Finite Group Databasebeta

← C2×#21435540 #29461635

Subgroups — C2×#21435540 #29461635

Order 15104.

1882 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838010C211yesmaximal, characteristic, complemented
2C2×#16838006C211yesmaximal, characteristic
3#21435540C2116yesmaximal, direct product factor
4C2×#16837710C211yesmaximal, characteristic, complemented
5C2×#16837709C211yesmaximal, characteristic, complemented
6C2×#16837704C211yesmaximal, characteristic, complemented
7C2×#16837700C211yesmaximal, characteristic, complemented
8C2×#16837647C211yesmaximal, characteristic, complemented
9C2×#16837645C211yesmaximal, characteristic, complemented
10C2×#16837630C211yesmaximal, characteristic, complemented
11C2×#16837628C211yesmaximal, characteristic, complemented
12C2×#16837599C211yesmaximal, characteristic, complemented
13C2×#16837605C211yesmaximal, characteristic, complemented
14C2×#16837605C211yesmaximal, characteristic, complemented
15C2×#16837427C211yesmaximal, characteristic, complemented
16C2×C59×#460C211yesmaximal, characteristic, complemented
17C22×#11745670C2211yescharacteristic
18C22×#11745670C2211yescharacteristic
19C22×#11745659C2211yescharacteristic
20C22×C8×D59C2211yescharacteristic
21#16838010—24no—
22#16838010C2218yescomplemented
23#16838006—24no—
24#16838006C2218yes—
25C2×#14273725C2211yescharacteristic
26C2×#14273722—21no—
27C2×#14273721—21no—
28C2×#14273719—21no—
29C2×#14273719C2211yescharacteristic
30C2×#14273718C2211yescharacteristic
31C2×#14273717—21no—
32C2×#14273708—21no—
33C2×#14273708—21no—
34C2×#14273707C2211yescharacteristic
35C2×#14273703C2211yescharacteristic
36C2×#14273699—21no—
37C2×#14273699—21no—
38C2×#14273698C2211yescharacteristic
39C2×#14273698C2211yescharacteristic
40C2×C4×Dic118C2211yescharacteristic
41C2×D4×Dic59C2211yescharacteristic
42C2×D4×Dic59C2211yescharacteristic
43C2×#14273684C2211yescharacteristic
44#16837710C2218yescomplemented
45#16837709C2218yescomplemented
46#16837704C2218yescomplemented
47#16837700C2218yescomplemented
48#16837647C2218yescomplemented
49#16837645C2218yescomplemented
50#16837630C2218yescomplemented
51#16837628C2218yescomplemented
52#16837605C2218yescomplemented
53#16837605C2218yescomplemented
54#16837599C2218yescomplemented
55C2×#14273661C2211yescharacteristic
56C2×#14273660C2211yescharacteristic
57C2×#14273659C2211yescharacteristic
58C2×#14273658C2211yescharacteristic
59#16837427C2218yescomplemented
60C2×C4⋊(C59⋊C8)C2211yescharacteristic
61C2×Dic59⋊C8C2211yescharacteristic
62C2×Dic59⋊C8C2211yescharacteristic
63C2×#14273652C2211yescharacteristic
64C2×#14273652C2211yescharacteristic
65C2×#14273651C2211yescharacteristic
66C2×#14273651C2211yescharacteristic
67C2×#14273648C2211yescharacteristic
68C2×#14273648C2211yescharacteristic
69C22×SD16×C59C2211yescharacteristic
70C22×SD16×C59C2211yescharacteristic
71C2×#127×C59C2211yescharacteristic
72C2×C4×Q8×C59C2211yescharacteristic
73C59×#460C2218yescomplemented
74C2×C4⋊C8×C59C2211yescharacteristic
75C2×#102×C59C2211yescharacteristic
76C2×#102×C59C2211yescharacteristic
77C22×Dic118C2311yescharacteristic
78C22×C22⋊D59—21no—
79C22×C22⋊D59—21no—
80C23×Dic59—21no—
81C23×Dic59—21no—
82C22×C4×D59C2311yescharacteristic
83C2×#11745670—42no—
84C2×#11745670—42no—
85C2×#11745670C2314yes—
86C2×#11745670C2314yes—
87C2×#11745659—42no—
88C2×#11745659C2314yes—
89C22×C59⋊C8C2311yescharacteristic
90C22×C59⋊C8C2311yescharacteristic
91C2×C8×D59—42no—
92C2×C8×D59C2314yes—
93#14273725—22no—
94#14273725C2314yes—
95#14273722—28no—
96#14273721—28no—
97#14273719—22no—
98#14273719—28no—
99#14273719C2314yes—
100#14273718—22no—
101#14273718C2314yes—
102#14273717—28no—
103#14273708—28no—
104#14273708—28no—
105#14273707—22no—
106#14273707C2314yes—
107#14273703—22no—
108#14273703C2314yes—
109#14273699—28no—
110#14273699—28no—
111#14273698—22no—
112#14273698—22no—
113#14273698C2314yes—
114#14273698C2314yes—
115C4×Dic118—22no—
116C4×Dic118C2314yes—
117D4×Dic59—22no—
118D4×Dic59—22no—
119D4×Dic59C2314yes—
120D4×Dic59C2314yes—
121#14273684D414yes—
122#14273684C2314yes—
123C2×C4⋊Dic59—21no—
124C2×C4⋊Dic59—21no—
125C2×C4⋊Dic59C2311yescharacteristic
126C2×C4⋊Dic59C2311yescharacteristic
127C2×C4⋊Dic59C2311yescharacteristic
128C2×Dic59⋊C4—21no—
129C2×Dic59⋊C4—21no—
130C2×Dic59⋊C4—21no—
131C2×Dic59⋊C4—21no—
132C2×Dic59⋊C4—21no—
133C2×Dic59⋊C4—21no—
134C2×Dic59⋊C4—21no—
135C2×Dic59⋊C4D411yescharacteristic
136C2×Dic59⋊C4D411yescharacteristic
137C2×C22⋊Dic59—21no—
138C2×C22⋊Dic59—21no—
139C2×C22⋊Dic59—21no—
140C2×C22⋊Dic59—21no—
141C2×(C2×D59)⋊C4—21no—
142C2×(C2×D59)⋊C4—21no—
143C2×(C2×D59)⋊C4D411yescharacteristic
144C2×(C2×D59)⋊C4D411yescharacteristic
145C2×C4×Dic59—21no—
146C2×C4×Dic59C2311yescharacteristic
147#14273661C2314yes—
148#14273660C2314yes—
149#14273659C2314yes—
150#14273658C2314yes—
151C4⋊(C59⋊C8)C2314yes—
152Dic59⋊C8C2314yes—
153Dic59⋊C8C2314yes—
154#14273652C2314yes—
155#14273652C2314yes—
156#14273651C2314yes—
157#14273651C2314yes—
158#14273648C2314yes—
159#14273648C2314yes—
160C22×Q8×C59C2311yescharacteristic
161C22×D4×C59—21no—
162C22×D4×C59—21no—
163C22×D4×C59C2311yescharacteristic
164C22×D4×C59C2311yescharacteristic
165C2×SD16×C59—42no—
166C2×SD16×C59—42no—
167C2×SD16×C59C2314yes—
168C2×SD16×C59C2314yes—
169C22×C8×C59C2311yescharacteristic
170C22×C8×C59C2311yescharacteristic
171#127×C59—22no—
172#127×C59C2314yes—
173C4×Q8×C59—22no—
174C4×Q8×C59C2314yes—
175C2×C4⋊C4×C59—21no—
176C2×C4⋊C4×C59C2311yescharacteristic
177C2×C42×C59—21no—
178C2×C42×C59C2311yescharacteristic
179C4⋊C8×C59C2314yes—
180#102×C59C2314yes—
181#102×C59C2314yes—
182C24×C59—21no—
183C24×C59—21no—
184C23×D59C2×D411yescharacteristic
185C2×Q8×C59—21no—
186C2×Q8×C59—22no—
187C2×Q8×C59—22no—
188C2×Q8×C59C2412yes—
189C2×D4×C59—21no—
190C2×D4×C59—21no—
191C2×D4×C59—24no—
192C2×D4×C59—24no—
193C2×D4×C59—22no—
194C2×D4×C59—22no—
195C2×D4×C59—22no—
196C2×D4×C59—22no—
197C2×D4×C59—82no—
198C2×D4×C59—82no—
199C2×D4×C59C2412yes—
200C2×D4×C59C2412yes—
201C22×C4×C59—21no—
202C22×C4×C59—21no—
203C22×C4×C59C2×D411yescharacteristic
204C22×C4×C59C2×D411yescharacteristic
205C22×C4×C59C2411yescharacteristic
206C2×C22⋊D59—24no—
207C2×C22⋊D59—24no—
208C2×C22⋊D59—82no—
209C2×C22⋊D59—82no—
210C22×Dic59—21no—
211C22×Dic59—21no—
212C22×Dic59—21no—
213C22×Dic59—21no—
214C22×Dic59—24no—
215C22×Dic59—24no—
216C22×Dic59—82no—
217C22×Dic59—82no—
218C22×Dic59C2×D411yescharacteristic
219C22×Dic59C2×D411yescharacteristic
220C22×Dic59C2×D411yescharacteristic
221C2×C4×D59—22no—
222C2×C4×D59—22no—
223C2×C4×D59C2×D412yes—
224C2×C4×D59C2412yes—
225C2×Dic118—22no—
226C2×Dic118—22no—
227C2×Dic118—21no—
228C2×Dic118C2412yes—
229SD16×C59—44no—
230SD16×C59—44no—
231C2×C8×C59—22no—
232C2×C8×C59—22no—
233C2×C8×C59C2412yes—
234C2×C8×C59C2412yes—
235C4⋊C4×C59—24no—
236C4⋊C4×C59—21no—
237C4⋊C4×C59C2412yes—
238C42×C59—24no—
239C42×C59C2×D412yes—
240C42×C59C2412yes—
241C22⋊Dic59—24no—
242C22⋊Dic59—24no—
243C22⋊Dic59—24no—
244C22⋊Dic59—24no—
245#11745670—44no—
246#11745670—44no—
247(C2×D59)⋊C4—24no—
248(C2×D59)⋊C4—24no—
249(C2×D59)⋊C4C2×D414yes—
250(C2×D59)⋊C4C2×D414yes—
251C4⋊Dic59—21no—
252C4⋊Dic59—21no—
253C4⋊Dic59—21no—
254C4⋊Dic59—24no—
255C4⋊Dic59—24no—
256C4⋊Dic59C2412yes—
257C4⋊Dic59C2412yes—
258C4⋊Dic59C2412yes—
259Dic59⋊C4—24no—
260Dic59⋊C4—24no—
261Dic59⋊C4—24no—
262Dic59⋊C4—24no—
263Dic59⋊C4—24no—
264Dic59⋊C4—24no—
265Dic59⋊C4—24no—
266Dic59⋊C4C2×D414yes—
267Dic59⋊C4C2×D414yes—
268C4×Dic59—24no—
269C4×Dic59C2×D412yes—
270C4×Dic59C2412yes—
271C2×C59⋊C8—22no—
272C2×C59⋊C8—22no—
273C2×C59⋊C8C2412yes—
274C2×C59⋊C8C2412yes—
275#11745659—44no—
276C8×D59—44no—
277C23×C59—22no—
278C23×C59—22no—
279C23×C59—42no—
280C23×C59—42no—
281C23×C59—42no—
282C23×C59—42no—
283C23×C59—42no—
284C23×C59—42no—
285C23×C59C22×D411yescharacteristic
286C22×D59—22no—
287C22×D59—22no—
288C22×D59—22no—
289C22×D59C22×D412yes—
290Q8×C59—22no—
291Q8×C59—22no—
292Q8×C59—42no—
293D4×C59—22no—
294D4×C59—22no—
295D4×C59—22no—
296D4×C59—22no—
297D4×C59—42no—
298D4×C59—42no—
299D4×C59—84no—
300D4×C59—84no—
301C2×C4×C59—22no—
302C2×C4×C59—22no—
303C2×C4×C59—22no—
304C2×C4×C59—22no—
305C2×C4×C59—42no—
306C2×C4×C59—42no—
307C2×C4×C59C22×D412yes—
308C2×C4×C59C22×D412yes—
309C2×C4×C59C22×D411yescharacteristic
310C2×C4×C59H(5,𝔽2)12yes—
311C2×C4×C592−1+412yes—
312C2×C4×C59C2511yescharacteristic
313C22⋊D59—84no—
314C22⋊D59—84no—
315C2×Dic59—22no—
316C2×Dic59—22no—
317C2×Dic59—22no—
318C2×Dic59—22no—
319C2×Dic59—22no—
320C2×Dic59—22no—
321C2×Dic59—22no—
322C2×Dic59—42no—
323C2×Dic59—42no—
324C2×Dic59—42no—
325C2×Dic59—42no—
326C2×Dic59—84no—
327C2×Dic59—84no—
328C2×Dic59C22×D412yes—
329C2×Dic59C22×D412yes—
330C2×Dic59C22×D412yes—
331C4×D59—24no—
332C4×D59—22no—
333C4×D59—22no—
334Dic118—22no—
335Dic118—22no—
336Dic118—42no—
337C8×C59—22no—
338C8×C59—22no—
339C59⋊C8—22no—
340C59⋊C8—22no—
341C2×#3260—591nomaximal, Sylow
342C22×C59—42no—
343C22×C59—42no—
344C22×C59—42no—
345C22×C59—42no—
346C22×C59—42no—
347C22×C59—42no—
348C22×C59—84no—
349C22×C59—84no—
350C22×C59#53712yes—
351C22×C59#57712yes—
352C22×C59#57712yes—
353C22×C59C23×D411yescharacteristic
354C2×D59—22no—
355C2×D59—22no—
356C2×D59—22no—
357C2×D59—44no—
358C4×C59—22no—
359C4×C59—22no—
360C4×C59—42no—
361C4×C59—42no—
362C4×C59#53712yes—
363C4×C59C2×H(5,𝔽2)11yescharacteristic
364C4×C59C2×2−1+411yescharacteristic
365Dic59—22no—
366Dic59—22no—
367Dic59—22no—
368Dic59—42no—
369Dic59—42no—
370Dic59—42no—
371Dic59—42no—
372C2×#541—591no—
373C2×#540—591no—
374#3260—5916no—
375C2×#479—591no—
376C2×#479—591no—
377C2×#478—591no—
378C2×#478—591no—
379C2×#468—591no—
380C2×#468—591no—
381C2×#465—591no—
382C2×#465—591no—
383C2×#460—591no—
384C2×#460D5911yescharacteristic, complemented
385C2×#461—591no—
386C2×#461—591no—
387C2×#424—591no—
388C2×C59—82no—
389C2×C59—82no—
390C2×C59#326014yescomplemented
391C2×C59C2×#53711yescharacteristic
392C2×C59C2×#57711yescharacteristic
393C2×C59C2×#57711yescharacteristic
394D59—42no—
395C22×SD16—591no—
396C22×SD16—591no—
397C22×SD16C2×D5911yescharacteristic
398C22×SD16C2×D5911yescharacteristic
399C22×M16—591no—
400C23×C8—591no—
401#541—598no—
402#541—1184no—
403#540—598no—
404#540—1184no—
405C2×C4⋊Q8—591no—
406C2×#127C2×D5911yescharacteristic
407C2×#126—1181no—
408C2×#126—1181no—
409C2×#125—591no—
410C2×#125—591no—
411C2×#125—1181no—
412C2×#125—1181no—
413C2×#123—1181no—
414C2×#123—1181no—
415C2×C22⋊Q8—591no—
416C2×C22⋊Q8—591no—
417C2×#121—591no—
418C2×#121—591no—
419C2×#121—1181no—
420C2×#121—1181no—
421C2×C4×Q8—591no—
422C2×C4×Q8C2×D5911yescharacteristic
423C2×C4×D4—591no—
424C2×C4×D4—591no—
425C2×#117—591no—
426#479—598no—
427#479—598no—
428#478—598no—
429#478—598no—
430#468—598no—
431#468—598no—
432#465—598no—
433#465—598no—
434#461—598no—
435#461—598no—
436#460—598no—
437#460C2×D5918yescomplemented
438C2×#107—591no—
439C2×#107—591no—
440C2×#106—591no—
441C2×#106—591no—
442#424—598no—
443C2×C4⋊C8—591no—
444C2×C4⋊C8—591no—
445C2×C4⋊C8—591no—
446C2×C4⋊C8C2×D5911yescharacteristic
447C2×#103—591no—
448C2×#103—591no—
449C2×#103—591no—
450C2×#103—591no—
451C2×#102—591no—
452C2×#102—591no—
453C2×#102C2×D5911yescharacteristic
454C2×#102C2×D5911yescharacteristic
455C59C2×#326011yescharacteristic, complemented, Sylow
456C22×Q8—591no—
457C22×Q8C22×D5911yescharacteristic
458C22×D4—21no—
459C22×D4—21no—
460C22×D4—1181no—
461C22×D4—1181no—
462C22×D4C22×D5911yescharacteristic
463C22×D4C22×D5911yescharacteristic
464C23×C4—591no—
465C23×C4—1181no—
466C23×C4—1181no—
467C2×SD16—42no—
468C2×SD16—42no—
469C2×SD16—594no—
470C2×SD16—594no—
471C2×SD16—2362no—
472C2×SD16—2362no—
473C2×SD16C22×D5914yes—
474C2×SD16C22×D5914yes—
475C2×M16—594no—
476C2×M16—2362no—
477C22×C8—591no—
478C22×C8—591no—
479C22×C8—594no—
480C22×C8—2362no—
481C22×C8C22×D5911yescharacteristic
482C22×C8C22×D5911yescharacteristic
483C4⋊Q8—594no—
484C4⋊Q8—1182no—
485#127—22no—
486#127C22×D5914yes—
487#126—1188no—
488#126—1188no—
489#125—594no—
490#125—594no—
491#125—1188no—
492#125—1182no—
493#125—1188no—
494#125—1182no—
495#123—1188no—
496#123—1188no—
497C22⋊Q8—594no—
498C22⋊Q8—594no—
499C22⋊Q8—1182no—
500C22⋊Q8—1182no—
501#121—594no—
502#121—594no—
503#121—1188no—
504#121—1188no—
505#121—1182no—
506#121—1182no—
507C4×Q8—22no—
508C4×Q8—594no—
509C4×Q8—1182no—
510C4×Q8C22×D5914yes—
511C4×D4—594no—
512C4×D4—594no—
513C4×D4—1182no—
514C4×D4—1182no—
515#117—594no—
516#117—594no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—591no—
519C2×C4⋊C4—591no—
520C2×C4⋊C4—591no—
521C2×C4⋊C4—591no—
522C2×C4⋊C4—591no—
523C2×C4⋊C4—1181no—
524C2×C4⋊C4—1181no—
525C2×C4⋊C4—1181no—
526C2×C4⋊C4—1181no—
527C2×C4⋊C4—1181no—
528C2×C4⋊C4—1181no—
529C2×C4⋊C4—1181no—
530C2×C4⋊C4—1181no—
531C2×C4⋊C4—1181no—
532C2×C4⋊C4C22×D5911yescharacteristic
533C2×C22⋊C4—591no—
534C2×C22⋊C4—591no—
535C2×C22⋊C4—1181no—
536C2×C22⋊C4—1181no—
537C2×C22⋊C4—1181no—
538C2×C22⋊C4—1181no—
539C2×C22⋊C4—1181no—
540C2×C22⋊C4—1181no—
541C2×C42—21no—
542C2×C42—591no—
543C2×C42—1181no—
544C2×C42C22×D5911yescharacteristic
545#107—594no—
546#107—594no—
547#106—594no—
548#106—594no—
549C4⋊C8—594no—
550C4⋊C8—594no—
551C4⋊C8—594no—
552C4⋊C8C22×D5914yes—
553#103—594no—
554#103—594no—
555#103—594no—
556#103—594no—
557#102—594no—
558#102—594no—
559#102C22×D5914yes—
560#102C22×D5914yes—
561C24—21no—
562C24—21no—
563C24—591no—
564C2×Q8—21no—
565C2×Q8—22no—
566C2×Q8—22no—
567C2×Q8—592no—
568C2×Q8—1181no—
569C2×Q8—1182no—
570C2×Q8—1182no—
571C2×Q8C23×D5912yes—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—24no—
575C2×D4—24no—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—82no—
581C2×D4—82no—
582C2×D4—1184no—
583C2×D4—1184no—
584C2×D4—4722no—
585C2×D4—4722no—
586C2×D4C23×D5912yes—
587C2×D4C23×D5912yes—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—591no—
591C22×C4—591no—
592C22×C4—591no—
593C22×C4—592no—
594C22×C4—592no—
595C22×C4—1184no—
596C22×C4—1184no—
597C22×C4—1182no—
598C22×C4—1182no—
599C22×C4—1181no—
600C22×C4—1181no—
601C22×C4—1181no—
602C22×C4—1181no—
603C22×C4—4722no—
604C22×C4—4722no—
605C22×C4D4×D5911yescharacteristic
606C22×C4D4×D5911yescharacteristic
607C22×C4C23×D5911yescharacteristic
608SD16—44no—
609SD16—44no—
610SD16—2364no—
611SD16—2364no—
612M16—2364no—
613C2×C8—22no—
614C2×C8—22no—
615C2×C8—592no—
616C2×C8—592no—
617C2×C8—1182no—
618C2×C8—1182no—
619C2×C8—2364no—
620C2×C8C23×D5912yes—
621C2×C8C23×D5912yes—
622C4⋊C4—24no—
623C4⋊C4—21no—
624C4⋊C4—594no—
625C4⋊C4—594no—
626C4⋊C4—592no—
627C4⋊C4—592no—
628C4⋊C4—592no—
629C4⋊C4—1184no—
630C4⋊C4—1184no—
631C4⋊C4—1184no—
632C4⋊C4—1184no—
633C4⋊C4—1184no—
634C4⋊C4—1184no—
635C4⋊C4—1181no—
636C4⋊C4—1181no—
637C4⋊C4—1181no—
638C4⋊C4—1184no—
639C4⋊C4—1184no—
640C4⋊C4—1184no—
641C4⋊C4C23×D5912yes—
642C22⋊C4—594no—
643C22⋊C4—594no—
644C22⋊C4—1184no—
645C22⋊C4—1184no—
646C22⋊C4—1184no—
647C22⋊C4—1184no—
648C22⋊C4—1184no—
649C22⋊C4—1184no—
650C42—24no—
651C42—592no—
652C42—592no—
653C42—1184no—
654C42D4×D5912yes—
655C42C23×D5912yes—
656C23—22no—
657C23—22no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—592no—
665C23—1182no—
666C23—1182no—
667C23—1182no—
668C23C2×D4×D5911yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—42no—
672Q8—1182no—
673Q8—1182no—
674Q8—2362no—
675D4—22no—
676D4—22no—
677D4—22no—
678D4—22no—
679D4—42no—
680D4—42no—
681D4—84no—
682D4—84no—
683D4—4724no—
684D4—4724no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—592no—
692C2×C4—592no—
693C2×C4—592no—
694C2×C4—1182no—
695C2×C4—1182no—
696C2×C4—1182no—
697C2×C4—1182no—
698C2×C4—1182no—
699C2×C4—1184no—
700C2×C4—1182no—
701C2×C4—1182no—
702C2×C4—1182no—
703C2×C4—1182no—
704C2×C4—4724no—
705C2×C4—4724no—
706C2×C4—2362no—
707C2×C4—2362no—
708C2×C4—2362no—
709C2×C4—2362no—
710C2×C4C2×D4×D5912yes—
711C2×C4C2×D4×D5912yes—
712C2×C4C2×D4×D5911yescharacteristic
713C2×C4#1427377212yes—
714C2×C4#1427377412yes—
715C2×C4C24×D5911yescharacteristic
716C8—22no—
717C8—22no—
718C8—1182no—
719C8—1182no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—84no—
727C22—84no—
728C22—1182no—
729C22—1182no—
730C22—1182no—
731C22—2364no—
732C22#1683798112yes—
733C22#1683820812yes—
734C22#1683821212yes—
735C22C22×D4×D5911yescharacteristic
736C4—22no—
737C4—22no—
738C4—42no—
739C4—42no—
740C4—1182no—
741C4—1182no—
742C4—1182no—
743C4—2362no—
744C4—2362no—
745C4—2362no—
746C4—2362no—
747C4#1683798112yes—
748C4C2×#1427377211yescharacteristic
749C4C2×#1427377411yescharacteristic
750C2—82no—
751C2—82no—
752C2—2362no—
753C2#2143554014yesdirect product factor
754C2C2×#1683798111yescharacteristic
755C2C2×#1683820811yescharacteristic
756C2C2×#1683821211yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#460C2
socleC23×C59C22×D4
prime radicalC2×#16838006C2
hypercenterC2×#460D59
hypocenterC59C2×#3260
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#460

Complements

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

NH ≅ G/Ntype
1. C2×#16838010C2semidirect
3. #21435540C2direct (N × H)
4. C2×#16837710C2semidirect
5. C2×#16837709C2semidirect
6. C2×#16837704C2semidirect
7. C2×#16837700C2semidirect
8. C2×#16837647C2semidirect
9. C2×#16837645C2semidirect
10. C2×#16837630C2semidirect
11. C2×#16837628C2semidirect
12. C2×#16837599C2semidirect
13. C2×#16837605C2semidirect
14. C2×#16837605C2semidirect
15. C2×#16837427C2semidirect
16. C2×C59×#460C2semidirect
22. #16838010C22semidirect
44. #16837710C22semidirect
45. #16837709C22semidirect
46. #16837704C22semidirect
47. #16837700C22semidirect
48. #16837647C22semidirect
49. #16837645C22semidirect
50. #16837630C22semidirect
51. #16837628C22semidirect
52. #16837605C22semidirect
53. #16837605C22semidirect
54. #16837599C22semidirect
59. #16837427C22semidirect
73. C59×#460C22semidirect
384. C2×#460D59semidirect
390. C2×C59#3260semidirect
437. #460C2×D59semidirect
455. C59C2×#3260semidirect
753. C2#21435540direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380102
C2×#168380062
#214355402
C2×#168377102
C2×#168377092
C2×#168377042
C2×#168377002
C2×#168376472
C2×#168376452
C2×#168376302
C2×#168376282
C2×#168375992
C2×#168376052
C2×#168374272
C2×C59×#4602
C2×#326059