Finite Group Databasebeta

← C2×#479×D59 #29456174

Subgroups — C2×#479×D59 #29456174

Order 15104.

2142 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#125×D59C211yesmaximal, characteristic
2C2×C4×Q8×D59C211yesmaximal, characteristic
3C2×#16837712C211yesmaximal, characteristic, complemented
4C2×#16837711C211yesmaximal, characteristic, complemented
5C2×#16837710C211yesmaximal, characteristic, complemented
6C2×#16837709C211yesmaximal, characteristic, complemented
7C2×#16837708C211yesmaximal, characteristic, complemented
8C2×#16837707C211yesmaximal, characteristic, complemented
9C2×#16837706C211yesmaximal, characteristic, complemented
10#479×D59C2116yesmaximal, direct product factor
11C2×#107×D59C211yesmaximal, characteristic
12C2×#106×D59C211yesmaximal, characteristic
13C2×C4⋊C8×D59C211yesmaximal, characteristic
14C2×#103×D59C211yesmaximal, characteristic
15C2×#103×D59C211yesmaximal, characteristic
16C2×C59×#479C211yesmaximal, characteristic, complemented
17C22×Q8×D59C2211yescharacteristic
18C22×C8×D59C2211yescharacteristic
19C22×C8×D59C2211yescharacteristic
20C2×#14273719C2211yescharacteristic
21C2×#14273718C2211yescharacteristic
22C2×#14273718C2211yescharacteristic
23C2×#14273717—21no—
24C2×#14273717—21no—
25#125×D59—24no—
26#125×D59C2218yes—
27C2×Q8×Dic59C2211yescharacteristic
28C2×C4×Dic118—21no—
29C2×C4×Dic118C2211yescharacteristic
30C2×#14273692—21no—
31C2×#14273692C2211yescharacteristic
32C4×Q8×D59—24no—
33C4×Q8×D59C2218yes—
34C2×C4⋊C4×D59—21no—
35C2×C4⋊C4×D59—21no—
36C2×C4⋊C4×D59—21no—
37C2×C4⋊C4×D59C2211yescharacteristic
38C2×C4⋊C4×D59C2211yescharacteristic
39C2×C4⋊C4×D59C2211yescharacteristic
40C2×C42×D59—21no—
41C2×C42×D59C2211yescharacteristic
42#16837712C2218yescomplemented
43#16837711C2218yescomplemented
44#16837710C2218yescomplemented
45#16837709C2218yescomplemented
46#16837708C2218yescomplemented
47#16837707C2218yescomplemented
48#16837706C2218yescomplemented
49C2×#14273661C2211yescharacteristic
50C2×#14273660C2211yescharacteristic
51C2×#14273660C2211yescharacteristic
52#107×D59C2218yes—
53C2×#14273659C2211yescharacteristic
54C2×#14273658C2211yescharacteristic
55C2×#14273658C2211yescharacteristic
56#106×D59C2218yes—
57C2×C4⋊(C59⋊C8)C2211yescharacteristic
58C2×Dic59⋊C8C2211yescharacteristic
59C2×Dic59⋊C8C2211yescharacteristic
60C4⋊C8×D59C2218yes—
61C2×#14273652C2211yescharacteristic
62C2×#14273652C2211yescharacteristic
63C2×#14273651C2211yescharacteristic
64C2×#14273651C2211yescharacteristic
65C2×#14273650C2211yescharacteristic
66C2×#14273650C2211yescharacteristic
67#103×D59C2218yes—
68#103×D59C2218yes—
69C2×#125×C59C2211yescharacteristic
70C2×C4×Q8×C59C2211yescharacteristic
71C59×#479C2218yescomplemented
72C2×#107×C59C2211yescharacteristic
73C2×#106×C59C2211yescharacteristic
74C2×C4⋊C8×C59C2211yescharacteristic
75C2×#103×C59C2211yescharacteristic
76C2×#103×C59C2211yescharacteristic
77C22×Dic118—21no—
78C22×Dic118C2311yescharacteristic
79C2×Q8×D59—22no—
80C2×Q8×D59—24no—
81C2×Q8×D59Q818yes—
82C2×Q8×D59C2314yes—
83C22×C4×D59—21no—
84C22×C4×D59—21no—
85C22×C4×D59—21no—
86C22×C4×D59—21no—
87C22×C4×D59D411yescharacteristic
88C22×C4×D59D411yescharacteristic
89C22×C4×D59C2311yescharacteristic
90C22×C59⋊C8C2311yescharacteristic
91C22×C59⋊C8C2311yescharacteristic
92C2×C8×D59—24no—
93C2×C8×D59—24no—
94C2×C8×D59C2314yes—
95C2×C8×D59C2314yes—
96#14273719—22no—
97#14273719C2314yes—
98#14273718—22no—
99#14273718—22no—
100#14273718C2314yes—
101#14273718C2314yes—
102#14273717—28no—
103#14273717—28no—
104Q8×Dic59—22no—
105Q8×Dic59C2314yes—
106C4×Dic118—22no—
107C4×Dic118—28no—
108C4×Dic118C2314yes—
109#14273692—22no—
110#14273692—28no—
111#14273692C2314yes—
112C2×C4⋊Dic59—21no—
113C2×C4⋊Dic59—21no—
114C2×C4⋊Dic59—21no—
115C2×C4⋊Dic59C2311yescharacteristic
116C2×C4⋊Dic59C2311yescharacteristic
117C2×C4⋊Dic59C2311yescharacteristic
118C2×Dic59⋊C4—21no—
119C2×Dic59⋊C4—21no—
120C2×Dic59⋊C4—21no—
121C2×Dic59⋊C4—21no—
122C2×Dic59⋊C4—21no—
123C2×Dic59⋊C4—21no—
124C2×Dic59⋊C4—21no—
125C2×Dic59⋊C4—21no—
126C2×Dic59⋊C4—21no—
127C4⋊C4×D59—22no—
128C4⋊C4×D59—22no—
129C4⋊C4×D59—28no—
130C4⋊C4×D59—28no—
131C4⋊C4×D59—28no—
132C4⋊C4×D59—22no—
133C4⋊C4×D59C2314yes—
134C4⋊C4×D59C2314yes—
135C4⋊C4×D59C2314yes—
136C2×C4×Dic59—21no—
137C2×C4×Dic59—21no—
138C2×C4×Dic59—21no—
139C2×C4×Dic59D411yescharacteristic
140C2×C4×Dic59D411yescharacteristic
141C2×C4×Dic59C2311yescharacteristic
142C42×D59—28no—
143C42×D59D414yes—
144C42×D59C2314yes—
145#14273661C2314yes—
146#14273660C2314yes—
147#14273660C2314yes—
148#14273659C2314yes—
149#14273658C2314yes—
150#14273658C2314yes—
151C4⋊(C59⋊C8)C2314yes—
152Dic59⋊C8C2314yes—
153Dic59⋊C8C2314yes—
154#14273652C2314yes—
155#14273652C2314yes—
156#14273651C2314yes—
157#14273651C2314yes—
158#14273650C2314yes—
159#14273650C2314yes—
160C22×Q8×C59C2311yescharacteristic
161C22×C8×C59C2311yescharacteristic
162C22×C8×C59C2311yescharacteristic
163#125×C59—22no—
164#125×C59C2314yes—
165C4×Q8×C59—22no—
166C4×Q8×C59C2314yes—
167C2×C4⋊C4×C59—21no—
168C2×C4⋊C4×C59—21no—
169C2×C4⋊C4×C59—21no—
170C2×C4⋊C4×C59C2311yescharacteristic
171C2×C4⋊C4×C59C2311yescharacteristic
172C2×C4⋊C4×C59C2311yescharacteristic
173C2×C42×C59—21no—
174C2×C42×C59C2311yescharacteristic
175#107×C59C2314yes—
176#106×C59C2314yes—
177C4⋊C8×C59C2314yes—
178#103×C59C2314yes—
179#103×C59C2314yes—
180C23×D59C2×D411yescharacteristic
181C2×Q8×C59—21no—
182C2×Q8×C59—22no—
183C2×Q8×C59C2×Q814yes—
184C2×Q8×C59C2412yes—
185C22×C4×C59—21no—
186C22×C4×C59—21no—
187C22×C4×C59—21no—
188C22×C4×C59—21no—
189C22×C4×C59C2×D411yescharacteristic
190C22×C4×C59C2×D411yescharacteristic
191C22×C4×C59C2411yescharacteristic
192C22×Dic59—21no—
193C22×Dic59—21no—
194C22×Dic59—21no—
195C22×Dic59—21no—
196C22×Dic59C2×D411yescharacteristic
197C22×Dic59C2×D411yescharacteristic
198C22×Dic59C2×D411yescharacteristic
199Q8×D59—216no—
200Q8×D59—28no—
201Q8×D59C2×Q8116yes—
202C2×C4×D59—28no—
203C2×C4×D59—24no—
204C2×C4×D59—24no—
205C2×C4×D59—24no—
206C2×C4×D59—24no—
207C2×C4×D59—24no—
208C2×C4×D59—24no—
209C2×C4×D59—44no—
210C2×C4×D59—44no—
211C2×C4×D59—44no—
212C2×C4×D59C2×D414yes—
213C2×C4×D59C2×D414yes—
214C2×C4×D59C2×D412yes—
215C2×C4×D59C2×Q814yes—
216C2×C4×D59#4114yes—
217C2×C4×D59C2412yes—
218C2×Dic118—21no—
219C2×Dic118—22no—
220C2×Dic118—28no—
221C2×Dic118—24no—
222C2×Dic118C2×Q814yes—
223C2×Dic118C2412yes—
224C2×C8×C59—22no—
225C2×C8×C59—22no—
226C2×C8×C59C2412yes—
227C2×C8×C59C2412yes—
228C4⋊C4×C59—24no—
229C4⋊C4×C59—24no—
230C4⋊C4×C59—24no—
231C4⋊C4×C59—21no—
232C4⋊C4×C59—21no—
233C4⋊C4×C59—21no—
234C4⋊C4×C59C2412yes—
235C4⋊C4×C59C2412yes—
236C4⋊C4×C59C2412yes—
237C42×C59—24no—
238C42×C59C2×D412yes—
239C42×C59C2412yes—
240C4⋊Dic59—21no—
241C4⋊Dic59—21no—
242C4⋊Dic59—21no—
243C4⋊Dic59—24no—
244C4⋊Dic59—24no—
245C4⋊Dic59—24no—
246C4⋊Dic59C2412yes—
247C4⋊Dic59C2412yes—
248C4⋊Dic59C2412yes—
249Dic59⋊C4—24no—
250Dic59⋊C4—24no—
251Dic59⋊C4—24no—
252Dic59⋊C4—24no—
253Dic59⋊C4—24no—
254Dic59⋊C4—24no—
255Dic59⋊C4—24no—
256Dic59⋊C4—24no—
257Dic59⋊C4—24no—
258C4×Dic59—24no—
259C4×Dic59—24no—
260C4×Dic59—24no—
261C4×Dic59C2×D412yes—
262C4×Dic59C2×D414yes—
263C4×Dic59C2×D414yes—
264C4×Dic59C2412yes—
265C2×C59⋊C8—22no—
266C2×C59⋊C8—22no—
267C2×C59⋊C8C2412yes—
268C2×C59⋊C8C2412yes—
269C8×D59—28no—
270C8×D59—28no—
271C23×C59C22×D411yescharacteristic
272C22×D59C22⋊Q814yes—
273C22×D59#13514yes—
274C22×D59#13714yes—
275C22×D59C22×D412yes—
276Q8×C59—24no—
277Q8×C59—22no—
278Q8×C59C22×Q814yes—
279C2×C4×C59—24no—
280C2×C4×C59—22no—
281C2×C4×C59—22no—
282C2×C4×C59—22no—
283C2×C4×C59—22no—
284C2×C4×C59—22no—
285C2×C4×C59—22no—
286C2×C4×C59—42no—
287C2×C4×C59—42no—
288C2×C4×C59—42no—
289C2×C4×C59C22×D412yes—
290C2×C4×C59C22×D412yes—
291C2×C4×C59C22×D411yescharacteristic
292C2×C4×C59C22×Q812yes—
293C2×C4×C59C2×#4112yes—
294C2×C4×C59C2511yescharacteristic
295C2×Dic59—24no—
296C2×Dic59—22no—
297C2×Dic59—22no—
298C2×Dic59—22no—
299C2×Dic59—22no—
300C2×Dic59—22no—
301C2×Dic59—22no—
302C2×Dic59—42no—
303C2×Dic59—42no—
304C2×Dic59—42no—
305C2×Dic59C22⋊Q814yes—
306C2×Dic59C22×D412yes—
307C2×Dic59C22×D412yes—
308C2×Dic59C22×D412yes—
309C4×D59—216no—
310C4×D59—28no—
311C4×D59—28no—
312C4×D59—48no—
313C4×D59—48no—
314C4×D59—48no—
315C4×D59C22⋊Q818yes—
316C4×D59C22×Q814yes—
317C4×D59C2×#4114yes—
318Dic118—24no—
319Dic118—22no—
320Dic118—216no—
321Dic118C22×Q814yes—
322C8×C59—22no—
323C8×C59—22no—
324C59⋊C8—22no—
325C59⋊C8—22no—
326C22×#479—591nomaximal, Sylow
327C22×C59C2×C22⋊Q812yes—
328C22×C59C2×#13512yes—
329C22×C59C2×#13712yes—
330C22×C59C23×D411yescharacteristic
331C2×D59#479116yesdirect product factor
332C2×D59C2×C22⋊Q814yes—
333C2×D59C2×#13514yes—
334C2×D59C2×#13714yes—
335C4×C59—24no—
336C4×C59—22no—
337C4×C59—22no—
338C4×C59—42no—
339C4×C59—42no—
340C4×C59—42no—
341C4×C59C2×C22⋊Q812yes—
342C4×C59C23×Q811yescharacteristic
343C4×C59C22×#4111yescharacteristic
344Dic59—24no—
345Dic59—22no—
346Dic59—22no—
347Dic59—42no—
348Dic59—42no—
349Dic59—42no—
350Dic59C2×C22⋊Q814yes—
351C22×#125—591no—
352C22×C4×Q8—591no—
353C2×#479—5916no—
354C2×#479—591no—
355C2×#479—591no—
356C2×#479—591no—
357C2×#479—591no—
358C2×#479—591no—
359C2×#479—591no—
360C2×#479—591no—
361C2×#479D5911yescharacteristic, direct product factor
362C22×#107—591no—
363C22×#106—591no—
364C22×C4⋊C8—591no—
365C22×#103—591no—
366C22×#103—591no—
367C2×C59C2×#47914yescomplemented
368C2×C59C22×C22⋊Q811yescharacteristic
369C2×C59C22×#13511yescharacteristic
370C2×C59C22×#13711yescharacteristic
371D59C2×#47918yesdirect product factor
372C23×Q8—591no—
373C23×C8—591no—
374C23×C8—591no—
375C2×#125—598no—
376C2×#125—591no—
377C2×#125—591no—
378C2×#125—591no—
379C2×#125—1181no—
380C2×#125—1181no—
381C2×#125—1184no—
382C2×#125C2×D5911yescharacteristic
383C2×C4×Q8—591no—
384C2×C4×Q8—598no—
385C2×C4×Q8—591no—
386C2×C4×Q8—591no—
387C2×C4×Q8—1181no—
388C2×C4×Q8—1181no—
389C2×C4×Q8—1184no—
390C2×C4×Q8C2×D5911yescharacteristic
391C22×C4⋊C4—591no—
392C22×C4⋊C4—591no—
393C22×C4⋊C4—591no—
394C22×C4⋊C4—1181no—
395C22×C4⋊C4—1181no—
396C22×C4⋊C4—1181no—
397C22×C42—591no—
398C22×C42—1181no—
399#479—598no—
400#479—598no—
401#479—598no—
402#479—598no—
403#479—598no—
404#479—598no—
405#479—598no—
406#479C2×D5918yesdirect product factor
407C2×#107—591no—
408C2×#107—591no—
409C2×#107—591no—
410C2×#107—598no—
411C2×#107C2×D5911yescharacteristic
412C2×#106—591no—
413C2×#106—591no—
414C2×#106—591no—
415C2×#106—598no—
416C2×#106C2×D5911yescharacteristic
417C2×C4⋊C8—591no—
418C2×C4⋊C8—591no—
419C2×C4⋊C8—591no—
420C2×C4⋊C8—598no—
421C2×C4⋊C8C2×D5911yescharacteristic
422C2×#103—591no—
423C2×#103—591no—
424C2×#103—591no—
425C2×#103—591no—
426C2×#103—591no—
427C2×#103—591no—
428C2×#103—598no—
429C2×#103—598no—
430C2×#103C2×D5911yescharacteristic
431C2×#103C2×D5911yescharacteristic
432C59C22×#47911yescharacteristic, complemented, Sylow
433C22×Q8—598no—
434C22×Q8—594no—
435C22×Q8—591no—
436C22×Q8—1181no—
437C22×Q8—1182no—
438C22×Q8—1184no—
439C22×Q8C22×D5911yescharacteristic
440C23×C4—591no—
441C23×C4—591no—
442C23×C4—591no—
443C23×C4—1181no—
444C23×C4—1181no—
445C23×C4—1181no—
446C23×C4—1181no—
447C22×C8—591no—
448C22×C8—591no—
449C22×C8—594no—
450C22×C8—594no—
451C22×C8—1184no—
452C22×C8—1184no—
453C22×C8C22×D5911yescharacteristic
454C22×C8C22×D5911yescharacteristic
455#125—22no—
456#125—594no—
457#125—594no—
458#125—594no—
459#125—1188no—
460#125—1188no—
461#125—1182no—
462#125—1182no—
463#125—1182no—
464#125C22×D5914yes—
465C4×Q8—22no—
466C4×Q8—594no—
467C4×Q8—594no—
468C4×Q8—594no—
469C4×Q8—1188no—
470C4×Q8—1188no—
471C4×Q8—1182no—
472C4×Q8—1182no—
473C4×Q8—1182no—
474C4×Q8C22×D5914yes—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—591no—
479C2×C4⋊C4—591no—
480C2×C4⋊C4—591no—
481C2×C4⋊C4—594no—
482C2×C4⋊C4—594no—
483C2×C4⋊C4—594no—
484C2×C4⋊C4—1182no—
485C2×C4⋊C4—1182no—
486C2×C4⋊C4—1182no—
487C2×C4⋊C4—1188no—
488C2×C4⋊C4—1188no—
489C2×C4⋊C4—1188no—
490C2×C4⋊C4—1181no—
491C2×C4⋊C4—1181no—
492C2×C4⋊C4—1181no—
493C2×C4⋊C4—1181no—
494C2×C4⋊C4—1181no—
495C2×C4⋊C4—1181no—
496C2×C4⋊C4—1181no—
497C2×C4⋊C4—1181no—
498C2×C4⋊C4—1181no—
499C2×C4⋊C4—1181no—
500C2×C4⋊C4—1181no—
501C2×C4⋊C4—1181no—
502C2×C4⋊C4C22×D5911yescharacteristic
503C2×C4⋊C4C22×D5911yescharacteristic
504C2×C4⋊C4C22×D5911yescharacteristic
505C2×C42—21no—
506C2×C42—591no—
507C2×C42—591no—
508C2×C42—591no—
509C2×C42—594no—
510C2×C42—594no—
511C2×C42—1188no—
512C2×C42—1181no—
513C2×C42—1181no—
514C2×C42—1181no—
515C2×C42C22×D5911yescharacteristic
516#107—594no—
517#107—594no—
518#107—594no—
519#107C22×D5914yes—
520#106—594no—
521#106—594no—
522#106—594no—
523#106C22×D5914yes—
524C4⋊C8—594no—
525C4⋊C8—594no—
526C4⋊C8—594no—
527C4⋊C8C22×D5914yes—
528#103—594no—
529#103—594no—
530#103—594no—
531#103—594no—
532#103—594no—
533#103—594no—
534#103C22×D5914yes—
535#103C22×D5914yes—
536C24—591no—
537C2×Q8—21no—
538C2×Q8—22no—
539C2×Q8—5916no—
540C2×Q8—594no—
541C2×Q8—592no—
542C2×Q8—1184no—
543C2×Q8—1188no—
544C2×Q8—11816no—
545C2×Q8—1188no—
546C2×Q8—1181no—
547C2×Q8—1182no—
548C2×Q8Q8×D5914yes—
549C2×Q8C23×D5912yes—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—591no—
555C22×C4—592no—
556C22×C4—594no—
557C22×C4—594no—
558C22×C4—592no—
559C22×C4—591no—
560C22×C4—591no—
561C22×C4—594no—
562C22×C4—594no—
563C22×C4—1184no—
564C22×C4—1184no—
565C22×C4—1184no—
566C22×C4—1188no—
567C22×C4—1184no—
568C22×C4—1184no—
569C22×C4—1184no—
570C22×C4—1181no—
571C22×C4—1181no—
572C22×C4—1181no—
573C22×C4—1181no—
574C22×C4—2364no—
575C22×C4—2364no—
576C22×C4—2364no—
577C22×C4D4×D5911yescharacteristic
578C22×C4D4×D5911yescharacteristic
579C22×C4C23×D5911yescharacteristic
580C2×C8—22no—
581C2×C8—22no—
582C2×C8—592no—
583C2×C8—592no—
584C2×C8—1188no—
585C2×C8—1188no—
586C2×C8—1182no—
587C2×C8—1182no—
588C2×C8C23×D5912yes—
589C2×C8C23×D5912yes—
590C4⋊C4—24no—
591C4⋊C4—24no—
592C4⋊C4—24no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—592no—
597C4⋊C4—592no—
598C4⋊C4—592no—
599C4⋊C4—1184no—
600C4⋊C4—1184no—
601C4⋊C4—1184no—
602C4⋊C4—1184no—
603C4⋊C4—1184no—
604C4⋊C4—1184no—
605C4⋊C4—1184no—
606C4⋊C4—1184no—
607C4⋊C4—1184no—
608C4⋊C4—1181no—
609C4⋊C4—1181no—
610C4⋊C4—1181no—
611C4⋊C4—1184no—
612C4⋊C4—1184no—
613C4⋊C4—1184no—
614C4⋊C4C23×D5912yes—
615C4⋊C4C23×D5912yes—
616C4⋊C4C23×D5912yes—
617C42—24no—
618C42—594no—
619C42—594no—
620C42—592no—
621C42—592no—
622C42—1184no—
623C42—1184no—
624C42—1184no—
625C42D4×D5912yes—
626C42C23×D5912yes—
627C23—594no—
628C23—594no—
629C23—594no—
630C23—592no—
631C23C2×D4×D5911yescharacteristic
632Q8—24no—
633Q8—22no—
634Q8—594no—
635Q8—11816no—
636Q8—1184no—
637Q8—1182no—
638Q8C2×Q8×D5914yes—
639C2×C4—24no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—594no—
650C2×C4—592no—
651C2×C4—598no—
652C2×C4—594no—
653C2×C4—594no—
654C2×C4—592no—
655C2×C4—592no—
656C2×C4—1188no—
657C2×C4—1188no—
658C2×C4—11816no—
659C2×C4—1184no—
660C2×C4—1182no—
661C2×C4—1182no—
662C2×C4—1182no—
663C2×C4—1182no—
664C2×C4—1182no—
665C2×C4—1182no—
666C2×C4—2368no—
667C2×C4—2368no—
668C2×C4—2368no—
669C2×C4—2362no—
670C2×C4—2362no—
671C2×C4—2362no—
672C2×C4C2×D4×D5912yes—
673C2×C4C2×D4×D5912yes—
674C2×C4C2×D4×D5911yescharacteristic
675C2×C4C2×Q8×D5912yes—
676C2×C4#41×D5912yes—
677C2×C4C24×D5911yescharacteristic
678C8—22no—
679C8—22no—
680C8—1182no—
681C8—1182no—
682C22—5916no—
683C22—594no—
684C22—594no—
685C22—594no—
686C22C22⋊Q8×D5912yes—
687C22#135×D5912yes—
688C22#137×D5912yes—
689C22C22×D4×D5911yescharacteristic
690C4—22no—
691C4—22no—
692C4—24no—
693C4—42no—
694C4—42no—
695C4—42no—
696C4—594no—
697C4—1182no—
698C4—1182no—
699C4—1184no—
700C4—2362no—
701C4—2362no—
702C4—2362no—
703C4C22⋊Q8×D5912yes—
704C4C22×Q8×D5911yescharacteristic
705C4C2×#41×D5911yescharacteristic
706C2—598no—
707C2#479×D5914yesdirect product factor
708C2C2×C22⋊Q8×D5911yescharacteristic
709C2C2×#135×D5911yescharacteristic
710C2C2×#137×D5911yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#479C2
socleC23×C59C22×D4
prime radicalC23×D59C2×D4
hypercenterC2×#479D59
hypocenterC59C22×#479
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#479

Complements

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

NH ≅ G/Ntype
3. C2×#16837712C2semidirect
4. C2×#16837711C2semidirect
5. C2×#16837710C2semidirect
6. C2×#16837709C2semidirect
7. C2×#16837708C2semidirect
8. C2×#16837707C2semidirect
9. C2×#16837706C2semidirect
10. #479×D59C2direct (N × H)
16. C2×C59×#479C2semidirect
42. #16837712C22semidirect
43. #16837711C22semidirect
44. #16837710C22semidirect
45. #16837709C22semidirect
46. #16837708C22semidirect
47. #16837707C22semidirect
48. #16837706C22semidirect
71. C59×#479C22semidirect
331. C2×D59#479direct (N × H)
361. C2×#479D59direct (N × H)
367. C2×C59C2×#479semidirect
371. D59C2×#479direct (N × H)
406. #479C2×D59direct (N × H)
432. C59C22×#479semidirect
707. C2#479×D59direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#125×D592
C2×C4×Q8×D592
C2×#168377122
C2×#168377112
C2×#168377102
C2×#168377092
C2×#168377082
C2×#168377072
C2×#168377062
#479×D592
C2×#107×D592
C2×#106×D592
C2×C4⋊C8×D592
C2×#103×D592
C2×C59×#4792
C22×#47959