Finite Group Databasebeta

← C2×#10619107 #13013132

Subgroups — C2×#10619107 #13013132

Order 1280.

10858 conjugacy classes of subgroups.

The subgroup lattice has 1108 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66287C211yesmaximal, characteristic, complemented
2C2×#66285C211yesmaximal, characteristic, complemented
3C2×C5×#577C211yesmaximal, characteristic, complemented
4C2×#66172C211yesmaximal, characteristic, complemented
5C2×#66169C211yesmaximal, characteristic, complemented
6#10619107C2132yesmaximal, direct product factor
7C2×#66113C213yesmaximal, complemented
8C2×#66111C213yesmaximal, complemented
9C2×#66108C213yesmaximal, complemented
10C2×#66107C213yesmaximal, complemented
11C2×#66104C213yesmaximal, complemented
12C2×D5×#135C213yesmaximal, complemented
13C2×#66096C213yesmaximal, complemented
14C22×#4062C213yesmaximal, complemented
15C2×#66085C211yesmaximal, characteristic, complemented
16C2×D5×#131C211yesmaximal, characteristic, complemented
17C2×C5×2−1+4C2211yescharacteristic, complemented
18C2×C5×H(5,𝔽2)C2211yescharacteristic, complemented
19#66287—28no—
20#66287C22116yescomplemented
21#66285—28no—
22#66285C22116yescomplemented
23C2×#4150—21no—
24C2×#4150C2213yescomplemented
25C2×#4150C2211yescharacteristic, complemented
26C2×#4149—23no—
27C2×#4149C2213yescomplemented
28C2×#4149C2211yescharacteristic, complemented
29C2×D5×#41—21no—
30C2×D5×#41—23no—
31C2×D5×#41C2211yescharacteristic
32C2×D5×#41C2213yescomplemented
33C2×D5×#41C2213yescomplemented
34C2×#4147—21no—
35C2×#4147C2213yescomplemented
36C22×#713—21no—
37C22×#713C2213yescomplemented
38C2×#4144—23no—
39C2×#4144C2213yescomplemented
40C22×#711—23no—
41C22×#711C2213yescomplemented
42C5×#577C22116yescomplemented
43C2×C5×#137C2213yescomplemented
44C2×C5×AGL(1,ℤ/8)C2213yescomplemented
45C2×C5×#135C2213yescomplemented
46C22×C5×SD16C2213yescomplemented
47C2×C5×#131C2211yescharacteristic, complemented
48#66172C22116yescomplemented
49#66169C22116yescomplemented
50C2×#4097C2213yescomplemented
51C2×#4096C2213yescomplemented
52C2×#4096C2213yescomplemented
53C2×#4095C2213yescomplemented
54C2×#4094C2211yescharacteristic, complemented
55C22×#689C2213yescomplemented
56C2×#4088C2213yescomplemented
57C2×#4078C2213yescomplemented
58C22×#686C2213yescomplemented
59#66113C22148yescomplemented
60#66111C22148yescomplemented
61#66108C22148yescomplemented
62#66107C22148yescomplemented
63#66104C22148yescomplemented
64D5×#135C22148yescomplemented
65C2×#4065C2213yescomplemented
66C2×#4064C2216yescomplemented
67C2×D5×Q16C2213yescomplemented
68#66096C22148yescomplemented
69C2×#4062C2213yescomplemented
70C2×#4062C2216yescomplemented
71C2×#4062C2216yescomplemented
72C2×#4062C2216yescomplemented
73C2×#4062C2211yescharacteristic, complemented
74C2×#4062C22148yescomplemented
75C2×#4061C2216yescomplemented
76C2×#4060C2216yescomplemented
77C2×D5×SD16C2213yescomplemented
78C2×D5×SD16C2213yescomplemented
79C2×#4058C2213yescomplemented
80C2×#4057C2216yescomplemented
81C2×D5×D8C2213yescomplemented
82#66085C22116yescomplemented
83D5×#131C22116yescomplemented
84C2×#4055C2213yescomplemented
85C2×#4054C2213yescomplemented
86C2×#4053C2213yescomplemented
87C2×D5×M16C2213yescomplemented
88C2×#4050C2213yescomplemented
89C22×#677C2213yescomplemented
90C2×#4047C2213yescomplemented
91C22×C8×D5C2213yescomplemented
92C2×#3584—51nomaximal, Sylow
93C5×2−1+4—24no—
94C5×2−1+4C2318yescomplemented
95C5×H(5,𝔽2)—24no—
96C5×H(5,𝔽2)C2318yescomplemented
97C2×C5×#41—21no—
98C2×C5×#41—23no—
99C2×C5×#41C2313yes—
100C2×C5×#41C2313yes—
101C2×C5×#41C2311yescharacteristic
102C22×C5×Q8—21no—
103C22×C5×Q8C2313yes—
104C22×C5×D4—23no—
105C22×C5×D4C2313yes—
106C22×C22⋊D5—23no—
107C22×C22⋊D5—26no—
108C23×Dic5—23no—
109#4150—24no—
110#4150—216no—
111#4150—212no—
112#4150C23124yescomplemented
113#4150C2318yescomplemented
114#4149—24no—
115#4149—248no—
116#4149—212no—
117#4149C23124yescomplemented
118#4149C2318yescomplemented
119D5×#41—216no—
120D5×#41—248no—
121D5×#41—212no—
122D5×#41—212no—
123D5×#41D418yes—
124D5×#41C2318yes—
125D5×#41C23124yescomplemented
126D5×#41C23124yescomplemented
127#4147—216no—
128#4147—212no—
129#4147C23124yescomplemented
130C2×#713—21no—
131C2×#713—216no—
132C2×#713—23no—
133C2×#713—23no—
134C2×#713—23no—
135C2×#713—212no—
136C2×#713D411yescharacteristic
137C2×#713C2316yes—
138C2×#713C2313yes—
139C2×#713C2311yescharacteristic
140C2×#713C23124yescomplemented
141C2×Q8×D5—21no—
142C2×Q8×D5—23no—
143C2×Q8×D5D411yescharacteristic
144C2×Q8×D5C2313yes—
145C2×Q8×D5C2313yes—
146#4144—248no—
147#4144—212no—
148#4144C23124yescomplemented
149C2×#711—23no—
150C2×#711—26no—
151C2×#711—23no—
152C2×#711—23no—
153C2×#711—248no—
154C2×#711—23no—
155C2×#711—23no—
156C2×#711—212no—
157C2×#711—23no—
158C2×#711D413yes—
159C2×#711C2316yes—
160C2×#711C2311yescharacteristic
161C2×#711C2313yes—
162C2×#711C23124yescomplemented
163C2×D4×D5—23no—
164C2×D4×D5—23no—
165C2×D4×D5—23no—
166C2×D4×D5—26no—
167C2×D4×D5—23no—
168C2×D4×D5D413yes—
169C2×D4×D5C2313yes—
170C2×D4×D5C2313yes—
171C2×#709—26no—
172C2×#709—23no—
173C2×#709—23no—
174C2×#709—23no—
175C2×#709—23no—
176C2×#709C2313yes—
177C2×#709C2313yes—
178C2×#709C2313yes—
179C22×D20—23no—
180C22×D20—23no—
181C22×D20C2313yes—
182C22×C4×D5—23no—
183C22×C4×D5—23no—
184C22×C4×D5—23no—
185C22×C4×D5C2313yes—
186C22×Dic10—23no—
187C22×Dic10C2313yes—
188C5×#137C23124yescomplemented
189C5×AGL(1,ℤ/8)C23124yescomplemented
190C5×#135C23124yescomplemented
191C2×C5×Q16C2313yes—
192C2×C5×SD16C2311yescharacteristic
193C2×C5×SD16C2313yes—
194C2×C5×SD16C2316yes—
195C2×C5×SD16C23124yescomplemented
196C2×C5×D8C2313yes—
197C5×#131C2318yescomplemented
198C2×C5×M16C2313yes—
199C22×C5×C8C2313yes—
200#4097C23124yescomplemented
201#4096C23124yescomplemented
202#4096C23124yescomplemented
203#4095C23124yescomplemented
204#4094C2318yescomplemented
205C2×#689C2316yes—
206C2×#689C2313yes—
207C2×#689C2311yescharacteristic
208C2×#689C23124yescomplemented
209#4088C23124yescomplemented
210C2×#688C2313yes—
211C2×#688C2313yes—
212C2×#687C2313yes—
213C2×#687C2313yes—
214#4078C23124yescomplemented
215C2×#686C2311yescharacteristic
216C2×#686C2313yes—
217C2×#686C2316yes—
218C2×#686C23124yescomplemented
219C2×#681C2313yes—
220C22×#168C2313yes—
221#4065C23124yescomplemented
222#4064C23148yescomplemented
223D5×Q16C23124yescomplemented
224#4062C23124yescomplemented
225#4062C23148yescomplemented
226#4062C23148yescomplemented
227#4062C23148yescomplemented
228#4062C2318yescomplemented
229#4061C23148yescomplemented
230#4060C23148yescomplemented
231D5×SD16C23124yescomplemented
232D5×SD16C23124yescomplemented
233#4058C23124yescomplemented
234#4057C23148yescomplemented
235D5×D8C23124yescomplemented
236#4055C23124yescomplemented
237#4054C23124yescomplemented
238#4053C23124yescomplemented
239D5×M16C23124yescomplemented
240C2×Dic20C2313yes—
241#4050C23124yescomplemented
242C2×D40C2313yes—
243C2×#677C2313yes—
244C2×#677C2316yes—
245C2×#677C2311yescharacteristic
246C2×#677C23124yescomplemented
247#4047C23124yescomplemented
248C2×#676C2316yes—
249C2×C8×D5C2311yescharacteristic
250C2×C8×D5C2313yes—
251C2×C8×D5C2313yes—
252C2×C8×D5C2313yes—
253C2×C8×D5C23124yescomplemented
254C2×#585—51no—
255C2×#585—51no—
256#3584—532no—
257C2×#578—51no—
258C2×#578—53no—
259C2×#577—53no—
260C2×#577—53no—
261C2×#577—51no—
262C2×#577D511yescharacteristic, complemented
263C2×#576—51no—
264C2×#576—53no—
265C2×#575—53no—
266C2×#575—53no—
267C22×#135—53no—
268C22×#135—53no—
269C22×#131—51no—
270C24×C5—23no—
271C23×D5—23no—
272C23×D5—23no—
273C23×D5—23no—
274C23×D5C2×D413yes—
275C5×#41—28no—
276C5×#41—224no—
277C5×#41—26no—
278C5×#41—26no—
279C5×#41C2×D414yes—
280C5×#41C24112yes—
281C5×#41C24112yes—
282C5×#41C2414yes—
283C2×C5×Q8—28no—
284C2×C5×Q8—23no—
285C2×C5×Q8—26no—
286C2×C5×Q8C2×D411yescharacteristic
287C2×C5×Q8C2413yes—
288C2×C5×Q8C2411yescharacteristic
289C2×C5×Q8C24112yes—
290C2×C5×D4—23no—
291C2×C5×D4—23no—
292C2×C5×D4—224no—
293C2×C5×D4—23no—
294C2×C5×D4—26no—
295C2×C5×D4C2×D413yes—
296C2×C5×D4C2411yescharacteristic
297C2×C5×D4C2413yes—
298C2×C5×D4C24112yes—
299C22×C4×C5—23no—
300C22×C4×C5—23no—
301C22×C4×C5—23no—
302C22×C4×C5C2413yes—
303C2×C22⋊D5—23no—
304C2×C22⋊D5—23no—
305C2×C22⋊D5—21no—
306C2×C22⋊D5—26no—
307C2×C22⋊D5—23no—
308C2×C22⋊D5—224no—
309C2×C22⋊D5—248no—
310C2×C22⋊D5—23no—
311C2×C22⋊D5—23no—
312C2×C22⋊D5C2×D416yes—
313C22×Dic5—23no—
314C22×Dic5—26no—
315C22×Dic5—21no—
316C22×Dic5—23no—
317C22×Dic5—224no—
318C22×Dic5C2×D413yes—
319#713—28no—
320#713—224no—
321#713—26no—
322#713—224no—
323#713—212no—
324#713—224no—
325#713—22no—
326#713C2×D418yes—
327#713C24112yes—
328#713C24124yes—
329#713C2414yes—
330Q8×D5—28no—
331Q8×D5—26no—
332Q8×D5—26no—
333Q8×D5—224no—
334Q8×D5C2×D418yes—
335Q8×D5C24112yes—
336Q8×D5C24112yes—
337#711—224no—
338#711—248no—
339#711—224no—
340#711—224no—
341#711—26no—
342#711—224no—
343#711—212no—
344#711—224no—
345#711—22no—
346#711—224no—
347#711C2×D4124yes—
348#711C24112yes—
349#711C24124yes—
350#711C2414yes—
351D4×D5—224no—
352D4×D5—224no—
353D4×D5—224no—
354D4×D5—248no—
355D4×D5—224no—
356D4×D5—26no—
357D4×D5—26no—
358D4×D5C2×D4124yes—
359D4×D5C24112yes—
360D4×D5C24112yes—
361#709—26no—
362#709—26no—
363#709—248no—
364#709—224no—
365#709—224no—
366#709—224no—
367#709—224no—
368#709C2×D4112yes—
369#709C24112yes—
370#709C24112yes—
371#709C24112yes—
372C2×D20—26no—
373C2×D20—23no—
374C2×D20—224no—
375C2×D20—21no—
376C2×D20—23no—
377C2×D20—26no—
378C2×D20—224no—
379C2×D20C2×D413yes—
380C2×D20C2413yes—
381C2×D20C24112yes—
382C2×D20C2411yescharacteristic
383C2×C4×D5—23no—
384C2×C4×D5—23no—
385C2×C4×D5—23no—
386C2×C4×D5—23no—
387C2×C4×D5—21no—
388C2×C4×D5—23no—
389C2×C4×D5—26no—
390C2×C4×D5—224no—
391C2×C4×D5—224no—
392C2×C4×D5—224no—
393C2×C4×D5C2×D413yes—
394C2×C4×D5C2×D413yes—
395C2×C4×D5C2×D4112yes—
396C2×C4×D5C2411yescharacteristic
397C2×C4×D5C2413yes—
398C2×C4×D5C24112yes—
399C2×Dic10—23no—
400C2×Dic10—26no—
401C2×Dic10—23no—
402C2×Dic10—23no—
403C2×Dic10—224no—
404C2×Dic10C2×D413yes—
405C2×Dic10C24112yes—
406C2×Dic10C2413yes—
407C2×Dic10C2411yescharacteristic
408C5×Q16C24112yes—
409C5×SD16C24112yes—
410C5×SD16C24124yes—
411C5×SD16C2414yes—
412C5×D8C24112yes—
413C5×M16C24112yes—
414C2×C5×C8C2411yescharacteristic
415C2×C5×C8C2413yes—
416C2×C5×C8C24112yes—
417#689C2414yes—
418#689C24112yes—
419#689C24124yes—
420#688C24112yes—
421#688C24112yes—
422#687C24112yes—
423#687C24112yes—
424#686C2414yes—
425#686C24112yes—
426#686C24124yes—
427#681C24112yes—
428C2×#168C24112yes—
429C2×#168C2411yescharacteristic
430C2×#168C2413yes—
431Dic20C24112yes—
432D40C24112yes—
433#677C24112yes—
434#677C24124yes—
435#677C2414yes—
436#676C24124yes—
437C8×D5C2414yes—
438C8×D5C24112yes—
439C8×D5C24112yes—
440C8×D5C24112yes—
441#585—516no—
442#585—516no—
443#585—108no—
444#585—108no—
445C2×2−1+4—53no—
446C2×2−1+4—51no—
447C2×2−1+4—53no—
448C2×2−1+4—101no—
449C2×2−1+4—101no—
450C2×2−1+4C2×D511yescharacteristic, complemented
451C2×H(5,𝔽2)—53no—
452C2×H(5,𝔽2)—51no—
453C2×H(5,𝔽2)—53no—
454C2×H(5,𝔽2)—103no—
455C2×H(5,𝔽2)—103no—
456C2×H(5,𝔽2)C2×D511yescharacteristic, complemented
457C22×#41—51no—
458C22×#41—53no—
459C22×#41—53no—
460C22×#41—53no—
461C22×#41—53no—
462C22×#41—103no—
463C22×#41—101no—
464C22×#41—101no—
465C22×#41—103no—
466#578—516no—
467#578—548no—
468#577—548no—
469#577—548no—
470#577—516no—
471#577C2×D5116yescomplemented
472#576—516no—
473#576—548no—
474#575—548no—
475#575—548no—
476C2×#137—53no—
477C2×#137—53no—
478C2×#137—56no—
479C2×#137—56no—
480C2×#137—53no—
481C2×#137C2×D513yescomplemented
482C2×AGL(1,ℤ/8)—53no—
483C2×AGL(1,ℤ/8)—53no—
484C2×AGL(1,ℤ/8)—56no—
485C2×AGL(1,ℤ/8)—56no—
486C2×AGL(1,ℤ/8)—53no—
487C2×AGL(1,ℤ/8)C2×D513yescomplemented
488C2×#135—53no—
489C2×#135—53no—
490C2×#135—548no—
491C2×#135—53no—
492C2×#135—51no—
493C2×#135—53no—
494C2×#135—56no—
495C2×#135—56no—
496C2×#135—56no—
497C2×#135—548no—
498C2×#135—53no—
499C2×#135—53no—
500C2×#135C2×D513yescomplemented
501C22×Q16—53no—
502C22×Q16—53no—
503C22×SD16—53no—
504C22×SD16—53no—
505C22×SD16—53no—
506C22×SD16C2×D513yescomplemented
507C22×D8—53no—
508C22×D8—53no—
509C2×#131—51no—
510C2×#131—516no—
511C2×#131—53no—
512C2×#131—53no—
513C2×#131C2×D511yescharacteristic, complemented
514C22×M16—53no—
515C23×C8—53no—
516C23×C5—23no—
517C23×C5—21no—
518C23×C5—212no—
519C23×C5—86no—
520C23×C5C22×D413yes—
521C22×D5—23no—
522C22×D5—21no—
523C22×D5—212no—
524C22×D5—212no—
525C22×D5—212no—
526C22×D5—46no—
527C22×D5—86no—
528C22×D5—86no—
529C22×D5—86no—
530C22×D5C22×D413yes—
531C22×D5C22×D411yescharacteristic
532C22×D5C22×D4112yes—
533C5×Q8—21no—
534C5×Q8—23no—
535C5×Q8—212no—
536C5×Q8C22×D414yes—
537C5×Q8C2512yes—
538C5×Q8C2516yes—
539C5×D4—212no—
540C5×D4—212no—
541C5×D4—21no—
542C5×D4—23no—
543C5×D4—212no—
544C5×D4C22×D4112yes—
545C5×D4C2516yes—
546C5×D4C2512yes—
547C2×C4×C5—21no—
548C2×C4×C5—23no—
549C2×C4×C5—212no—
550C2×C4×C5—212no—
551C2×C4×C5—212no—
552C2×C4×C5C22×D413yes—
553C2×C4×C5C22×D416yes—
554C2×C4×C5C2511yescharacteristic
555C2×C4×C5C2516yes—
556C22⋊D5—212no—
557C22⋊D5—212no—
558C22⋊D5—24no—
559C22⋊D5—224no—
560C22⋊D5—212no—
561C22⋊D5—212no—
562C22⋊D5—212no—
563C22⋊D5C22×D4124yes—
564C2×Dic5—21no—
565C2×Dic5—23no—
566C2×Dic5—212no—
567C2×Dic5—224no—
568C2×Dic5—24no—
569C2×Dic5—212no—
570C2×Dic5C22×D413yes—
571C2×Dic5C22×D411yescharacteristic
572C2×Dic5C22×D4112yes—
573D20—224no—
574D20—212no—
575D20—24no—
576D20—23no—
577D20—212no—
578D20—21no—
579D20C22×D4112yes—
580D20C2516yes—
581D20C2512yes—
582C4×D5—212no—
583C4×D5—212no—
584C4×D5—212no—
585C4×D5—212no—
586C4×D5—24no—
587C4×D5—212no—
588C4×D5—224no—
589C4×D5C22×D4112yes—
590C4×D5C22×D412yes—
591C4×D5C22×D4112yes—
592C4×D5C22×D416yes—
593C4×D5C2512yes—
594C4×D5C2516yes—
595Dic10—23no—
596Dic10—212no—
597Dic10—21no—
598Dic10—212no—
599Dic10—212no—
600Dic10C22×D4112yes—
601Dic10C2516yes—
602Dic10C2512yes—
603C5×C8C2512yes—
604C5×C8C2516yes—
605#168C2512yes—
606#168C2516yes—
6072−1+4—24no—
6082−1+4—524no—
6092−1+4—58no—
6102−1+4—524no—
6112−1+4—1016no—
6122−1+4—1012no—
6132−1+4—1016no—
6142−1+4—1012no—
6152−1+4—104no—
6162−1+4C22×D518yescomplemented
617H(5,𝔽2)—24no—
618H(5,𝔽2)—524no—
619H(5,𝔽2)—58no—
620H(5,𝔽2)—524no—
621H(5,𝔽2)—1048no—
622H(5,𝔽2)—1012no—
623H(5,𝔽2)—1048no—
624H(5,𝔽2)—1012no—
625H(5,𝔽2)—104no—
626H(5,𝔽2)C22×D518yescomplemented
627C2×#41—21no—
628C2×#41—23no—
629C2×#41—58no—
630C2×#41—58no—
631C2×#41—51no—
632C2×#41—53no—
633C2×#41—53no—
634C2×#41—524no—
635C2×#41—524no—
636C2×#41—51no—
637C2×#41—53no—
638C2×#41—56no—
639C2×#41—524no—
640C2×#41—53no—
641C2×#41—51no—
642C2×#41—56no—
643C2×#41—524no—
644C2×#41—53no—
645C2×#41—53no—
646C2×#41—103no—
647C2×#41—103no—
648C2×#41—106no—
649C2×#41—103no—
650C2×#41—103no—
651C2×#41—103no—
652C2×#41—103no—
653C2×#41—103no—
654C2×#41—103no—
655C2×#41—1012no—
656C2×#41—103no—
657C2×#41—103no—
658C2×#41—1012no—
659C2×#41—1012no—
660C2×#41—1012no—
661C2×#41—106no—
662C2×#41—103no—
663C2×#41—1048no—
664C2×#41—103no—
665C2×#41—1016no—
666C2×#41—1016no—
667C2×#41—1048no—
668C2×#41—101no—
669C2×#41—103no—
670C2×#41C22×D513yes—
671C2×#41C22×D513yes—
672C2×#41C22×D511yescharacteristic
673C22×Q8—21no—
674C22×Q8—51no—
675C22×Q8—53no—
676C22×Q8—53no—
677C22×Q8—53no—
678C22×Q8—103no—
679C22×Q8—103no—
680C22×Q8—101no—
681C22×Q8C22×D513yes—
682C22×D4—23no—
683C22×D4—53no—
684C22×D4—53no—
685C22×D4—53no—
686C22×D4—53no—
687C22×D4—103no—
688C22×D4—103no—
689C22×D4—106no—
690C22×D4—103no—
691C22×D4—103no—
692C22×D4—103no—
693C22×D4—106no—
694C22×D4—103no—
695C22×D4—103no—
696C22×D4C22×D513yes—
697C23×C4—53no—
698C23×C4—103no—
699C23×C4—103no—
700C23×C4—103no—
701C23×C4—103no—
702#137—524no—
703#137—524no—
704#137—548no—
705#137—548no—
706#137—524no—
707#137C22×D5124yescomplemented
708AGL(1,ℤ/8)—524no—
709AGL(1,ℤ/8)—524no—
710AGL(1,ℤ/8)—548no—
711AGL(1,ℤ/8)—548no—
712AGL(1,ℤ/8)—524no—
713AGL(1,ℤ/8)C22×D5124yescomplemented
714#135—524no—
715#135—524no—
716#135—524no—
717#135—58no—
718#135—524no—
719#135—548no—
720#135—548no—
721#135—548no—
722#135—524no—
723#135—524no—
724#135C22×D5124yescomplemented
725C2×Q16—51no—
726C2×Q16—53no—
727C2×Q16—56no—
728C2×Q16—524no—
729C2×Q16—524no—
730C2×Q16—53no—
731C2×Q16C22×D513yes—
732C2×SD16—53no—
733C2×SD16—53no—
734C2×SD16—53no—
735C2×SD16—53no—
736C2×SD16—524no—
737C2×SD16—524no—
738C2×SD16—51no—
739C2×SD16—53no—
740C2×SD16—56no—
741C2×SD16—524no—
742C2×SD16C22×D511yescharacteristic
743C2×SD16C22×D513yes—
744C2×SD16C22×D516yes—
745C2×SD16C22×D5124yescomplemented
746C2×D8—53no—
747C2×D8—51no—
748C2×D8—56no—
749C2×D8—524no—
750C2×D8—524no—
751C2×D8—53no—
752C2×D8C22×D513yes—
753#131—58no—
754#131—524no—
755#131—524no—
756#131C22×D518yescomplemented
757C2×M16—53no—
758C2×M16—524no—
759C2×M16—56no—
760C2×M16C22×D513yes—
761C22×C8—53no—
762C22×C8—51no—
763C22×C8—53no—
764C22×C8—53no—
765C22×C8—53no—
766C22×C8—524no—
767C22×C8C22×D513yes—
768C22×C5—26no—
769C22×C5—26no—
770C22×C5—22no—
771C22×C5—42no—
772C22×C5—46no—
773C22×C5—812no—
774C22×C5C23×D416yes—
775C22×C5C23×D411yescharacteristic
776C2×D5—22no—
777C2×D5—26no—
778C2×D5—26no—
779C2×D5—22no—
780C2×D5—412no—
781C2×D5—46no—
782C2×D5—42no—
783C2×D5—812no—
784C2×D5—812no—
785C2×D5—812no—
786C2×D5C23×D416yes—
787C2×D5C23×D412yes—
788C4×C5—22no—
789C4×C5—26no—
790C4×C5C23×D411yescharacteristic
791C4×C5C23×D416yes—
792C4×C5C2611yescharacteristic
793Dic5—22no—
794Dic5—26no—
795Dic5C23×D416yes—
796Dic5C23×D412yes—
797C24—23no—
798C24—53no—
799C24—103no—
800C24—103no—
801C24—103no—
802#41—28no—
803#41—224no—
804#41—26no—
805#41—26no—
806#41—58no—
807#41—524no—
808#41—512no—
809#41—512no—
810#41—54no—
811#41—512no—
812#41—524no—
813#41—512no—
814#41—54no—
815#41—524no—
816#41—512no—
817#41—512no—
818#41—1024no—
819#41—1024no—
820#41—1048no—
821#41—1024no—
822#41—1024no—
823#41—1024no—
824#41—1024no—
825#41—106no—
826#41—102no—
827#41—1024no—
828#41—1024no—
829#41—1012no—
830#41—106no—
831#41—102no—
832#41—1024no—
833#41—1024no—
834#41—1012no—
835#41—1048no—
836#41—1024no—
837#41—1024no—
838#41—108no—
839#41—1024no—
840#41—106no—
841#41—106no—
842#41D4×D514yes—
843#41C23×D5112yes—
844#41C23×D5112yes—
845#41C23×D514yes—
846C2×Q8—28no—
847C2×Q8—23no—
848C2×Q8—26no—
849C2×Q8—58no—
850C2×Q8—53no—
851C2×Q8—512no—
852C2×Q8—512no—
853C2×Q8—51no—
854C2×Q8—53no—
855C2×Q8—512no—
856C2×Q8—103no—
857C2×Q8—103no—
858C2×Q8—1024no—
859C2×Q8—106no—
860C2×Q8—106no—
861C2×Q8—1024no—
862C2×Q8—108no—
863C2×Q8—103no—
864C2×Q8—106no—
865C2×Q8D4×D511yescharacteristic
866C2×Q8C23×D511yescharacteristic
867C2×Q8C23×D513yes—
868C2×Q8C23×D5112yes—
869C2×D4—23no—
870C2×D4—23no—
871C2×D4—224no—
872C2×D4—23no—
873C2×D4—26no—
874C2×D4—56no—
875C2×D4—524no—
876C2×D4—512no—
877C2×D4—512no—
878C2×D4—53no—
879C2×D4—53no—
880C2×D4—51no—
881C2×D4—512no—
882C2×D4—1024no—
883C2×D4—101no—
884C2×D4—103no—
885C2×D4—106no—
886C2×D4—1024no—
887C2×D4—106no—
888C2×D4—106no—
889C2×D4—103no—
890C2×D4—103no—
891C2×D4—1048no—
892C2×D4—1024no—
893C2×D4—1024no—
894C2×D4—1024no—
895C2×D4—1048no—
896C2×D4—101no—
897C2×D4—103no—
898C2×D4—106no—
899C2×D4—1024no—
900C2×D4—103no—
901C2×D4—103no—
902C2×D4—1024no—
903C2×D4—103no—
904C2×D4—106no—
905C2×D4D4×D513yes—
906C2×D4C23×D513yes—
907C2×D4C23×D5112yes—
908C2×D4C23×D511yescharacteristic
909C22×C4—23no—
910C22×C4—23no—
911C22×C4—23no—
912C22×C4—53no—
913C22×C4—53no—
914C22×C4—53no—
915C22×C4—512no—
916C22×C4—51no—
917C22×C4—53no—
918C22×C4—512no—
919C22×C4—101no—
920C22×C4—103no—
921C22×C4—106no—
922C22×C4—1024no—
923C22×C4—1024no—
924C22×C4—1024no—
925C22×C4—103no—
926C22×C4—103no—
927C22×C4—101no—
928C22×C4—103no—
929C22×C4—106no—
930C22×C4—1024no—
931C22×C4—103no—
932C22×C4—103no—
933C22×C4—103no—
934C22×C4C23×D513yes—
935Q16—54no—
936Q16—512no—
937Q16—524no—
938Q16—512no—
939Q16C23×D5112yes—
940SD16—512no—
941SD16—512no—
942SD16—512no—
943SD16—512no—
944SD16—54no—
945SD16—512no—
946SD16—524no—
947SD16C23×D514yes—
948SD16C23×D5112yes—
949SD16C23×D5124yes—
950D8—512no—
951D8—54no—
952D8—524no—
953D8—512no—
954D8C23×D5112yes—
955M16—512no—
956M16—524no—
957M16C23×D5112yes—
958C2×C8—51no—
959C2×C8—53no—
960C2×C8—512no—
961C2×C8—54no—
962C2×C8—512no—
963C2×C8—512no—
964C2×C8—512no—
965C2×C8C23×D511yescharacteristic
966C2×C8C23×D513yes—
967C2×C8C23×D5112yes—
968C2×C5—26no—
969C2×C5—42no—
970C2×C5—46no—
971C2×C5#358412yescomplemented
972C2×C5C24×D411yescharacteristic
973D5—22no—
974D5—26no—
975D5—46no—
976D5—42no—
977C23—21no—
978C23—23no—
979C23—212no—
980C23—51no—
981C23—53no—
982C23—512no—
983C23—86no—
984C23—1012no—
985C23—1012no—
986C23—103no—
987C23—101no—
988C23—1012no—
989C23—206no—
990C23—406no—
991C23—406no—
992C23—406no—
993C23C2×D4×D513yes—
994Q8—212no—
995Q8—23no—
996Q8—21no—
997Q8—512no—
998Q8—52no—
999Q8—56no—
1000Q8—1012no—
1001Q8—1012no—
1002Q8—1012no—
1003Q8—101no—
1004Q8—103no—
1005Q8C2×D4×D514yes—
1006Q8C24×D512yes—
1007Q8C24×D516yes—
1008D4—212no—
1009D4—212no—
1010D4—212no—
1011D4—23no—
1012D4—21no—
1013D4—524no—
1014D4—512no—
1015D4—56no—
1016D4—52no—
1017D4—104no—
1018D4—1012no—
1019D4—1024no—
1020D4—1012no—
1021D4—1012no—
1022D4—104no—
1023D4—1012no—
1024D4—1024no—
1025D4—1012no—
1026D4—1012no—
1027D4—1012no—
1028D4—101no—
1029D4—103no—
1030D4C2×D4×D5112yes—
1031D4C24×D516yes—
1032D4C24×D512yes—
1033C2×C4—212no—
1034C2×C4—21no—
1035C2×C4—23no—
1036C2×C4—212no—
1037C2×C4—212no—
1038C2×C4—512no—
1039C2×C4—51no—
1040C2×C4—53no—
1041C2×C4—52no—
1042C2×C4—512no—
1043C2×C4—512no—
1044C2×C4—56no—
1045C2×C4—52no—
1046C2×C4—56no—
1047C2×C4—104no—
1048C2×C4—1012no—
1049C2×C4—1024no—
1050C2×C4—1012no—
1051C2×C4—1012no—
1052C2×C4—104no—
1053C2×C4—1012no—
1054C2×C4—1024no—
1055C2×C4—1012no—
1056C2×C4—101no—
1057C2×C4—103no—
1058C2×C4—1012no—
1059C2×C4—1012no—
1060C2×C4C2×D4×D516yes—
1061C2×C4C2×D4×D513yes—
1062C2×C4C24×D516yes—
1063C2×C4C24×D511yescharacteristic
1064C8—52no—
1065C8—56no—
1066C8C24×D512yes—
1067C8C24×D516yes—
1068C5C2×#358411yescharacteristic, complemented, Sylow
1069C22—26no—
1070C22—22no—
1071C22—26no—
1072C22—46no—
1073C22—42no—
1074C22—52no—
1075C22—56no—
1076C22—812no—
1077C22—102no—
1078C22—106no—
1079C22—106no—
1080C22—102no—
1081C22—2012no—
1082C22—206no—
1083C22—202no—
1084C22—4012no—
1085C22—4012no—
1086C22—4012no—
1087C22C22×D4×D516yes—
1088C22C22×D4×D511yescharacteristic
1089C4—22no—
1090C4—26no—
1091C4—52no—
1092C4—56no—
1093C4—102no—
1094C4—106no—
1095C4C22×D4×D516yes—
1096C4C22×D4×D511yescharacteristic
1097C4C25×D511yescharacteristic
1098C2—26no—
1099C2—46no—
1100C2—42no—
1101C2—102no—
1102C2—106no—
1103C2—206no—
1104C2—202no—
1105C2#1061910712yesdirect product factor
1106C2C23×D4×D511yescharacteristic
subgroupG/H
centerC22C22×D4×D5
commutator, cosocleC4×C5C26
FrattiniC4C25×D5
FittingC2×C5×#577C2
socleC22×C5C23×D4
hypercenterC2×#577D5
hypocenterC5C2×#3584
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#577

Complements

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

NH ≅ G/Ntype
1. C2×#66287C2semidirect
2. C2×#66285C2semidirect
3. C2×C5×#577C2semidirect
4. C2×#66172C2semidirect
5. C2×#66169C2semidirect
6. #10619107C2direct (N × H)
7. C2×#66113C2semidirect
8. C2×#66111C2semidirect
9. C2×#66108C2semidirect
10. C2×#66107C2semidirect
11. C2×#66104C2semidirect
12. C2×D5×#135C2semidirect
13. C2×#66096C2semidirect
14. C22×#4062C2semidirect
15. C2×#66085C2semidirect
16. C2×D5×#131C2semidirect
17. C2×C5×2−1+4C22semidirect
18. C2×C5×H(5,𝔽2)C22semidirect
20. #66287C22semidirect
22. #66285C22semidirect
24. C2×#4150C22semidirect
25. C2×#4150C22semidirect
27. C2×#4149C22semidirect
28. C2×#4149C22semidirect
32. C2×D5×#41C22semidirect
33. C2×D5×#41C22semidirect
35. C2×#4147C22semidirect
37. C22×#713C22semidirect
39. C2×#4144C22semidirect
41. C22×#711C22semidirect
42. C5×#577C22semidirect
43. C2×C5×#137C22semidirect
44. C2×C5×AGL(1,ℤ/8)C22semidirect
45. C2×C5×#135C22semidirect
46. C22×C5×SD16C22semidirect
47. C2×C5×#131C22semidirect
48. #66172C22semidirect
49. #66169C22semidirect
50. C2×#4097C22semidirect
51. C2×#4096C22semidirect
52. C2×#4096C22semidirect
53. C2×#4095C22semidirect
54. C2×#4094C22semidirect
55. C22×#689C22semidirect
56. C2×#4088C22semidirect
57. C2×#4078C22semidirect
58. C22×#686C22semidirect
59. #66113C22semidirect
60. #66111C22semidirect
61. #66108C22semidirect
62. #66107C22semidirect
63. #66104C22semidirect
64. D5×#135C22semidirect
65. C2×#4065C22semidirect
66. C2×#4064C22semidirect
67. C2×D5×Q16C22semidirect
68. #66096C22semidirect
69. C2×#4062C22semidirect
70. C2×#4062C22semidirect
71. C2×#4062C22semidirect
72. C2×#4062C22semidirect
73. C2×#4062C22semidirect
74. C2×#4062C22semidirect
75. C2×#4061C22semidirect
76. C2×#4060C22semidirect
77. C2×D5×SD16C22semidirect
78. C2×D5×SD16C22semidirect
79. C2×#4058C22semidirect
80. C2×#4057C22semidirect
81. C2×D5×D8C22semidirect
82. #66085C22semidirect
83. D5×#131C22semidirect
84. C2×#4055C22semidirect
85. C2×#4054C22semidirect
86. C2×#4053C22semidirect
87. C2×D5×M16C22semidirect
88. C2×#4050C22semidirect
89. C22×#677C22semidirect
90. C2×#4047C22semidirect
91. C22×C8×D5C22semidirect
94. C5×2−1+4C23semidirect
96. C5×H(5,𝔽2)C23semidirect
112. #4150C23semidirect
113. #4150C23semidirect
117. #4149C23semidirect
118. #4149C23semidirect
125. D5×#41C23semidirect
126. D5×#41C23semidirect
129. #4147C23semidirect
140. C2×#713C23semidirect
148. #4144C23semidirect
162. C2×#711C23semidirect
188. C5×#137C23semidirect
189. C5×AGL(1,ℤ/8)C23semidirect
190. C5×#135C23semidirect
195. C2×C5×SD16C23semidirect
197. C5×#131C23semidirect
200. #4097C23semidirect
201. #4096C23semidirect
202. #4096C23semidirect
203. #4095C23semidirect
204. #4094C23semidirect
208. C2×#689C23semidirect
209. #4088C23semidirect
214. #4078C23semidirect
218. C2×#686C23semidirect
221. #4065C23semidirect
222. #4064C23semidirect
223. D5×Q16C23semidirect
224. #4062C23semidirect
225. #4062C23semidirect
226. #4062C23semidirect
227. #4062C23semidirect
228. #4062C23semidirect
229. #4061C23semidirect
230. #4060C23semidirect
231. D5×SD16C23semidirect
232. D5×SD16C23semidirect
233. #4058C23semidirect
234. #4057C23semidirect
235. D5×D8C23semidirect
236. #4055C23semidirect
237. #4054C23semidirect
238. #4053C23semidirect
239. D5×M16C23semidirect
241. #4050C23semidirect
246. C2×#677C23semidirect
247. #4047C23semidirect
253. C2×C8×D5C23semidirect
262. C2×#577D5semidirect
450. C2×2−1+4C2×D5semidirect
456. C2×H(5,𝔽2)C2×D5semidirect
471. #577C2×D5semidirect
481. C2×#137C2×D5semidirect
487. C2×AGL(1,ℤ/8)C2×D5semidirect
500. C2×#135C2×D5semidirect
506. C22×SD16C2×D5semidirect
513. C2×#131C2×D5semidirect
616. 2−1+4C22×D5semidirect
626. H(5,𝔽2)C22×D5semidirect
707. #137C22×D5semidirect
713. AGL(1,ℤ/8)C22×D5semidirect
724. #135C22×D5semidirect
745. C2×SD16C22×D5semidirect
756. #131C22×D5semidirect
971. C2×C5#3584semidirect
1068. C5C2×#3584semidirect
1105. C2#10619107direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#662872
C2×#662852
C2×C5×#5772
C2×#661722
C2×#661692
#106191072
C2×#661132
C2×#661112
C2×#661082
C2×#661072
C2×#661042
C2×D5×#1352
C2×#660962
C22×#40622
C2×#660852
C2×D5×#1312
C2×#35845