Finite Group Databasebeta

← C2×#10618614 #13007607

Subgroups — C2×#10618614 #13007607

Order 1280.

12366 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4149C211yesmaximal, characteristic, complemented
2C23×#713C211yesmaximal, characteristic, complemented
3C2×C5×#548C211yesmaximal, characteristic, complemented
4C2×#66168C211yesmaximal, characteristic, complemented
5C2×#66151C211yesmaximal, characteristic, complemented
6#10618614C2132yesmaximal, direct product factor
7C2×#66010C213yesmaximal, complemented
8C2×#66008C213yesmaximal, complemented
9C2×#65964C213yesmaximal, complemented
10C2×#65963C213yesmaximal, complemented
11C2×#65943C213yesmaximal, complemented
12C2×D5×#121C213yesmaximal, complemented
13C2×#65911C211yesmaximal, characteristic, complemented
14C2×#65908C211yesmaximal, characteristic, complemented
15C2×D4×D20C213yesmaximal, complemented
16C2×#65881C213yesmaximal, complemented
17C22×C5×#41C2211yescharacteristic, complemented
18C23×C5×Q8C2211yescharacteristic, complemented
19C2×#4149—216no—
20C2×#4149C22116yescomplemented
21C22×#713—216no—
22C22×#713C2211yescharacteristic
23C22×#713C2211yescharacteristic, complemented
24C22×#713C2213yescomplemented
25C22×#713C2213yescomplemented
26C22×#713C2211yescharacteristic, complemented
27C22×#713C22116yescomplemented
28C22×D4×D5C2213yescomplemented
29C22×D4×D5C2213yescomplemented
30C22×D4×D5C2216yescomplemented
31C22×#709C2213yescomplemented
32C23×D20C2213yescomplemented
33C23×D20C2213yescomplemented
34C23×C4×D5C2213yescomplemented
35C5×#548C22116yescomplemented
36C2×C5×#124C2213yescomplemented
37C2×C5×C22⋊Q8C2213yescomplemented
38C2×C5×#121C2213yescomplemented
39C2×C4×C5×Q8C2211yescharacteristic, complemented
40C2×C4×C5×D4C2213yescomplemented
41#66168C22116yescomplemented
42#66151C22116yescomplemented
43C2×#4093C2213yescomplemented
44C2×#4092C2213yescomplemented
45C2×Q8×Dic5C2211yescharacteristic, complemented
46C2×#4086C2213yescomplemented
47C2×#4085C2213yescomplemented
48C2×#4084C2213yescomplemented
49C2×#4083C2213yescomplemented
50C2×#4076C2213yescomplemented
51C2×#4076C2213yescomplemented
52C2×C4×C22⋊D5C2213yescomplemented
53C2×C4×C22⋊D5C2213yescomplemented
54#66010C22148yescomplemented
55#66008C22148yescomplemented
56#65964C22148yescomplemented
57#65963C22148yescomplemented
58#65943C22148yescomplemented
59D5×#121C22148yescomplemented
60#65911C22116yescomplemented
61#65908C22116yescomplemented
62D4×D20C22148yescomplemented
63#65881C22148yescomplemented
64C2×#4042C2213yescomplemented
65C2×#4041C2216yescomplemented
66C2×#4041C2213yescomplemented
67C2×#4041C2213yescomplemented
68C2×#4040C2213yescomplemented
69C2×#4039C2213yescomplemented
70C2×D5×C4⋊C4C2213yescomplemented
71C2×#4030C2216yescomplemented
72C2×#4030C2216yescomplemented
73C2×#4030C2213yescomplemented
74C2×#4029C2213yescomplemented
75C2×#4028C2216yescomplemented
76C2×#4028C2213yescomplemented
77C2×#4028C2216yescomplemented
78C2×D5×C22⋊C4C2216yescomplemented
79C2×#4024C2211yescharacteristic, complemented
80C2×#4020C2213yescomplemented
81C2×C4×D20C2213yescomplemented
82C2×C4×D20C2213yescomplemented
83C2×#4018C2213yescomplemented
84C2×#3488—51nomaximal, Sylow
85C24×D5C2313yes—
86C24×D5C2316yes—
87C2×C5×#41—28no—
88C2×C5×#41C2318yescomplemented
89C22×C5×Q8—28no—
90C22×C5×Q8C2313yes—
91C22×C5×Q8C2311yescharacteristic
92C22×C5×Q8C2318yescomplemented
93C22×C5×D4C2313yes—
94C22×C5×D4C2313yes—
95C23×C4×C5C2313yes—
96C23×C4×C5C2313yes—
97C22×C22⋊D5C2313yes—
98C22×C22⋊D5C2313yes—
99C22×C22⋊D5C2313yes—
100C22×C22⋊D5C2313yes—
101C22×C22⋊D5C2316yes—
102C23×Dic5C2311yescharacteristic
103#4149—2128no—
104C2×#713—28no—
105C2×#713—28no—
106C2×#713—2128no—
107C2×#713—224no—
108C2×#713—224no—
109C2×#713D4116yescomplemented
110C2×#713C2318yes—
111C2×#713C2318yescomplemented
112C2×#713C2318yescomplemented
113C2×#713C23124yescomplemented
114C2×#713C23124yescomplemented
115C2×D4×D5—224no—
116C2×D4×D5—224no—
117C2×D4×D5—424no—
118C2×D4×D5C23124yescomplemented
119C2×D4×D5C23124yescomplemented
120C2×D4×D5C23148yescomplemented
121C2×#709—224no—
122C2×#709C23124yescomplemented
123C22×D20—224no—
124C22×D20—224no—
125C22×D20C2313yes—
126C22×D20C2313yes—
127C22×D20C2316yes—
128C22×D20C2313yes—
129C22×D20C2313yes—
130C22×D20C2316yes—
131C22×D20C2313yes—
132C22×D20C23124yescomplemented
133C22×D20C23124yescomplemented
134C22×C4×D5—224no—
135C22×C4×D5C2313yes—
136C22×C4×D5C2313yes—
137C22×C4×D5C2313yes—
138C22×C4×D5C2313yes—
139C22×C4×D5C2316yes—
140C22×C4×D5C2313yes—
141C22×C4×D5C23124yescomplemented
142C22×Dic10C2311yescharacteristic
143C5×#124C23124yescomplemented
144C5×C22⋊Q8C23124yescomplemented
145C5×#121C23124yescomplemented
146C4×C5×Q8C2318yescomplemented
147C4×C5×D4C23124yescomplemented
148C2×C5×C4⋊C4C2313yes—
149C2×C5×C4⋊C4C2313yes—
150C2×C5×C22⋊C4C2311yescharacteristic
151C2×C5×C22⋊C4C2316yes—
152C2×C5×C22⋊C4C2313yes—
153C2×C42×C5C2313yes—
154C2×C22⋊Dic5C2311yescharacteristic
155C2×C22⋊Dic5C2313yes—
156#4093C23124yescomplemented
157#4092C23124yescomplemented
158Q8×Dic5C2318yescomplemented
159#4086C23124yescomplemented
160#4085C23124yescomplemented
161#4084C23124yescomplemented
162#4083C23124yescomplemented
163#4076C23124yescomplemented
164#4076C23124yescomplemented
165C4×C22⋊D5C23124yescomplemented
166C4×C22⋊D5C23124yescomplemented
167C2×#685C2313yes—
168C2×#685C2313yes—
169C2×#685C2313yes—
170C2×#685C2313yes—
171C2×#685C2316yes—
172C2×#685C2313yes—
173C2×#685C2313yes—
174C2×C4⋊Dic5C2311yescharacteristic
175C2×C4⋊Dic5C2313yes—
176C2×#683C2311yescharacteristic
177C2×#683C2313yes—
178C2×#683C2311yescharacteristic
179C2×#683C2313yes—
180C2×C4×Dic5C2313yes—
181#4042C23124yescomplemented
182#4041C23148yescomplemented
183#4041C23124yescomplemented
184#4041C23124yescomplemented
185#4040C23124yescomplemented
186#4039C23124yescomplemented
187D5×C4⋊C4C23124yescomplemented
188#4030C23124yescomplemented
189#4030C23148yescomplemented
190#4030C23148yescomplemented
191#4029C23124yescomplemented
192#4028C23124yescomplemented
193#4028C23148yescomplemented
194#4028C23148yescomplemented
195D5×C22⋊C4C23148yescomplemented
196#4024C2318yescomplemented
197#4020C23124yescomplemented
198C4×D20C23124yescomplemented
199C4×D20C23124yescomplemented
200#4018C23124yescomplemented
201C22×H(5,𝔽2)—51no—
202C23×#41—51no—
203#3488—532no—
204C2×#550—51no—
205C2×#550—51no—
206C2×#548—51no—
207C2×#548D511yescharacteristic, complemented
208C2×#546—53no—
209C2×#546—53no—
210C2×D42—53no—
211C2×D42—53no—
212C2×#537—53no—
213C2×#535—53no—
214C2×#525—53no—
215C22×#121—53no—
216C2×#520—51no—
217C24×C5C2413yes—
218C24×C5C2411yescharacteristic
219C23×D5—212no—
220C23×D5—212no—
221C23×D5—224no—
222C23×D5—46no—
223C23×D5—412no—
224C23×D5—412no—
225C23×D5C2413yes—
226C23×D5C2413yes—
227C23×D5C24112yes—
228C23×D5C2413yes—
229C23×D5C24124yes—
230C5×#41—232no—
231C2×C5×Q8—232no—
232C2×C5×Q8—212no—
233C2×C5×Q8C2×D418yescomplemented
234C2×C5×Q8C24112yes—
235C2×C5×Q8C2414yes—
236C2×C5×D4—212no—
237C2×C5×D4—212no—
238C2×C5×D4C24112yes—
239C2×C5×D4C24112yes—
240C22×C4×C5—212no—
241C22×C4×C5—212no—
242C22×C4×C5C2411yescharacteristic
243C22×C4×C5C2413yes—
244C22×C4×C5C2413yes—
245C22×C4×C5C2411yescharacteristic
246C22×C4×C5C24112yes—
247C22×C4×C5C24112yes—
248C22×C4×C5C2413yes—
249C2×C22⋊D5—212no—
250C2×C22⋊D5—212no—
251C2×C22⋊D5—212no—
252C2×C22⋊D5—412no—
253C2×C22⋊D5—46no—
254C2×C22⋊D5C24112yes—
255C2×C22⋊D5C24112yes—
256C2×C22⋊D5C24112yes—
257C2×C22⋊D5C24124yes—
258C2×C22⋊D5C24112yes—
259C22×Dic5—24no—
260C22×Dic5C2411yescharacteristic
261C22×Dic5C2411yescharacteristic
262C22×Dic5C2413yes—
263C22×Dic5C2411yescharacteristic
264C22×Dic5C2414yes—
265C22×Dic5C2411yescharacteristic
266#713—232no—
267#713—232no—
268#713—296no—
269#713—296no—
270#713C2×D4164yescomplemented
271D4×D5—296no—
272D4×D5—296no—
273D4×D5—496no—
274#709—296no—
275C2×D20—212no—
276C2×D20—224no—
277C2×D20—212no—
278C2×D20—212no—
279C2×D20—296no—
280C2×D20—296no—
281C2×D20—46no—
282C2×D20—412no—
283C2×D20C2×D4124yescomplemented
284C2×D20C24112yes—
285C2×D20C24112yes—
286C2×D20C24112yes—
287C2×D20C24124yes—
288C2×D20C24124yes—
289C2×D20C24112yes—
290C2×D20C24112yes—
291C2×C4×D5—212no—
292C2×C4×D5—212no—
293C2×C4×D5—212no—
294C2×C4×D5—212no—
295C2×C4×D5—296no—
296C2×C4×D5—412no—
297C2×C4×D5C2×D4124yescomplemented
298C2×C4×D5C24112yes—
299C2×C4×D5C24112yes—
300C2×C4×D5C24112yes—
301C2×C4×D5C24112yes—
302C2×C4×D5C24124yes—
303C2×C4×D5C24112yes—
304C2×Dic10—24no—
305C2×Dic10C2414yes—
306C5×C4⋊C4C24112yes—
307C5×C4⋊C4C24112yes—
308C5×C22⋊C4C2414yes—
309C5×C22⋊C4C24112yes—
310C5×C22⋊C4C24124yes—
311C42×C5C24112yes—
312C22⋊Dic5C2414yes—
313C22⋊Dic5C24112yes—
314#685C24112yes—
315#685C24112yes—
316#685C24112yes—
317#685C24112yes—
318#685C24124yes—
319#685C24112yes—
320#685C24112yes—
321C4⋊Dic5C2414yes—
322C4⋊Dic5C24112yes—
323#683C2414yes—
324#683C24112yes—
325#683C2414yes—
326#683C24112yes—
327C4×Dic5C24112yes—
328C2×H(5,𝔽2)—516no—
329C2×H(5,𝔽2)—1016no—
330C22×#41—51no—
331C22×#41—53no—
332C22×#41—53no—
333C22×#41—51no—
334C22×#41—51no—
335C22×#41—516no—
336C22×#41—53no—
337C22×#41—1016no—
338C22×#41C2×D511yescharacteristic, complemented
339C23×Q8C2×D511yescharacteristic, complemented
340C23×D4—53no—
341C23×D4—53no—
342C23×D4—56no—
343C23×D4—53no—
344C23×D4—53no—
345C24×C4—53no—
346#550—516no—
347#550—516no—
348#548—516no—
349#548C2×D5116yescomplemented
350#546—548no—
351#546—548no—
352D42—548no—
353D42—548no—
354#537—548no—
355#535—548no—
356C2×#127—53no—
357C2×#127—53no—
358C2×#124—53no—
359C2×#124C2×D513yescomplemented
360#525—548no—
361C2×#123—53no—
362C2×#123—53no—
363C2×C22⋊Q8—53no—
364C2×C22⋊Q8—53no—
365C2×C22⋊Q8—51no—
366C2×C22⋊Q8C2×D513yescomplemented
367C2×#121—53no—
368C2×#121—53no—
369C2×#121—53no—
370C2×#121—53no—
371C2×#121—548no—
372C2×#121—53no—
373C2×#121—56no—
374C2×#121—53no—
375C2×#121—56no—
376C2×#121—53no—
377C2×#121—56no—
378C2×#121C2×D513yescomplemented
379C2×#120—53no—
380C2×#120—53no—
381C2×#120—56no—
382C2×#120—56no—
383#520—516no—
384C2×C4×Q8—51no—
385C2×C4×Q8C2×D511yescharacteristic, complemented
386C2×C4×D4—53no—
387C2×C4×D4—53no—
388C2×C4×D4—53no—
389C2×C4×D4—53no—
390C2×C4×D4—53no—
391C2×C4×D4C2×D513yescomplemented
392C2×#117—53no—
393C22×C4⋊C4—53no—
394C22×C22⋊C4—56no—
395C23×C5—22no—
396C23×C5—22no—
397C23×C5—26no—
398C23×C5—26no—
399C23×C5—26no—
400C23×C5H(5,𝔽2)14yescomplemented
401C23×C5C2516yes—
402C23×C5C2512yes—
403C23×C5C2511yescharacteristic
404C22×D5—26no—
405C22×D5—26no—
406C22×D5—26no—
407C22×D5—26no—
408C22×D5—26no—
409C22×D5—26no—
410C22×D5—224no—
411C22×D5—26no—
412C22×D5—26no—
413C22×D5—224no—
414C22×D5—248no—
415C22×D5—412no—
416C22×D5—424no—
417C22×D5—424no—
418C22×D5—448no—
419C22×D5—848no—
420C22×D5C22×D4112yes—
421C22×D5C2516yes—
422C22×D5C2516yes—
423C22×D5C2516yes—
424C5×Q8—224no—
425C5×Q8C22×D4116yescomplemented
426C5×D4—224no—
427C5×D4—224no—
428C2×C4×C5—22no—
429C2×C4×C5—26no—
430C2×C4×C5—26no—
431C2×C4×C5—22no—
432C2×C4×C5—224no—
433C2×C4×C5—224no—
434C2×C4×C5C22×D4112yes—
435C2×C4×C5C2512yes—
436C2×C4×C5C2516yes—
437C2×C4×C5C2516yes—
438C2×C4×C5C2512yes—
439C2×C4×C5C2516yes—
440C22⋊D5—224no—
441C22⋊D5—224no—
442C22⋊D5—224no—
443C22⋊D5—424no—
444C22⋊D5—412no—
445C2×Dic5—22no—
446C2×Dic5—22no—
447C2×Dic5—26no—
448C2×Dic5—22no—
449C2×Dic5—28no—
450C2×Dic5C22×D414yes—
451C2×Dic5C2512yes—
452C2×Dic5C2516yes—
453C2×Dic5C2512yes—
454C2×Dic5C2512yes—
455C2×Dic5C2512yes—
456D20—224no—
457D20—248no—
458D20—224no—
459D20—224no—
460D20—412no—
461D20—424no—
462D20C22×D4148yescomplemented
463C4×D5—224no—
464C4×D5—224no—
465C4×D5—224no—
466C4×D5—224no—
467C4×D5—424no—
468C4×D5C22×D4148yescomplemented
469Dic10—28no—
470C25—53no—
471C25—56no—
472H(5,𝔽2)—10128no—
473C2×#41—28no—
474C2×#41—516no—
475C2×#41—58no—
476C2×#41—524no—
477C2×#41—524no—
478C2×#41—58no—
479C2×#41—58no—
480C2×#41—524no—
481C2×#41—1024no—
482C2×#41—1024no—
483C2×#41—1024no—
484C2×#41—10128no—
485C2×#41—108no—
486C2×#41—108no—
487C2×#41C22×D518yescomplemented
488C22×Q8—28no—
489C22×Q8—51no—
490C22×Q8C22×D513yes—
491C22×Q8C22×D511yescharacteristic
492C22×Q8C22×D518yescomplemented
493C22×D4—53no—
494C22×D4—53no—
495C22×D4—53no—
496C22×D4—53no—
497C22×D4—56no—
498C22×D4—524no—
499C22×D4—524no—
500C22×D4—548no—
501C22×D4—53no—
502C22×D4—56no—
503C22×D4—53no—
504C22×D4—53no—
505C22×D4—53no—
506C22×D4—524no—
507C22×D4—524no—
508C22×D4—53no—
509C22×D4—56no—
510C22×D4—1024no—
511C22×D4—1024no—
512C22×D4—1024no—
513C22×D4—1024no—
514C22×D4—2024no—
515C22×D4C22×D513yes—
516C22×D4C22×D513yes—
517C23×C4—53no—
518C23×C4—51no—
519C23×C4—53no—
520C23×C4—53no—
521C23×C4—53no—
522C23×C4—53no—
523C23×C4—524no—
524C23×C4—56no—
525C23×C4—1024no—
526C23×C4C22×D513yes—
527C23×C4C22×D513yes—
528#127—524no—
529#127—524no—
530#124—524no—
531#124C22×D5124yescomplemented
532#123—524no—
533#123—524no—
534C22⋊Q8—524no—
535C22⋊Q8—524no—
536C22⋊Q8—58no—
537C22⋊Q8C22×D5124yescomplemented
538#121—524no—
539#121—524no—
540#121—524no—
541#121—524no—
542#121—524no—
543#121—548no—
544#121—524no—
545#121—548no—
546#121—524no—
547#121—548no—
548#121C22×D5124yescomplemented
549#120—524no—
550#120—524no—
551#120—548no—
552#120—548no—
553C4×Q8—58no—
554C4×Q8C22×D518yescomplemented
555C4×D4—524no—
556C4×D4—524no—
557C4×D4—524no—
558C4×D4—524no—
559C4×D4—524no—
560C4×D4C22×D5124yescomplemented
561#117—524no—
562C2×C4⋊C4—53no—
563C2×C4⋊C4—53no—
564C2×C4⋊C4—51no—
565C2×C4⋊C4—51no—
566C2×C4⋊C4—51no—
567C2×C4⋊C4—53no—
568C2×C4⋊C4—524no—
569C2×C4⋊C4C22×D513yes—
570C2×C4⋊C4C22×D513yes—
571C2×C22⋊C4—53no—
572C2×C22⋊C4—51no—
573C2×C22⋊C4—53no—
574C2×C22⋊C4—56no—
575C2×C22⋊C4—53no—
576C2×C22⋊C4—53no—
577C2×C22⋊C4—53no—
578C2×C22⋊C4—53no—
579C2×C22⋊C4—53no—
580C2×C22⋊C4—548no—
581C2×C22⋊C4C22×D516yes—
582C2×C22⋊C4C22×D511yescharacteristic
583C2×C22⋊C4C22×D513yes—
584C2×C42—53no—
585C2×C42C22×D513yes—
586C22×C5—22no—
587C22×C5—22no—
588C22×C5—28no—
589C22×C5—26no—
590C22×C5—26no—
591C22×C5—26no—
592C22×C5—412no—
593C22×C5C23×D412yes—
594C22×C5C2×H(5,𝔽2)12yes—
595C22×C5C2×H(5,𝔽2)14yescomplemented
596C22×C5#58512yes—
597C22×C5C2611yescharacteristic
598C2×D5—26no—
599C2×D5—26no—
600C2×D5—224no—
601C2×D5—26no—
602C2×D5—26no—
603C2×D5—26no—
604C2×D5—26no—
605C2×D5—26no—
606C2×D5—26no—
607C2×D5—448no—
608C2×D5—412no—
609C2×D5—412no—
610C2×D5—848no—
611C2×D5C23×D4112yes—
612C4×C5—22no—
613C4×C5—26no—
614C4×C5—26no—
615C4×C5—22no—
616C4×C5C23×D4112yes—
617Dic5—22no—
618Dic5—22no—
619Dic5—26no—
620Dic5—22no—
621Dic5C23×D414yes—
622C24—53no—
623C24—53no—
624C24—53no—
625C24—512no—
626C24—524no—
627C24—1012no—
628C24—1024no—
629C24—1012no—
630C24—206no—
631C24—2012no—
632C24—2012no—
633C24C23×D513yes—
634C24C23×D511yescharacteristic
635#41—232no—
636#41—564no—
637#41—1096no—
638#41—1096no—
639#41—1096no—
640#41—1032no—
641#41—1032no—
642C2×Q8—232no—
643C2×Q8—212no—
644C2×Q8—54no—
645C2×Q8—104no—
646C2×Q8D4×D518yescomplemented
647C2×Q8C23×D5112yes—
648C2×Q8C23×D514yes—
649C2×D4—212no—
650C2×D4—212no—
651C2×D4—512no—
652C2×D4—512no—
653C2×D4—512no—
654C2×D4—512no—
655C2×D4—524no—
656C2×D4—524no—
657C2×D4—512no—
658C2×D4—524no—
659C2×D4—512no—
660C2×D4—512no—
661C2×D4—512no—
662C2×D4—512no—
663C2×D4—524no—
664C2×D4—1096no—
665C2×D4—1096no—
666C2×D4—1012no—
667C2×D4—1024no—
668C2×D4—1096no—
669C2×D4—1012no—
670C2×D4—1096no—
671C2×D4—1012no—
672C2×D4—1012no—
673C2×D4—1012no—
674C2×D4—1012no—
675C2×D4—2012no—
676C2×D4—206no—
677C2×D4—2012no—
678C2×D4—206no—
679C2×D4—2096no—
680C2×D4C23×D5112yes—
681C2×D4C23×D5112yes—
682C22×C4—212no—
683C22×C4—212no—
684C22×C4—51no—
685C22×C4—524no—
686C22×C4—512no—
687C22×C4—54no—
688C22×C4—51no—
689C22×C4—53no—
690C22×C4—51no—
691C22×C4—51no—
692C22×C4—512no—
693C22×C4—512no—
694C22×C4—512no—
695C22×C4—512no—
696C22×C4—524no—
697C22×C4—1012no—
698C22×C4—1096no—
699C22×C4—1012no—
700C22×C4—104no—
701C22×C4—1012no—
702C22×C4—1012no—
703C22×C4—2012no—
704C22×C4C23×D5112yes—
705C22×C4C23×D5112yes—
706C22×C4C23×D511yescharacteristic
707C22×C4C23×D513yes—
708C22×C4C23×D513yes—
709C22×C4C23×D511yescharacteristic
710C22×C4C23×D513yes—
711C4⋊C4—512no—
712C4⋊C4—512no—
713C4⋊C4—54no—
714C4⋊C4—54no—
715C4⋊C4—54no—
716C4⋊C4—512no—
717C4⋊C4C23×D5112yes—
718C4⋊C4C23×D5112yes—
719C22⋊C4—512no—
720C22⋊C4—54no—
721C22⋊C4—512no—
722C22⋊C4—524no—
723C22⋊C4—512no—
724C22⋊C4—512no—
725C22⋊C4—512no—
726C22⋊C4—512no—
727C22⋊C4—512no—
728C22⋊C4C23×D5124yes—
729C22⋊C4C23×D514yes—
730C22⋊C4C23×D5112yes—
731C42—512no—
732C42C23×D5112yes—
733C2×C5—24no—
734C2×C5—46no—
735C2×C5#348814yescomplemented
736C2×C5C24×D411yescharacteristic
737C2×C5C22×H(5,𝔽2)11yescharacteristic
738C2×C5C2×#58511yescharacteristic
739D5—212no—
740D5—46no—
741D5—46no—
742C23—22no—
743C23—22no—
744C23—26no—
745C23—26no—
746C23—26no—
747C23—512no—
748C23—56no—
749C23—56no—
750C23—56no—
751C23—1024no—
752C23—1048no—
753C23—106no—
754C23—106no—
755C23—106no—
756C23—106no—
757C23—106no—
758C23—106no—
759C23—1024no—
760C23—106no—
761C23—106no—
762C23—2012no—
763C23—2024no—
764C23—2024no—
765C23—2048no—
766C23—4048no—
767C23#414914yescomplemented
768C23C24×D516yes—
769C23C24×D512yes—
770C23C24×D511yescharacteristic
771Q8—224no—
772Q8—108no—
773Q8C2×D4×D5116yescomplemented
774D4—224no—
775D4—224no—
776D4—548no—
777D4—1024no—
778D4—1048no—
779D4—1024no—
780D4—1024no—
781D4—1024no—
782D4—1024no—
783D4—1024no—
784D4—2024no—
785D4—2012no—
786D4—2024no—
787D4—2012no—
788C2×C4—22no—
789C2×C4—26no—
790C2×C4—26no—
791C2×C4—22no—
792C2×C4—224no—
793C2×C4—224no—
794C2×C4—54no—
795C2×C4—52no—
796C2×C4—548no—
797C2×C4—52no—
798C2×C4—56no—
799C2×C4—52no—
800C2×C4—52no—
801C2×C4—1024no—
802C2×C4—1024no—
803C2×C4—108no—
804C2×C4—102no—
805C2×C4—102no—
806C2×C4—106no—
807C2×C4—102no—
808C2×C4—1024no—
809C2×C4—1024no—
810C2×C4—2024no—
811C2×C4C2×D4×D5112yes—
812C2×C4C24×D512yes—
813C2×C4C24×D516yes—
814C2×C4C24×D516yes—
815C2×C4C24×D512yes—
816C2×C4C24×D516yes—
817C5C2×#348811yescharacteristic, complemented, Sylow
818C22—22no—
819C22—22no—
820C22—28no—
821C22—26no—
822C22—26no—
823C22—26no—
824C22—412no—
825C22—512no—
826C22—106no—
827C22—106no—
828C22—1024no—
829C22—106no—
830C22—106no—
831C22—106no—
832C22—106no—
833C22—106no—
834C22—106no—
835C22—2048no—
836C22—2012no—
837C22—2012no—
838C22—4048no—
839C22C22×D4×D512yes—
840C22C2×#414912yes—
841C22C2×#414914yescomplemented
842C22#6628712yes—
843C22C25×D511yescharacteristic
844C4—22no—
845C4—26no—
846C4—26no—
847C4—22no—
848C4—54no—
849C4—102no—
850C4—102no—
851C4—106no—
852C4—102no—
853C4C22×D4×D5112yes—
854C2—24no—
855C2—46no—
856C2—1012no—
857C2—206no—
858C2—206no—
859C2#1061861414yesdirect product factor
860C2C23×D4×D511yescharacteristic
861C2C22×#414911yescharacteristic
862C2C2×#6628711yescharacteristic
subgroupG/H
centerC23C24×D5
commutator, cosocleC22×C5C26
FrattiniC22C25×D5
FittingC2×C5×#548C2
socleC23×C5C25
hypercenterC2×#548D5
hypocenterC5C2×#3488
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C22×#4149C2semidirect
2. C23×#713C2semidirect
3. C2×C5×#548C2semidirect
4. C2×#66168C2semidirect
5. C2×#66151C2semidirect
6. #10618614C2direct (N × H)
7. C2×#66010C2semidirect
8. C2×#66008C2semidirect
9. C2×#65964C2semidirect
10. C2×#65963C2semidirect
11. C2×#65943C2semidirect
12. C2×D5×#121C2semidirect
13. C2×#65911C2semidirect
14. C2×#65908C2semidirect
15. C2×D4×D20C2semidirect
16. C2×#65881C2semidirect
17. C22×C5×#41C22semidirect
18. C23×C5×Q8C22semidirect
20. C2×#4149C22semidirect
23. C22×#713C22semidirect
24. C22×#713C22semidirect
25. C22×#713C22semidirect
26. C22×#713C22semidirect
27. C22×#713C22semidirect
28. C22×D4×D5C22semidirect
29. C22×D4×D5C22semidirect
30. C22×D4×D5C22semidirect
31. C22×#709C22semidirect
32. C23×D20C22semidirect
33. C23×D20C22semidirect
34. C23×C4×D5C22semidirect
35. C5×#548C22semidirect
36. C2×C5×#124C22semidirect
37. C2×C5×C22⋊Q8C22semidirect
38. C2×C5×#121C22semidirect
39. C2×C4×C5×Q8C22semidirect
40. C2×C4×C5×D4C22semidirect
41. #66168C22semidirect
42. #66151C22semidirect
43. C2×#4093C22semidirect
44. C2×#4092C22semidirect
45. C2×Q8×Dic5C22semidirect
46. C2×#4086C22semidirect
47. C2×#4085C22semidirect
48. C2×#4084C22semidirect
49. C2×#4083C22semidirect
50. C2×#4076C22semidirect
51. C2×#4076C22semidirect
52. C2×C4×C22⋊D5C22semidirect
53. C2×C4×C22⋊D5C22semidirect
54. #66010C22semidirect
55. #66008C22semidirect
56. #65964C22semidirect
57. #65963C22semidirect
58. #65943C22semidirect
59. D5×#121C22semidirect
60. #65911C22semidirect
61. #65908C22semidirect
62. D4×D20C22semidirect
63. #65881C22semidirect
64. C2×#4042C22semidirect
65. C2×#4041C22semidirect
66. C2×#4041C22semidirect
67. C2×#4041C22semidirect
68. C2×#4040C22semidirect
69. C2×#4039C22semidirect
70. C2×D5×C4⋊C4C22semidirect
71. C2×#4030C22semidirect
72. C2×#4030C22semidirect
73. C2×#4030C22semidirect
74. C2×#4029C22semidirect
75. C2×#4028C22semidirect
76. C2×#4028C22semidirect
77. C2×#4028C22semidirect
78. C2×D5×C22⋊C4C22semidirect
79. C2×#4024C22semidirect
80. C2×#4020C22semidirect
81. C2×C4×D20C22semidirect
82. C2×C4×D20C22semidirect
83. C2×#4018C22semidirect
88. C2×C5×#41C23semidirect
92. C22×C5×Q8C23semidirect
109. C2×#713D4semidirect
111. C2×#713C23semidirect
112. C2×#713C23semidirect
113. C2×#713C23semidirect
114. C2×#713C23semidirect
118. C2×D4×D5C23semidirect
119. C2×D4×D5C23semidirect
120. C2×D4×D5C23semidirect
122. C2×#709C23semidirect
132. C22×D20C23semidirect
133. C22×D20C23semidirect
141. C22×C4×D5C23semidirect
143. C5×#124C23semidirect
144. C5×C22⋊Q8C23semidirect
145. C5×#121C23semidirect
146. C4×C5×Q8C23semidirect
147. C4×C5×D4C23semidirect
156. #4093C23semidirect
157. #4092C23semidirect
158. Q8×Dic5C23semidirect
159. #4086C23semidirect
160. #4085C23semidirect
161. #4084C23semidirect
162. #4083C23semidirect
163. #4076C23semidirect
164. #4076C23semidirect
165. C4×C22⋊D5C23semidirect
166. C4×C22⋊D5C23semidirect
181. #4042C23semidirect
182. #4041C23semidirect
183. #4041C23semidirect
184. #4041C23semidirect
185. #4040C23semidirect
186. #4039C23semidirect
187. D5×C4⋊C4C23semidirect
188. #4030C23semidirect
189. #4030C23semidirect
190. #4030C23semidirect
191. #4029C23semidirect
192. #4028C23semidirect
193. #4028C23semidirect
194. #4028C23semidirect
195. D5×C22⋊C4C23semidirect
196. #4024C23semidirect
197. #4020C23semidirect
198. C4×D20C23semidirect
199. C4×D20C23semidirect
200. #4018C23semidirect
207. C2×#548D5semidirect
233. C2×C5×Q8C2×D4semidirect
270. #713C2×D4semidirect
283. C2×D20C2×D4semidirect
297. C2×C4×D5C2×D4semidirect
338. C22×#41C2×D5semidirect
339. C23×Q8C2×D5semidirect
349. #548C2×D5semidirect
359. C2×#124C2×D5semidirect
366. C2×C22⋊Q8C2×D5semidirect
378. C2×#121C2×D5semidirect
385. C2×C4×Q8C2×D5semidirect
391. C2×C4×D4C2×D5semidirect
400. C23×C5H(5,𝔽2)semidirect
425. C5×Q8C22×D4semidirect
462. D20C22×D4semidirect
468. C4×D5C22×D4semidirect
487. C2×#41C22×D5semidirect
492. C22×Q8C22×D5semidirect
531. #124C22×D5semidirect
537. C22⋊Q8C22×D5semidirect
548. #121C22×D5semidirect
554. C4×Q8C22×D5semidirect
560. C4×D4C22×D5semidirect
595. C22×C5C2×H(5,𝔽2)semidirect
646. C2×Q8D4×D5semidirect
735. C2×C5#3488semidirect
767. C23#4149semidirect
773. Q8C2×D4×D5semidirect
817. C5C2×#3488semidirect
841. C22C2×#4149semidirect
859. C2#10618614direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#41492
C23×#7132
C2×C5×#5482
C2×#661682
C2×#661512
#106186142
C2×#660102
C2×#660082
C2×#659642
C2×#659632
C2×#659432
C2×D5×#1212
C2×#659112
C2×#659082
C2×D4×D202
C2×#658812
C2×#34885