4—54no—
1051C22⋊C4—512no—
1052C22⋊C4—512no—
1053C22⋊C4—512no—
1054C22⋊C4—524no—
1055C22⋊C4C23×D514yes—
1056C22⋊C4C23×D5112yes—
1057C22⋊C4C23×D516yes—
1058C22⋊C4C23×D5124yes—
1059C42—52no—
1060C42—51no—
1061C42—56no—
1062C42—53no—
1063C42—56no—
1064C42—56no—
1065C42—56no—
1066C42C23×D511yescharacteristic
1067C42C23×D513yes—
1068C42C23×D516yes—
1069C2×C5—26no—
1070C2×C5—42no—
1071C2×C5—46no—
1072C2×C5C24×D411yescharacteristic
1073C2×C5C2×#58512yes—
1074D5—22no—
1075D5—26no—
1076D5—46no—
1077D5—42no—
1078C23—212no—
1079C23—412no—
1080C23—53no—
1081C23—51no—
1082C23—512no—
1083C23—52no—
1084C23—56no—
1085C23—1012no—
1086C23—1012no—
1087C23—1012no—
1088C23—206no—
1089C23—2012no—
1090C23—2012no—
1091C23—2012no—
1092C23C24×D512yes—
1093C23C24×D516yes—
1094C23C24×D513yes—
1095Q8—212no—
1096Q8—26no—
1097Q8—22no—
1098Q8—512no—
1099Q8—1012no—
1100Q8—1012no—
1101Q8—1012no—
1102Q8—102no—
1103Q8—106no—
1104Q8C2×D4×D514yes—
1105D4—212no—
1106D4—212no—
1107D4—212no—
1108D4—26no—
1109D4—22no—
1110D4—412no—
1111D4—524no—
1112D4—512no—
1113D4—104no—
1114D4—1012no—
1115D4—1024no—
1116D4—1012no—
1117D4—1012no—
1118D4—108no—
1119D4—1024no—
1120D4—104no—
1121D4—1012no—
1122D4—1024no—
1123D4—1012no—
1124D4—1012no—
1125D4—1012no—
1126D4—102no—
1127D4—106no—
1128D4—2012no—
1129D4—2024no—
1130D4C2×D4×D5112yes—
1131C2×C4—212no—
1132C2×C4—212no—
1133C2×C4—212no—
1134C2×C4—46no—
1135C2×C4—512no—
1136C2×C4—52no—
1137C2×C4—51no—
1138C2×C4—53no—
1139C2×C4—54no—
1140C2×C4—512no—
1141C2×C4—512no—
1142C2×C4—512no—
1143C2×C4—56no—
1144C2×C4—52no—
1145C2×C4—56no—
1146C2×C4—104no—
1147C2×C4—1012no—
1148C2×C4—1024no—
1149C2×C4—104no—
1150C2×C4—1012no—
1151C2×C4—1012no—
1152C2×C4—1012no—
1153C2×C4—104no—
1154C2×C4—1012no—
1155C2×C4—1024no—
1156C2×C4—1012no—
1157C2×C4—1012no—
1158C2×C4—1012no—
1159C2×C4—1012no—
1160C2×C4—206no—
1161C2×C4—206no—
1162C2×C4C2×D4×D5112yes—
1163C2×C4C24×D512yes—
1164C2×C4C24×D516yes—
1165C2×C4C24×D512yes—
1166C2×C4C24×D516yes—
1167C2×C4C24×D511yescharacteristic
1168C2×C4C24×D513yes—
1169C5#6281211yescharacteristic, complemented, Sylow
1170C22—26no—
1171C22—22no—
1172C22—26no—
1173C22—24no—
1174C22—212no—
1175C22—52no—
1176C22—56no—
1177C22—812no—
1178C22—102no—
1179C22—106no—
1180C22—106no—
1181C22—102no—
1182C22—104no—
1183C22—1012no—
1184C22—2012no—
1185C22—4012no—
1186C22—4012no—
1187C22—4012no—
1188C22C22×D4×D516yes—
1189C22C25×D511yescharacteristic
1190C4—22no—
1191C4—26no—
1192C4—22no—
1193C4—26no—
1194C4—52no—
1195C4—56no—
1196C4—54no—
1197C4—102no—
1198C4—106no—
1199C4—106no—
1200C4C22×D4×D516yes—
1201C4C22×D4×D512yes—
1202C2—26no—
1203C2—46no—
1204C2—42no—
1205C2—102no—
1206C2—106no—
1207C2—206no—
1208C2—202no—
1209C2C23×D4×D511yescharacteristic
1210C2D5×#58512yes—
subgroupG/H
center, FrattiniC22C25×D5
commutator, socle, cosocleC22×C5C26
FittingC5×#3500C2
hypercenter#3500D5
hypocenterC5#62812
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ #3500

Complements

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

NH ≅ G/Ntype
1. C2×#66287C2semidirect
2. C2×#66285C2semidirect
3. C5×#3500C2semidirect
4. #10619193C2semidirect
5. #10619183C2semidirect
6. #10618638C2semidirect
7. #10618611C2semidirect
8. #10618566C2semidirect
9. #10618527C2semidirect
10. #10618241C2semidirect
11. #10618239C2semidirect
12. #10618217C2semidirect
13. #10618214C2semidirect
14. #10618145C2semidirect
15. D5×#532C2semidirect
16. #10617977C2semidirect
17. C2×#66002C2semidirect
18. #10617748C2semidirect
19. C4×D5×#41C2semidirect
20. C2×C5×2−1+4C22semidirect
21. C2×C5×H(5,𝔽2)C22semidirect
24. C2×#4150C22semidirect
25. C2×#4150C22semidirect
26. C2×#4150C22semidirect
27. C2×#4149C22semidirect
28. C2×#4149C22semidirect
29. C2×#4149C22semidirect
31. C2×D5×#41C22semidirect
32. C2×D5×#41C22semidirect
33. C2×D5×#41C22semidirect
34. C2×D5×#41C22semidirect
35. C2×#4147C22semidirect
36. C2×#4147C22semidirect
37. C22×#713C22semidirect
38. C22×#713C22semidirect
39. C2×#4144C22semidirect
40. C2×#4144C22semidirect
41. C22×#711C22semidirect
42. C22×#711C22semidirect
43. C5×#548C22semidirect
44. C5×#546C22semidirect
45. C5×#536C22semidirect
46. C5×#535C22semidirect
47. C5×#532C22semidirect
48. C2×C5×#124C22semidirect
49. C4×C5×#41C22semidirect
50. #66168C22semidirect
51. #66166C22semidirect
52. #66166C22semidirect
53. #66164C22semidirect
54. #41×Dic5C22semidirect
55. #66159C22semidirect
56. #66158C22semidirect
57. #66150C22semidirect
58. Q8×C22⋊D5C22semidirect
59. C2×#4090C22semidirect
60. #66139C22semidirect
61. C2×#4086C22semidirect
62. D4×C22⋊D5C22semidirect
63. #66059C22semidirect
64. #66058C22semidirect
65. D5×C4⋊Q8C22semidirect
66. #66050C22semidirect
67. #66049C22semidirect
68. D5×#127C22semidirect
69. #66011C22semidirect
70. #66010C22semidirect
71. #66009C22semidirect
72. #66008C22semidirect
73. D5×#124C22semidirect
74. D5×#124C22semidirect
75. #66002C22semidirect
76. #66002C22semidirect
77. #66002C22semidirect
78. #66002C22semidirect
79. #66002C22semidirect
80. #66002C22semidirect
81. #66002C22semidirect
82. #65990C22semidirect
83. #65989C22semidirect
84. #65987C22semidirect
85. #65966C22semidirect
86. #65965C22semidirect
87. #65963C22semidirect
88. #65961C22semidirect
89. #65944C22semidirect
90. #65943C22semidirect
91. #65942C22semidirect
92. #65940C22semidirect
93. D5×#121C22semidirect
94. #65933C22semidirect
95. #65930C22semidirect
96. #65924C22semidirect
97. #65923C22semidirect
98. #65920C22semidirect
99. #65910C22semidirect
100. C4×#713C22semidirect
101. C4×Q8×D5C22semidirect
102. #65888C22semidirect
103. #65886C22semidirect
104. #65884C22semidirect
105. #65882C22semidirect
106. C4×D4×D5C22semidirect
107. C4×D4×D5C22semidirect
108. C4×#711C22semidirect
109. #65860C22semidirect
110. #65859C22semidirect
111. #65856C22semidirect
112. D5×#117C22semidirect
113. #65824C22semidirect
114. C2×#4030C22semidirect
115. C2×#4027C22semidirect
116. #65811C22semidirect
117. C2×#4021C22semidirect
118. C4×#709C22semidirect
119. C2×C42×D5C22semidirect
146. D5×#41D4semidirect
317. #3500D5semidirect
340. C5×#41C2×D4semidirect
389. #713C2×D4semidirect
394. Q8×D5C2×D4semidirect
405. #711C2×D4semidirect
414. D4×D5C2×D4semidirect
422. #709C2×D4semidirect
438. C2×C4×D5C2×D4semidirect
500. C2×2−1+4C2×D5semidirect
506. C2×H(5,𝔽2)C2×D5semidirect
523. #548C2×D5semidirect
532. #546C2×D5semidirect
543. #536C2×D5semidirect
549. #535C2×D5semidirect
566. #532C2×D5semidirect
574. C2×#124C2×D5semidirect
586. C4×#41C2×D5semidirect
906. Dic5#585semidirect
943. #41D4×D5semidirect
1169. C5#62812semidirect

Maximal subgroups

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

subgroupindex
C2×#662872
C2×#662852
C5×#35002
#106191932
#106191832
#106186382
#106186112
#106185662
#106185272
#106182412
#106182392
#106182172
#106182142
#106181452
D5×#5322
#106179772
C2×#660022
#106177482
C4×D5×#412
#628125