Finite Group Databasebeta

← C2×#10619109 #13013144

Subgroups — C2×#10619109 #13013144

Order 1280.

10794 conjugacy classes of subgroups.

The subgroup lattice has 1104 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×2−1+4C211yesmaximal, characteristic, complemented
2C2×#66285C211yesmaximal, characteristic, complemented
3C2×C5×#577C211yesmaximal, characteristic, complemented
4C2×#66172C211yesmaximal, characteristic, complemented
5C2×#66170C211yesmaximal, characteristic, complemented
6#10619109C2132yesmaximal, direct product factor
7C2×#66113C213yesmaximal, complemented
8C2×D5×#137C213yesmaximal, complemented
9C2×#66109C213yesmaximal, complemented
10C2×#66107C213yesmaximal, complemented
11C2×#66105C213yesmaximal, complemented
12C2×#66102C213yesmaximal, complemented
13C2×#66096C213yesmaximal, complemented
14C22×#4061C213yesmaximal, complemented
15C2×#66087C211yesmaximal, characteristic, complemented
16C2×#66084C211yesmaximal, characteristic, complemented
17C2×C5×2−1+4C2211yescharacteristic, complemented
18C2×C5×H(5,𝔽2)C2211yescharacteristic, complemented
19D5×2−1+4—28no—
20D5×2−1+4C22116yescomplemented
21#66285—28no—
22#66285C22116yescomplemented
23C2×#4150—21no—
24C2×#4150—23no—
25C2×#4150C2213yescomplemented
26C2×#4150C2213yescomplemented
27C2×#4150C2211yescharacteristic, complemented
28C2×#4150C2211yescharacteristic, complemented
29C2×D5×#41—21no—
30C2×D5×#41—23no—
31C2×D5×#41C2213yes—
32C2×D5×#41C2211yescharacteristic
33C2×D5×#41C2213yescomplemented
34C2×#4147—21no—
35C2×#4147C2213yescomplemented
36C22×Q8×D5—21no—
37C22×Q8×D5C2213yescomplemented
38C2×#4144—23no—
39C2×#4144C2213yescomplemented
40C22×#711—23no—
41C22×#711C2213yes—
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#66170C22116yescomplemented
50C2×#4097C2213yescomplemented
51C2×#4097C2213yescomplemented
52C2×#4096C2213yescomplemented
53C2×#4096C2213yescomplemented
54C2×#4094C2211yescharacteristic, complemented
55C22×#689C2213yescomplemented
56C2×#4088C2213yescomplemented
57C22×#687C2213yescomplemented
58C2×#4078C2213yescomplemented
59#66113C22148yescomplemented
60D5×#137C22148yescomplemented
61#66109C22148yescomplemented
62#66107C22148yescomplemented
63#66105C22148yescomplemented
64#66102C22148yescomplemented
65C2×#4064C2213yescomplemented
66C2×#4064C2213yescomplemented
67C2×D5×Q16C2216yescomplemented
68#66096C22148yescomplemented
69C2×#4062C2216yescomplemented
70C2×#4061C2213yescomplemented
71C2×#4061C2216yescomplemented
72C2×#4061C2216yescomplemented
73C2×#4061C2216yescomplemented
74C2×#4061C2213yescomplemented
75C2×#4061C22148yescomplemented
76C2×#4060C2213yescomplemented
77C2×#4060C2211yescharacteristic, complemented
78C2×D5×SD16C2216yescomplemented
79C2×#4058C2216yescomplemented
80C2×#4057C2213yescomplemented
81C2×#4057C2213yescomplemented
82#66087C22116yescomplemented
83#66084C22116yescomplemented
84C2×#4055C2213yescomplemented
85C2×#4055C2213yescomplemented
86C2×#4053C2213yescomplemented
87C2×D5×M16C2213yescomplemented
88C22×Dic20C2213yescomplemented
89C2×#4050C2213yescomplemented
90C2×#4047C2213yescomplemented
91C22×#676C2213yescomplemented
92C2×#3586—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—24no—
111#4150—216no—
112#4150—248no—
113#4150—212no—
114#4150—212no—
115#4150C23124yescomplemented
116#4150C23124yescomplemented
117#4150C2318yescomplemented
118#4150C2318yescomplemented
119D5×#41—216no—
120D5×#41—248no—
121D5×#41—212no—
122D5×#41—212no—
123D5×#41D418yes—
124D5×#41C23124yes—
125D5×#41C2318yes—
126D5×#41C23124yescomplemented
127#4147—216no—
128#4147—212no—
129#4147C23124yescomplemented
130C2×#713—23no—
131C2×#713D411yescharacteristic
132C2×#713C2313yes—
133C2×#713C2311yescharacteristic
134C2×Q8×D5—21no—
135C2×Q8×D5—21no—
136C2×Q8×D5—216no—
137C2×Q8×D5—23no—
138C2×Q8×D5—23no—
139C2×Q8×D5—212no—
140C2×Q8×D5—23no—
141C2×Q8×D5D411yescharacteristic
142C2×Q8×D5C2316yes—
143C2×Q8×D5C2313yes—
144C2×Q8×D5C2313yes—
145C2×Q8×D5C23124yescomplemented
146#4144—248no—
147#4144—212no—
148#4144C23124yescomplemented
149C2×#711—23no—
150C2×#711—23no—
151C2×#711—26no—
152C2×#711—26no—
153C2×#711—23no—
154C2×#711—23no—
155C2×#711—248no—
156C2×#711—23no—
157C2×#711—23no—
158C2×#711—212no—
159C2×#711—23no—
160C2×#711D413yes—
161C2×#711C2313yes—
162C2×#711C2313yes—
163C2×#711C2316yes—
164C2×#711C23124yes—
165C2×D4×D5—23no—
166C2×D4×D5—23no—
167C2×D4×D5—23no—
168C2×D4×D5D413yes—
169C2×D4×D5C2311yescharacteristic
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×C4×D5—23no—
180C22×C4×D5—23no—
181C22×C4×D5—23no—
182C22×C4×D5C2313yes—
183C22×Dic10—23no—
184C22×Dic10—23no—
185C22×Dic10—23no—
186C22×Dic10C2313yes—
187C22×Dic10C2313yes—
188C5×#137C23124yescomplemented
189C5×AGL(1,ℤ/8)C23124yescomplemented
190C5×#135C23124yescomplemented
191C2×C5×Q16C2313yes—
192C2×C5×SD16C2316yes—
193C2×C5×SD16C2313yes—
194C2×C5×SD16C2311yescharacteristic
195C2×C5×SD16C23124yescomplemented
196C2×C5×D8C2313yes—
197C5×#131C2318yescomplemented
198C2×C5×M16C2313yes—
199C22×C5×C8C2313yes—
200#4097C23124yescomplemented
201#4097C23124yescomplemented
202#4096C23124yescomplemented
203#4096C23124yescomplemented
204#4094C2318yescomplemented
205C2×#689C2313yes—
206C2×#689C2316yes—
207C2×#689C2313yes—
208C2×#689C23124yescomplemented
209#4088C23124yescomplemented
210C2×#688C2313yes—
211C2×#688C2311yescharacteristic
212C2×#687C2313yes—
213C2×#687C2313yes—
214C2×#687C2316yes—
215C2×#687C23124yescomplemented
216#4078C23124yescomplemented
217C2×#686C2311yescharacteristic
218C2×#686C2313yes—
219C2×#681C2313yes—
220C22×#168C2313yes—
221#4064C23124yescomplemented
222#4064C23124yescomplemented
223D5×Q16C23148yescomplemented
224#4062C23148yescomplemented
225#4061C23124yescomplemented
226#4061C23148yescomplemented
227#4061C23148yescomplemented
228#4061C23148yescomplemented
229#4061C23124yescomplemented
230#4060C23124yescomplemented
231#4060C2318yescomplemented
232D5×SD16C23148yescomplemented
233#4058C23148yescomplemented
234#4057C23124yescomplemented
235#4057C23124yescomplemented
236#4055C23124yescomplemented
237#4055C23124yescomplemented
238#4053C23124yescomplemented
239D5×M16C23124yescomplemented
240C2×Dic20C2313yes—
241C2×Dic20C2316yes—
242C2×Dic20C23124yescomplemented
243#4050C23124yescomplemented
244C2×D40C2311yescharacteristic
245C2×#677C2313yes—
246C2×#677C2313yes—
247#4047C23124yescomplemented
248C2×#676C2311yescharacteristic
249C2×#676C2313yes—
250C2×#676C2313yes—
251C2×#676C2313yes—
252C2×#676C23124yescomplemented
253C2×C8×D5C2316yes—
254C2×#585—51no—
255C22×2−1+4—51no—
256#3586—532no—
257C2×#578—51no—
258C2×#578—53no—
259C2×#578—53no—
260C2×#578—51no—
261C2×#577—51no—
262C2×#577—53no—
263C2×#577—53no—
264C2×#577D511yescharacteristic, complemented
265C2×#575—53no—
266C2×#575—53no—
267C22×#137—53no—
268C22×#137—53no—
269C2×#568—51no—
270C24×C5—23no—
271C23×D5—21no—
272C23×D5—23no—
273C23×D5C2×D413yes—
274C5×#41—28no—
275C5×#41—224no—
276C5×#41—26no—
277C5×#41—26no—
278C5×#41C2×D414yes—
279C5×#41C24112yes—
280C5×#41C24112yes—
281C5×#41C2414yes—
282C2×C5×Q8—28no—
283C2×C5×Q8—23no—
284C2×C5×Q8—26no—
285C2×C5×Q8C2×D411yescharacteristic
286C2×C5×Q8C2413yes—
287C2×C5×Q8C2411yescharacteristic
288C2×C5×Q8C24112yes—
289C2×C5×D4—23no—
290C2×C5×D4—23no—
291C2×C5×D4—224no—
292C2×C5×D4—23no—
293C2×C5×D4—26no—
294C2×C5×D4C2×D413yes—
295C2×C5×D4C2411yescharacteristic
296C2×C5×D4C2413yes—
297C2×C5×D4C24112yes—
298C22×C4×C5—23no—
299C22×C4×C5—23no—
300C22×C4×C5—23no—
301C22×C4×C5C2413yes—
302C2×C22⋊D5—23no—
303C2×C22⋊D5—23no—
304C2×C22⋊D5—23no—
305C2×C22⋊D5—23no—
306C2×C22⋊D5—26no—
307C2×C22⋊D5—224no—
308C2×C22⋊D5—248no—
309C2×C22⋊D5—21no—
310C2×C22⋊D5—23no—
311C2×C22⋊D5C2×D416yes—
312C22×Dic5—23no—
313C22×Dic5—23no—
314C22×Dic5—23no—
315C22×Dic5—26no—
316C22×Dic5—23no—
317C22×Dic5—224no—
318C22×Dic5C2×D413yes—
319#713—224no—
320#713—26no—
321#713—22no—
322#713C2×D418yes—
323#713C24112yes—
324#713C2414yes—
325Q8×D5—28no—
326Q8×D5—28no—
327Q8×D5—26no—
328Q8×D5—224no—
329Q8×D5—212no—
330Q8×D5—224no—
331Q8×D5—26no—
332Q8×D5—224no—
333Q8×D5C2×D418yes—
334Q8×D5C24112yes—
335Q8×D5C24124yes—
336Q8×D5C24112yes—
337#711—224no—
338#711—224no—
339#711—248no—
340#711—248no—
341#711—224no—
342#711—224no—
343#711—224no—
344#711—26no—
345#711—224no—
346#711—212no—
347#711—26no—
348#711—224no—
349#711C2×D4124yes—
350#711C24112yes—
351#711C24124yes—
352#711C24112yes—
353D4×D5—224no—
354D4×D5—224no—
355D4×D5—224no—
356D4×D5—26no—
357D4×D5—22no—
358D4×D5C2×D4124yes—
359D4×D5C24112yes—
360D4×D5C2414yes—
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—21no—
373C2×D20—23no—
374C2×D20C2×D413yes—
375C2×D20C2411yescharacteristic
376C2×D20C2411yescharacteristic
377C2×C4×D5—23no—
378C2×C4×D5—23no—
379C2×C4×D5—26no—
380C2×C4×D5—224no—
381C2×C4×D5—23no—
382C2×C4×D5—23no—
383C2×C4×D5—21no—
384C2×C4×D5—23no—
385C2×C4×D5—224no—
386C2×C4×D5—224no—
387C2×C4×D5C2×D413yes—
388C2×C4×D5C2×D413yes—
389C2×C4×D5C2×D4112yes—
390C2×C4×D5C2411yescharacteristic
391C2×C4×D5C2413yes—
392C2×C4×D5C24112yes—
393C2×Dic10—23no—
394C2×Dic10—23no—
395C2×Dic10—26no—
396C2×Dic10—26no—
397C2×Dic10—23no—
398C2×Dic10—26no—
399C2×Dic10—23no—
400C2×Dic10—224no—
401C2×Dic10—224no—
402C2×Dic10—224no—
403C2×Dic10C2×D413yes—
404C2×Dic10C24112yes—
405C2×Dic10C24112yes—
406C2×Dic10C2413yes—
407C2×Dic10C2413yes—
408C5×Q16C24112yes—
409C5×SD16C24112yes—
410C5×SD16C24124yes—
411C5×SD16C2414yes—
412C5×D8C24112yes—
413C5×M16C24112yes—
414C2×C5×C8C2411yescharacteristic
415C2×C5×C8C2413yes—
416C2×C5×C8C24112yes—
417#689C24112yes—
418#689C24112yes—
419#689C24124yes—
420#688C2414yes—
421#688C24112yes—
422#687C24112yes—
423#687C24112yes—
424#687C24124yes—
425#686C2414yes—
426#686C24112yes—
427#681C24112yes—
428C2×#168C24112yes—
429C2×#168C2413yes—
430C2×#168C2411yescharacteristic
431Dic20C24112yes—
432Dic20C24124yes—
433D40C2414yes—
434#677C24112yes—
435#677C24112yes—
436#676C2414yes—
437#676C24112yes—
438#676C24112yes—
439#676C24112yes—
440C8×D5C24124yes—
441#585—516no—
442#585—108no—
443C2×2−1+4—516no—
444C2×2−1+4—53no—
445C2×2−1+4—53no—
446C2×2−1+4—51no—
447C2×2−1+4—51no—
448C2×2−1+4—53no—
449C2×2−1+4—101no—
450C2×2−1+4—101no—
451C2×2−1+4—103no—
452C2×2−1+4—108no—
453C2×2−1+4C2×D511yescharacteristic, complemented
454C2×H(5,𝔽2)—53no—
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—103no—
462C22×#41—103no—
463C22×#41—101no—
464C23×Q8—53no—
465C23×Q8—101no—
466#578—516no—
467#578—548no—
468#578—548no—
469#578—516no—
470#577—516no—
471#577—548no—
472#577—548no—
473#577C2×D5116yescomplemented
474#575—548no—
475#575—548no—
476C2×#137—53no—
477C2×#137—53no—
478C2×#137—53no—
479C2×#137—548no—
480C2×#137—53no—
481C2×#137—53no—
482C2×#137—56no—
483C2×#137—53no—
484C2×#137—56no—
485C2×#137—56no—
486C2×#137—53no—
487C2×#137—548no—
488C2×#137—53no—
489C2×#137—53no—
490C2×#137C2×D513yescomplemented
491C2×AGL(1,ℤ/8)—53no—
492C2×AGL(1,ℤ/8)—51no—
493C2×AGL(1,ℤ/8)—53no—
494C2×AGL(1,ℤ/8)—53no—
495C2×AGL(1,ℤ/8)—53no—
496C2×AGL(1,ℤ/8)C2×D513yescomplemented
497C2×#135—53no—
498C2×#135—53no—
499C2×#135—56no—
500C2×#135—56no—
501C2×#135—53no—
502C2×#135C2×D513yescomplemented
503C22×Q16—53no—
504C22×Q16—56no—
505C22×Q16—53no—
506C22×SD16—53no—
507C22×SD16—56no—
508C22×SD16C2×D513yescomplemented
509#568—516no—
510C2×#131—51no—
511C2×#131—53no—
512C2×#131—53no—
513C2×#131C2×D511yescharacteristic, complemented
514C22×M16—53no—
515C22×M16—53no—
516C23×C5—21no—
517C23×C5—23no—
518C23×C5—212no—
519C23×C5—86no—
520C23×C5C22×D413yes—
521C22×D5—21no—
522C22×D5—21no—
523C22×D5—24no—
524C22×D5—212no—
525C22×D5—46no—
526C22×D5—44no—
527C22×D5—86no—
528C22×D5C22×D411yescharacteristic
529C22×D5C22×D413yes—
530C22×D5C22×D4112yes—
531C5×Q8—23no—
532C5×Q8—212no—
533C5×Q8—21no—
534C5×Q8C22×D414yes—
535C5×Q8C2516yes—
536C5×Q8C2512yes—
537C5×D4—212no—
538C5×D4—212no—
539C5×D4—23no—
540C5×D4—212no—
541C5×D4—21no—
542C5×D4C22×D4112yes—
543C5×D4C2512yes—
544C5×D4C2516yes—
545C2×C4×C5—21no—
546C2×C4×C5—23no—
547C2×C4×C5—212no—
548C2×C4×C5—212no—
549C2×C4×C5—212no—
550C2×C4×C5C22×D413yes—
551C2×C4×C5C22×D416yes—
552C2×C4×C5C2511yescharacteristic
553C2×C4×C5C2516yes—
554C22⋊D5—212no—
555C22⋊D5—212no—
556C22⋊D5—212no—
557C22⋊D5—212no—
558C22⋊D5—224no—
559C22⋊D5—24no—
560C22⋊D5—212no—
561C22⋊D5C22×D4124yes—
562C2×Dic5—23no—
563C2×Dic5—212no—
564C2×Dic5—23no—
565C2×Dic5—212no—
566C2×Dic5—212no—
567C2×Dic5—224no—
568C2×Dic5—212no—
569C2×Dic5C22×D413yes—
570C2×Dic5C22×D411yescharacteristic
571C2×Dic5C22×D4112yes—
572D20—24no—
573D20—212no—
574D20—21no—
575D20—21no—
576D20C22×D4112yes—
577D20C2512yes—
578D20C2512yes—
579C4×D5—212no—
580C4×D5—212no—
581C4×D5—224no—
582C4×D5—212no—
583C4×D5—212no—
584C4×D5—24no—
585C4×D5—212no—
586C4×D5C22×D4112yes—
587C4×D5C22×D4112yes—
588C4×D5C22×D412yes—
589C4×D5C22×D416yes—
590C4×D5C2516yes—
591C4×D5C2512yes—
592Dic10—23no—
593Dic10—212no—
594Dic10—23no—
595Dic10—212no—
596Dic10—212no—
597Dic10—224no—
598Dic10—212no—
599Dic10C22×D4112yes—
600Dic10C2516yes—
601Dic10C2516yes—
602C5×C8C2516yes—
603C5×C8C2512yes—
604#168C2516yes—
605#168C2512yes—
6062−1+4—24no—
6072−1+4—524no—
6082−1+4—58no—
6092−1+4—524no—
6102−1+4—58no—
6112−1+4—524no—
6122−1+4—1016no—
6132−1+4—1012no—
6142−1+4—1016no—
6152−1+4—1048no—
6162−1+4—1012no—
6172−1+4—1012no—
6182−1+4—104no—
6192−1+4—104no—
6202−1+4C22×D518yescomplemented
621H(5,𝔽2)—24no—
622H(5,𝔽2)—524no—
623H(5,𝔽2)—1048no—
624H(5,𝔽2)—1012no—
625H(5,𝔽2)C22×D518yescomplemented
626C2×#41—21no—
627C2×#41—23no—
628C2×#41—58no—
629C2×#41—58no—
630C2×#41—51no—
631C2×#41—53no—
632C2×#41—53no—
633C2×#41—524no—
634C2×#41—524no—
635C2×#41—53no—
636C2×#41—51no—
637C2×#41—53no—
638C2×#41—56no—
639C2×#41—53no—
640C2×#41—524no—
641C2×#41—53no—
642C2×#41—53no—
643C2×#41—103no—
644C2×#41—103no—
645C2×#41—103no—
646C2×#41—106no—
647C2×#41—103no—
648C2×#41—103no—
649C2×#41—103no—
650C2×#41—103no—
651C2×#41—103no—
652C2×#41—1012no—
653C2×#41—1012no—
654C2×#41—1012no—
655C2×#41—106no—
656C2×#41—106no—
657C2×#41—103no—
658C2×#41—1048no—
659C2×#41—103no—
660C2×#41—1048no—
661C2×#41—1016no—
662C2×#41—103no—
663C2×#41—103no—
664C2×#41C22×D513yes—
665C2×#41C22×D513yes—
666C2×#41C22×D511yescharacteristic
667C22×Q8—21no—
668C22×Q8—51no—
669C22×Q8—56no—
670C22×Q8—53no—
671C22×Q8—53no—
672C22×Q8—524no—
673C22×Q8—53no—
674C22×Q8—53no—
675C22×Q8—103no—
676C22×Q8—103no—
677C22×Q8—103no—
678C22×Q8—103no—
679C22×Q8—103no—
680C22×Q8—1012no—
681C22×Q8—1016no—
682C22×Q8—103no—
683C22×Q8—101no—
684C22×Q8—101no—
685C22×Q8C22×D513yes—
686C22×D4—23no—
687C22×D4—53no—
688C22×D4—53no—
689C22×D4—51no—
690C22×D4—103no—
691C22×D4—103no—
692C22×D4—103no—
693C22×D4—106no—
694C22×D4—103no—
695C22×D4C22×D513yes—
696C23×C4—53no—
697C23×C4—103no—
698C23×C4—103no—
699C23×C4—103no—
700C23×C4—103no—
701#137—524no—
702#137—524no—
703#137—524no—
704#137—524no—
705#137—524no—
706#137—548no—
707#137—524no—
708#137—548no—
709#137—548no—
710#137—524no—
711#137—524no—
712#137—524no—
713#137C22×D5124yescomplemented
714AGL(1,ℤ/8)—524no—
715AGL(1,ℤ/8)—58no—
716AGL(1,ℤ/8)—524no—
717AGL(1,ℤ/8)—524no—
718AGL(1,ℤ/8)—524no—
719AGL(1,ℤ/8)C22×D5124yescomplemented
720#135—524no—
721#135—524no—
722#135—548no—
723#135—548no—
724#135—524no—
725#135C22×D5124yescomplemented
726C2×Q16—53no—
727C2×Q16—53no—
728C2×Q16—56no—
729C2×Q16—524no—
730C2×Q16—548no—
731C2×Q16—56no—
732C2×Q16—53no—
733C2×Q16—524no—
734C2×Q16C22×D513yes—
735C2×SD16—53no—
736C2×SD16—51no—
737C2×SD16—53no—
738C2×SD16—56no—
739C2×SD16—524no—
740C2×SD16—53no—
741C2×SD16—548no—
742C2×SD16—53no—
743C2×SD16—53no—
744C2×SD16C22×D516yes—
745C2×SD16C22×D513yes—
746C2×SD16C22×D511yescharacteristic
747C2×SD16C22×D5124yescomplemented
748C2×D8—53no—
749C2×D8—51no—
750C2×D8—51no—
751C2×D8C22×D513yes—
752#131—58no—
753#131—524no—
754#131—524no—
755#131C22×D518yescomplemented
756C2×M16—53no—
757C2×M16—524no—
758C2×M16—53no—
759C2×M16—51no—
760C2×M16—53no—
761C2×M16—53no—
762C2×M16—524no—
763C2×M16C22×D513yes—
764C22×C8—53no—
765C22×C8—56no—
766C22×C8C22×D513yes—
767C22×C5—26no—
768C22×C5—22no—
769C22×C5—26no—
770C22×C5—42no—
771C22×C5—46no—
772C22×C5—812no—
773C22×C5C23×D416yes—
774C22×C5C23×D411yescharacteristic
775C2×D5—22no—
776C2×D5—26no—
777C2×D5—22no—
778C2×D5—22no—
779C2×D5—412no—
780C2×D5—48no—
781C2×D5—42no—
782C2×D5—42no—
783C2×D5—812no—
784C2×D5C23×D412yes—
785C2×D5C23×D416yes—
786C4×C5—22no—
787C4×C5—26no—
788C4×C5C23×D411yescharacteristic
789C4×C5C23×D416yes—
790C4×C5C2611yescharacteristic
791Dic5—26no—
792Dic5—26no—
793Dic5C23×D416yes—
794Dic5C23×D412yes—
795C24—23no—
796C24—53no—
797C24—101no—
798C24—103no—
799#41—28no—
800#41—224no—
801#41—26no—
802#41—26no—
803#41—58no—
804#41—524no—
805#41—512no—
806#41—512no—
807#41—512no—
808#41—54no—
809#41—512no—
810#41—524no—
811#41—512no—
812#41—512no—
813#41—512no—
814#41—1024no—
815#41—1024no—
816#41—1024no—
817#41—1048no—
818#41—1024no—
819#41—1024no—
820#41—106no—
821#41—1024no—
822#41—1024no—
823#41—1012no—
824#41—1024no—
825#41—106no—
826#41—102no—
827#41—106no—
828#41—1048no—
829#41—1048no—
830#41—1024no—
831#41—1024no—
832#41—1024no—
833#41—1024no—
834#41—106no—
835#41—106no—
836#41D4×D514yes—
837#41C23×D5112yes—
838#41C23×D5112yes—
839#41C23×D514yes—
840C2×Q8—28no—
841C2×Q8—23no—
842C2×Q8—26no—
843C2×Q8—58no—
844C2×Q8—53no—
845C2×Q8—524no—
846C2×Q8—512no—
847C2×Q8—512no—
848C2×Q8—53no—
849C2×Q8—53no—
850C2×Q8—512no—
851C2×Q8—512no—
852C2×Q8—103no—
853C2×Q8—106no—
854C2×Q8—103no—
855C2×Q8—1024no—
856C2×Q8—1024no—
857C2×Q8—1024no—
858C2×Q8—106no—
859C2×Q8—1024no—
860C2×Q8—1024no—
861C2×Q8—1012no—
862C2×Q8—106no—
863C2×Q8—1024no—
864C2×Q8—108no—
865C2×Q8—108no—
866C2×Q8—103no—
867C2×Q8—103no—
868C2×Q8—106no—
869C2×Q8—106no—
870C2×Q8D4×D511yescharacteristic
871C2×Q8C23×D513yes—
872C2×Q8C23×D511yescharacteristic
873C2×Q8C23×D5112yes—
874C2×D4—23no—
875C2×D4—23no—
876C2×D4—224no—
877C2×D4—23no—
878C2×D4—26no—
879C2×D4—56no—
880C2×D4—524no—
881C2×D4—512no—
882C2×D4—54no—
883C2×D4—53no—
884C2×D4—51no—
885C2×D4—51no—
886C2×D4—101no—
887C2×D4—103no—
888C2×D4—102no—
889C2×D4—106no—
890C2×D4—103no—
891C2×D4—101no—
892C2×D4—1024no—
893C2×D4—1024no—
894C2×D4—1024no—
895C2×D4—1048no—
896C2×D4—103no—
897C2×D4—106no—
898C2×D4—103no—
899C2×D4—1024no—
900C2×D4—103no—
901C2×D4—103no—
902C2×D4D4×D513yes—
903C2×D4C23×D511yescharacteristic
904C2×D4C23×D513yes—
905C2×D4C23×D5112yes—
906C22×C4—23no—
907C22×C4—23no—
908C22×C4—23no—
909C22×C4—53no—
910C22×C4—53no—
911C22×C4—53no—
912C22×C4—512no—
913C22×C4—53no—
914C22×C4—51no—
915C22×C4—512no—
916C22×C4—101no—
917C22×C4—103no—
918C22×C4—1024no—
919C22×C4—1024no—
920C22×C4—103no—
921C22×C4—103no—
922C22×C4—1024no—
923C22×C4—106no—
924C22×C4—103no—
925C22×C4—106no—
926C22×C4—103no—
927C22×C4—1024no—
928C22×C4—103no—
929C22×C4—103no—
930C22×C4—103no—
931C22×C4—103no—
932C22×C4C23×D513yes—
933Q16—512no—
934Q16—512no—
935Q16—524no—
936Q16—524no—
937Q16—512no—
938Q16C23×D5112yes—
939SD16—512no—
940SD16—54no—
941SD16—512no—
942SD16—524no—
943SD16—512no—
944SD16—512no—
945SD16—512no—
946SD16C23×D5124yes—
947SD16C23×D5112yes—
948SD16C23×D514yes—
949D8—512no—
950D8—54no—
951D8—54no—
952D8C23×D5112yes—
953M16—512no—
954M16—512no—
955M16—54no—
956M16—512no—
957M16—512no—
958M16C23×D5112yes—
959C2×C8—51no—
960C2×C8—53no—
961C2×C8—512no—
962C2×C8—524no—
963C2×C8C23×D513yes—
964C2×C8C23×D511yescharacteristic
965C2×C8C23×D5112yes—
966C2×C5—26no—
967C2×C5—42no—
968C2×C5—46no—
969C2×C5#358612yescomplemented
970C2×C5C24×D411yescharacteristic
971D5—22no—
972D5—26no—
973D5—42no—
974D5—42no—
975C23—21no—
976C23—23no—
977C23—212no—
978C23—51no—
979C23—53no—
980C23—512no—
981C23—86no—
982C23—104no—
983C23—1012no—
984C23—101no—
985C23—101no—
986C23—206no—
987C23—204no—
988C23—406no—
989C23C2×D4×D513yes—
990Q8—212no—
991Q8—23no—
992Q8—21no—
993Q8—512no—
994Q8—56no—
995Q8—56no—
996Q8—1012no—
997Q8—1024no—
998Q8—1012no—
999Q8—1012no—
1000Q8—103no—
1001Q8—1012no—
1002Q8—103no—
1003Q8C2×D4×D514yes—
1004Q8C24×D516yes—
1005Q8C24×D512yes—
1006D4—212no—
1007D4—212no—
1008D4—212no—
1009D4—23no—
1010D4—21no—
1011D4—524no—
1012D4—512no—
1013D4—52no—
1014D4—52no—
1015D4—104no—
1016D4—1012no—
1017D4—1012no—
1018D4—104no—
1019D4—1012no—
1020D4—1024no—
1021D4—1012no—
1022D4—1012no—
1023D4—1012no—
1024D4—101no—
1025D4—101no—
1026D4C2×D4×D5112yes—
1027D4C24×D512yes—
1028D4C24×D516yes—
1029C2×C4—212no—
1030C2×C4—21no—
1031C2×C4—23no—
1032C2×C4—212no—
1033C2×C4—212no—
1034C2×C4—512no—
1035C2×C4—51no—
1036C2×C4—53no—
1037C2×C4—52no—
1038C2×C4—512no—
1039C2×C4—512no—
1040C2×C4—56no—
1041C2×C4—56no—
1042C2×C4—52no—
1043C2×C4—104no—
1044C2×C4—1012no—
1045C2×C4—1012no—
1046C2×C4—1012no—
1047C2×C4—1024no—
1048C2×C4—1012no—
1049C2×C4—1024no—
1050C2×C4—1012no—
1051C2×C4—1012no—
1052C2×C4—1012no—
1053C2×C4—103no—
1054C2×C4—103no—
1055C2×C4—1012no—
1056C2×C4—1012no—
1057C2×C4C2×D4×D516yes—
1058C2×C4C2×D4×D513yes—
1059C2×C4C24×D516yes—
1060C2×C4C24×D511yescharacteristic
1061C8—52no—
1062C8—56no—
1063C8C24×D516yes—
1064C8C24×D512yes—
1065C5C2×#358611yescharacteristic, complemented, Sylow
1066C22—26no—
1067C22—22no—
1068C22—26no—
1069C22—46no—
1070C22—42no—
1071C22—52no—
1072C22—56no—
1073C22—812no—
1074C22—102no—
1075C22—106no—
1076C22—102no—
1077C22—102no—
1078C22—2012no—
1079C22—208no—
1080C22—202no—
1081C22—202no—
1082C22—4012no—
1083C22C22×D4×D516yes—
1084C22C22×D4×D511yescharacteristic
1085C4—22no—
1086C4—26no—
1087C4—52no—
1088C4—56no—
1089C4—106no—
1090C4—106no—
1091C4C22×D4×D516yes—
1092C4C22×D4×D511yescharacteristic
1093C4C25×D511yescharacteristic
1094C2—26no—
1095C2—46no—
1096C2—42no—
1097C2—102no—
1098C2—106no—
1099C2—202no—
1100C2—202no—
1101C2#1061910912yesdirect product factor
1102C2C23×D4×D511yescharacteristic
subgroupG/H
centerC22C22×D4×D5
commutator, cosocleC4×C5C26
FrattiniC4C25×D5
FittingC2×C5×#577C2
socleC22×C5C23×D4
hypercenterC2×#577D5
hypocenterC5C2×#3586
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×D5×2−1+4C2semidirect
2. C2×#66285C2semidirect
3. C2×C5×#577C2semidirect
4. C2×#66172C2semidirect
5. C2×#66170C2semidirect
6. #10619109C2direct (N × H)
7. C2×#66113C2semidirect
8. C2×D5×#137C2semidirect
9. C2×#66109C2semidirect
10. C2×#66107C2semidirect
11. C2×#66105C2semidirect
12. C2×#66102C2semidirect
13. C2×#66096C2semidirect
14. C22×#4061C2semidirect
15. C2×#66087C2semidirect
16. C2×#66084C2semidirect
17. C2×C5×2−1+4C22semidirect
18. C2×C5×H(5,𝔽2)C22semidirect
20. D5×2−1+4C22semidirect
22. #66285C22semidirect
25. C2×#4150C22semidirect
26. C2×#4150C22semidirect
27. C2×#4150C22semidirect
28. C2×#4150C22semidirect
33. C2×D5×#41C22semidirect
35. C2×#4147C22semidirect
37. C22×Q8×D5C22semidirect
39. C2×#4144C22semidirect
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. #66170C22semidirect
50. C2×#4097C22semidirect
51. C2×#4097C22semidirect
52. C2×#4096C22semidirect
53. C2×#4096C22semidirect
54. C2×#4094C22semidirect
55. C22×#689C22semidirect
56. C2×#4088C22semidirect
57. C22×#687C22semidirect
58. C2×#4078C22semidirect
59. #66113C22semidirect
60. D5×#137C22semidirect
61. #66109C22semidirect
62. #66107C22semidirect
63. #66105C22semidirect
64. #66102C22semidirect
65. C2×#4064C22semidirect
66. C2×#4064C22semidirect
67. C2×D5×Q16C22semidirect
68. #66096C22semidirect
69. C2×#4062C22semidirect
70. C2×#4061C22semidirect
71. C2×#4061C22semidirect
72. C2×#4061C22semidirect
73. C2×#4061C22semidirect
74. C2×#4061C22semidirect
75. C2×#4061C22semidirect
76. C2×#4060C22semidirect
77. C2×#4060C22semidirect
78. C2×D5×SD16C22semidirect
79. C2×#4058C22semidirect
80. C2×#4057C22semidirect
81. C2×#4057C22semidirect
82. #66087C22semidirect
83. #66084C22semidirect
84. C2×#4055C22semidirect
85. C2×#4055C22semidirect
86. C2×#4053C22semidirect
87. C2×D5×M16C22semidirect
88. C22×Dic20C22semidirect
89. C2×#4050C22semidirect
90. C2×#4047C22semidirect
91. C22×#676C22semidirect
94. C5×2−1+4C23semidirect
96. C5×H(5,𝔽2)C23semidirect
115. #4150C23semidirect
116. #4150C23semidirect
117. #4150C23semidirect
118. #4150C23semidirect
126. D5×#41C23semidirect
129. #4147C23semidirect
145. C2×Q8×D5C23semidirect
148. #4144C23semidirect
188. C5×#137C23semidirect
189. C5×AGL(1,ℤ/8)C23semidirect
190. C5×#135C23semidirect
195. C2×C5×SD16C23semidirect
197. C5×#131C23semidirect
200. #4097C23semidirect
201. #4097C23semidirect
202. #4096C23semidirect
203. #4096C23semidirect
204. #4094C23semidirect
208. C2×#689C23semidirect
209. #4088C23semidirect
215. C2×#687C23semidirect
216. #4078C23semidirect
221. #4064C23semidirect
222. #4064C23semidirect
223. D5×Q16C23semidirect
224. #4062C23semidirect
225. #4061C23semidirect
226. #4061C23semidirect
227. #4061C23semidirect
228. #4061C23semidirect
229. #4061C23semidirect
230. #4060C23semidirect
231. #4060C23semidirect
232. D5×SD16C23semidirect
233. #4058C23semidirect
234. #4057C23semidirect
235. #4057C23semidirect
236. #4055C23semidirect
237. #4055C23semidirect
238. #4053C23semidirect
239. D5×M16C23semidirect
242. C2×Dic20C23semidirect
243. #4050C23semidirect
247. #4047C23semidirect
252. C2×#676C23semidirect
264. C2×#577D5semidirect
453. C2×2−1+4C2×D5semidirect
456. C2×H(5,𝔽2)C2×D5semidirect
473. #577C2×D5semidirect
490. C2×#137C2×D5semidirect
496. C2×AGL(1,ℤ/8)C2×D5semidirect
502. C2×#135C2×D5semidirect
508. C22×SD16C2×D5semidirect
513. C2×#131C2×D5semidirect
620. 2−1+4C22×D5semidirect
625. H(5,𝔽2)C22×D5semidirect
713. #137C22×D5semidirect
719. AGL(1,ℤ/8)C22×D5semidirect
725. #135C22×D5semidirect
747. C2×SD16C22×D5semidirect
755. #131C22×D5semidirect
969. C2×C5#3586semidirect
1065. C5C2×#3586semidirect
1101. C2#10619109direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D5×2−1+42
C2×#662852
C2×C5×#5772
C2×#661722
C2×#661702
#106191092
C2×#661132
C2×D5×#1372
C2×#661092
C2×#661072
C2×#661052
C2×#661022
C2×#660962
C22×#40612
C2×#660872
C2×#660842
C2×#35865