Finite Group Databasebeta

← C79×#18962 #34130651

Subgroups — C79×#18962 #34130651

Order 20224.

964 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C79×#3546C211yesmaximal, characteristic, complemented
2C79×#3253C211yesmaximal, characteristic, complemented
3C79×#3247C211yesmaximal, characteristic, complemented
4C79×#3207C211yesmaximal, characteristic, complemented
5C79×#1638C211yesmaximal, characteristic, complemented
6C79×#1635C211yesmaximal, characteristic, complemented
7C79×#1631C211yesmaximal, characteristic, complemented
8C79×#1629C211yesmaximal, characteristic, complemented
9C79×#1628C211yesmaximal, characteristic, complemented
10C79×#1625C211yesmaximal, characteristic, complemented
11C79×#1621C211yesmaximal, characteristic, complemented
12C79×#1619C211yesmaximal, characteristic, complemented
13C79×#1547C211yesmaximal, characteristic, complemented
14C79×#1495C211yesmaximal, characteristic, complemented
15C79×#1480C211yesmaximal, characteristic, complemented
16#560×C79—22no—
17#556×C79C2211yescharacteristic
18#553×C79—21no—
19#550×C79—21no—
20#550×C79C2211yescharacteristic
21#547×C79C2211yescharacteristic
22#546×C79—21no—
23#546×C79—21no—
24D42×C79C2211yescharacteristic
25#542×C79—21no—
26#538×C79—22no—
27#537×C79—21no—
28#535×C79—21no—
29#535×C79—21no—
30#532×C79C2211yescharacteristic
31#532×C79C2211yescharacteristic
32#532×C79C2211yescharacteristic, complemented
33#529×C79C2211yescharacteristic
34#493×C79C2211yescharacteristic
35#492×C79C2211yescharacteristic
36#487×C79C2211yescharacteristic, complemented
37#486×C79C2211yescharacteristic, complemented
38#478×C79—21no—
39#477×C79C2211yescharacteristic, complemented
40#476×C79—21no—
41#476×C79C2211yescharacteristic
42#476×C79C2211yescharacteristic
43#476×C79C2211yescharacteristic, complemented
44#469×C79—21no—
45#469×C79—21no—
46#466×C79—21no—
47#465×C79—21no—
48#463×C79—21no—
49#463×C79—22no—
50#460×C79C2211yescharacteristic, complemented
51#459×C79—21no—
52#459×C79C2211yescharacteristic
53#459×C79C2211yescharacteristic
54#459×C79C2211yescharacteristic, complemented
55#449×C79—22no—
56#431×C79C2211yescharacteristic, complemented
57#423×C79C2211yescharacteristic, complemented
58C2×C4⋊C8×C79C2211yescharacteristic, complemented
59#332×C79C2211yescharacteristic, complemented
60#332×C79C2211yescharacteristic, complemented
61#331×C79C2211yescharacteristic
62#331×C79C2211yescharacteristic
63Q8⋊C8×C79C2211yescharacteristic, complemented
64Q8⋊C8×C79C2211yescharacteristic, complemented
65D4⋊C8×C79C2211yescharacteristic
66D4⋊C8×C79C2211yescharacteristic
67D4⋊C8×C79C2211yescharacteristic
68D4⋊C8×C79C2211yescharacteristic
69D4⋊C8×C79C2211yescharacteristic, complemented
70D4⋊C8×C79C2211yescharacteristic, complemented
71C2×#41×C79—21no—
72C2×#41×C79—21no—
73C2×#41×C79—21no—
74C2×#41×C79—21no—
75C2×#41×C79—21no—
76C22×D4×C79—21no—
77C22×D4×C79—21no—
78C2×SD16×C79—21no—
79C2×SD16×C79—22no—
80C2×D8×C79—22no—
81C2×D8×C79—21no—
82C2×D8×C79—21no—
83C2×D8×C79—21no—
84C2×M16×C79—21no—
85C22×C8×C79—21no—
86C4⋊Q8×C79D411yescharacteristic
87C4⋊Q8×C79C2311yescharacteristic
88C4⋊Q8×C79C2311yescharacteristic
89#127×C79—22no—
90#127×C79—21no—
91#127×C79D411yescharacteristic
92#127×C79C2311yescharacteristic
93#127×C79C2311yescharacteristic
94#126×C79—22no—
95#126×C79—22no—
96#126×C79—21no—
97#125×C79D411yescharacteristic
98#124×C79—22no—
99#124×C79—21no—
100#124×C79—21no—
101#124×C79—21no—
102#124×C79—21no—
103#124×C79D411yescharacteristic
104#123×C79—22no—
105#123×C79—22no—
106#123×C79—21no—
107#123×C79—22no—
108C22⋊Q8×C79—22no—
109C22⋊Q8×C79—21no—
110C22⋊Q8×C79—21no—
111C22⋊Q8×C79D411yescharacteristic
112#121×C79—22no—
113#121×C79—22no—
114#121×C79—22no—
115#121×C79—22no—
116#121×C79—22no—
117#121×C79—21no—
118#121×C79—22no—
119#121×C79—21no—
120#121×C79—21no—
121#121×C79—21no—
122#121×C79—21no—
123#121×C79—21no—
124#121×C79—21no—
125#121×C79—21no—
126#121×C79D412yes—
127#121×C79D411yescharacteristic
128#121×C79D411yescharacteristic
129#121×C79D411yescharacteristic
130#120×C79—22no—
131#120×C79—22no—
132#120×C79—22no—
133#120×C79—22no—
134C4×Q8×C79—21no—
135C4×Q8×C79C2311yescharacteristic
136C4×D4×C79—22no—
137C4×D4×C79—21no—
138C4×D4×C79—21no—
139C4×D4×C79—21no—
140C4×D4×C79—21no—
141C4×D4×C79—21no—
142C4×D4×C79—21no—
143C4×D4×C79D412yes—
144C4×D4×C79C2311yescharacteristic
145C4×D4×C79C2311yescharacteristic
146C4×D4×C79C2311yescharacteristic
147#117×C79—21no—
148#117×C79—21no—
149C2×C4⋊C4×C79—21no—
150C2×C22⋊C4×C79—22no—
151C2×C42×C79C2311yescharacteristic
152#107×C79—21no—
153#106×C79—21no—
154#106×C79—21no—
155#106×C79—21no—
156C4⋊C8×C79—21no—
157C4⋊C8×C79—21no—
158C4⋊C8×C79—21no—
159C4⋊C8×C79C2311yescharacteristic
160C4⋊C8×C79C2311yescharacteristic
161C4⋊C8×C79C2311yescharacteristic
162C4⋊C8×C79C2311yescharacteristic
163#103×C79—21no—
164#103×C79—22no—
165#102×C79—21no—
166#102×C79—21no—
167#102×C79—21no—
168#102×C79—22no—
169#102×C79—21no—
170#102×C79—21no—
171#102×C79—21no—
172#102×C79—21no—
173C22⋊C8×C79—21no—
174C4×C8×C79C2311yescharacteristic
175C4×C8×C79C2311yescharacteristic
176C24×C79—22no—
177#41×C79—81no—
178#41×C79—81no—
179#41×C79—81no—
180#41×C79—81no—
181#41×C79—81no—
182#41×C79—81no—
183#41×C79—81no—
184#41×C79—81no—
185#41×C79—82no—
186C2×Q8×C79—21no—
187C2×Q8×C79—21no—
188C2×Q8×C79—21no—
189C2×Q8×C79C2×D411yescharacteristic
190C2×D4×C79—22no—
191C2×D4×C79—22no—
192C2×D4×C79—22no—
193C2×D4×C79—22no—
194C2×D4×C79—22no—
195C2×D4×C79—21no—
196C2×D4×C79—21no—
197C2×D4×C79—22no—
198C2×D4×C79—21no—
199C2×D4×C79—21no—
200C2×D4×C79—21no—
201C2×D4×C79—21no—
202C2×D4×C79—21no—
203C2×D4×C79—21no—
204C2×D4×C79—21no—
205C2×D4×C79—21no—
206C2×D4×C79—41no—
207C2×D4×C79—81no—
208C2×D4×C79—81no—
209C2×D4×C79—81no—
210C2×D4×C79—81no—
211C2×D4×C79C2×D411yescharacteristic
212C2×D4×C79C2×D411yescharacteristic
213C2×D4×C79C2×D411yescharacteristic
214C2×D4×C79C2×D412yes—
215C22×C4×C79—22no—
216C22×C4×C79—22no—
217C22×C4×C79—21no—
218C22×C4×C79—21no—
219C22×C4×C79—21no—
220C22×C4×C79—22no—
221C22×C4×C79—41no—
222C22×C4×C79C2×D411yescharacteristic
223C22×C4×C79C2×D411yescharacteristic
224C22×C4×C79C2×D411yescharacteristic
225SD16×C79—81no—
226SD16×C79—82no—
227D8×C79—81no—
228D8×C79—81no—
229D8×C79—81no—
230D8×C79—82no—
231M16×C79—81no—
232C2×C8×C79—21no—
233C2×C8×C79—21no—
234C2×C8×C79—21no—
235C2×C8×C79—21no—
236C2×C8×C79—21no—
237C2×C8×C79—21no—
238C2×C8×C79—81no—
239C4⋊C4×C79—22no—
240C4⋊C4×C79—22no—
241C4⋊C4×C79—21no—
242C4⋊C4×C79—21no—
243C4⋊C4×C79—21no—
244C4⋊C4×C79—21no—
245C4⋊C4×C79—21no—
246C4⋊C4×C79—21no—
247C4⋊C4×C79—21no—
248C4⋊C4×C79—21no—
249C4⋊C4×C79C2×D412yes—
250C4⋊C4×C79C2×D411yescharacteristic
251C4⋊C4×C79C2×D411yescharacteristic
252C4⋊C4×C79C2×D411yescharacteristic
253C4⋊C4×C79C2×D411yescharacteristic
254C22⋊C4×C79—22no—
255C22⋊C4×C79—22no—
256C22⋊C4×C79—22no—
257C22⋊C4×C79—22no—
258C22⋊C4×C79—22no—
259C22⋊C4×C79—21no—
260C22⋊C4×C79—21no—
261C22⋊C4×C79—21no—
262C22⋊C4×C79—21no—
263C22⋊C4×C79—21no—
264C22⋊C4×C79—21no—
265C22⋊C4×C79—22no—
266C22⋊C4×C79—22no—
267C22⋊C4×C79—21no—
268C22⋊C4×C79—21no—
269C22⋊C4×C79—21no—
270C22⋊C4×C79—41no—
271C22⋊C4×C79—41no—
272C42×C79—22no—
273C42×C79—21no—
274C42×C79C2×D411yescharacteristic
275C42×C79C2×D411yescharacteristic
276C42×C79C2×D411yescharacteristic
277C42×C79C2411yescharacteristic
278C23×C79—21no—
279C23×C79—21no—
280C23×C79—22no—
281C23×C79—21no—
282C23×C79—41no—
283C23×C79—82no—
284C23×C79—82no—
285C23×C79—82no—
286C23×C79#12011yescharacteristic
287Q8×C79—21no—
288Q8×C79—21no—
289Q8×C79—42no—
290Q8×C79—41no—
291Q8×C79—41no—
292Q8×C79—81no—
293D4×C79—21no—
294D4×C79—21no—
295D4×C79—21no—
296D4×C79—21no—
297D4×C79—21no—
298D4×C79—21no—
299D4×C79—42no—
300D4×C79—42no—
301D4×C79—41no—
302D4×C79—41no—
303D4×C79—41no—
304D4×C79—41no—
305D4×C79—41no—
306D4×C79—41no—
307D4×C79—41no—
308D4×C79—41no—
309D4×C79—81no—
310D4×C79—81no—
311D4×C79—81no—
312D4×C79—81no—
313D4×C79—81no—
314D4×C79—82no—
315D4×C79—82no—
316D4×C79—82no—
317D4×C79—82no—
318D4×C79—82no—
319D4×C79—82no—
320D4×C79—82no—
321C2×C4×C79—21no—
322C2×C4×C79—21no—
323C2×C4×C79—21no—
324C2×C4×C79—21no—
325C2×C4×C79—21no—
326C2×C4×C79—21no—
327C2×C4×C79—21no—
328C2×C4×C79—22no—
329C2×C4×C79—21no—
330C2×C4×C79—21no—
331C2×C4×C79—41no—
332C2×C4×C79—41no—
333C2×C4×C79—41no—
334C2×C4×C79—41no—
335C2×C4×C79—41no—
336C2×C4×C79—41no—
337C2×C4×C79—41no—
338C2×C4×C79—41no—
339C2×C4×C79—82no—
340C2×C4×C79—82no—
341C2×C4×C79—82no—
342C2×C4×C79—82no—
343C2×C4×C79#12011yescharacteristic
344C2×C4×C79#12011yescharacteristic
345C2×C4×C79#12011yescharacteristic
346C2×C4×C79C22×D411yescharacteristic
347C2×C4×C79C22×D411yescharacteristic
348C2×C4×C79C22×D411yescharacteristic
349C8×C79—41no—
350C8×C79—41no—
351C8×C79—41no—
352C8×C79—41no—
353C8×C79—41no—
354C8×C79—41no—
355C22×C79—21no—
356C22×C79—21no—
357C22×C79—21no—
358C22×C79—41no—
359C22×C79—41no—
360C22×C79—41no—
361C22×C79—41no—
362C22×C79—42no—
363C22×C79—42no—
364C22×C79—41no—
365C22×C79—41no—
366C22×C79—42no—
367C22×C79—41no—
368C22×C79—41no—
369C22×C79—41no—
370C22×C79—81no—
371C22×C79—81no—
372C22×C79—81no—
373C22×C79—164no—
374C22×C79C2×#12011yescharacteristic
375C4×C79—21no—
376C4×C79—21no—
377C4×C79—21no—
378C4×C79—21no—
379C4×C79—41no—
380C4×C79—41no—
381C4×C79—41no—
382C4×C79—41no—
383C4×C79—42no—
384C4×C79—41no—
385C4×C79—81no—
386C4×C79#57611yescharacteristic
387C4×C79#57611yescharacteristic
388C4×C79#57711yescharacteristic
389C4×C79#57711yescharacteristic
390#18962C7911yesmaximal, characteristic, direct product factor, Sylow
391C2×C79—41no—
392C2×C79—81no—
393C2×C79—82no—
394C2×C79—81no—
395C2×C79—81no—
396C2×C79—161no—
397C2×C79#301211yescharacteristic
398C2×C79#301211yescharacteristic
399C2×C79#302111yescharacteristic
400#3546C2×C7911yescharacteristic, complemented
401#3253C2×C7911yescharacteristic, complemented
402#3247C2×C7911yescharacteristic, complemented
403#3207C2×C7911yescharacteristic, complemented
404#1638C2×C7911yescharacteristic, complemented
405#1635C2×C7911yescharacteristic, complemented
406#1631C2×C7911yescharacteristic, complemented
407#1629C2×C7911yescharacteristic, complemented
408#1628C2×C7911yescharacteristic, complemented
409#1625C2×C7911yescharacteristic, complemented
410#1621C2×C7911yescharacteristic, complemented
411#1619C2×C7911yescharacteristic, complemented
412#1547C2×C7911yescharacteristic, complemented
413#1495C2×C7911yescharacteristic, complemented
414#1480C2×C7911yescharacteristic, complemented
415C79#1896211yescharacteristic, direct product factor, Sylow
416#560—22no—
417#556C22×C7911yescharacteristic
418#553—21no—
419#550—21no—
420#550C22×C7911yescharacteristic
421#547C22×C7911yescharacteristic
422#546—21no—
423#546—21no—
424D42C22×C7911yescharacteristic
425#542—21no—
426#538—22no—
427#537—21no—
428#535—21no—
429#535—21no—
430#532C22×C7911yescharacteristic
431#532C22×C7911yescharacteristic
432#532C22×C7911yescharacteristic, complemented
433#529C22×C7911yescharacteristic
434#493C22×C7911yescharacteristic
435#492C22×C7911yescharacteristic
436#487C22×C7911yescharacteristic, complemented
437#486C22×C7911yescharacteristic, complemented
438#478—21no—
439#477C22×C7911yescharacteristic, complemented
440#476—21no—
441#476C22×C7911yescharacteristic
442#476C22×C7911yescharacteristic
443#476C22×C7911yescharacteristic, complemented
444#469—21no—
445#469—21no—
446#466—21no—
447#465—21no—
448#463—21no—
449#463—22no—
450#460C22×C7911yescharacteristic, complemented
451#459—21no—
452#459C22×C7911yescharacteristic
453#459C22×C7911yescharacteristic
454#459C22×C7911yescharacteristic, complemented
455#449—22no—
456#431C22×C7911yescharacteristic, complemented
457#423C22×C7911yescharacteristic, complemented
458C2×C4⋊C8C22×C7911yescharacteristic, complemented
459#332C22×C7911yescharacteristic, complemented
460#332C22×C7911yescharacteristic, complemented
461#331C22×C7911yescharacteristic
462#331C22×C7911yescharacteristic
463Q8⋊C8C22×C7911yescharacteristic, complemented
464Q8⋊C8C22×C7911yescharacteristic, complemented
465D4⋊C8C22×C7911yescharacteristic
466D4⋊C8C22×C7911yescharacteristic
467D4⋊C8C22×C7911yescharacteristic
468D4⋊C8C22×C7911yescharacteristic
469D4⋊C8C22×C7911yescharacteristic, complemented
470D4⋊C8C22×C7911yescharacteristic, complemented
471C2×#41—21no—
472C2×#41—21no—
473C2×#41—21no—
474C2×#41—21no—
475C2×#41—21no—
476C22×D4—21no—
477C22×D4—21no—
478C2×SD16—21no—
479C2×SD16—22no—
480C2×D8—22no—
481C2×D8—21no—
482C2×D8—21no—
483C2×D8—21no—
484C2×M16—21no—
485C22×C8—21no—
486C4⋊Q8D4×C7911yescharacteristic
487C4⋊Q8C23×C7911yescharacteristic
488C4⋊Q8C23×C7911yescharacteristic
489#127—22no—
490#127—21no—
491#127D4×C7911yescharacteristic
492#127C23×C7911yescharacteristic
493#127C23×C7911yescharacteristic
494#126—22no—
495#126—22no—
496#126—21no—
497#125D4×C7911yescharacteristic
498#124—22no—
499#124—21no—
500#124—21no—
501#124—21no—
502#124—21no—
503#124D4×C7911yescharacteristic
504#123—22no—
505#123—22no—
506#123—21no—
507#123—22no—
508C22⋊Q8—22no—
509C22⋊Q8—21no—
510C22⋊Q8—21no—
511C22⋊Q8D4×C7911yescharacteristic
512#121—22no—
513#121—22no—
514#121—22no—
515#121—22no—
516#121—22no—
517#121—21no—
518#121—22no—
519#121—21no—
520#121—21no—
521#121—21no—
522#121—21no—
523#121—21no—
524#121—21no—
525#121—21no—
526#121D4×C7911yescharacteristic
527#121D4×C7911yescharacteristic
528#121D4×C7911yescharacteristic
529#121D4×C7912yes—
530#120—22no—
531#120—22no—
532#120—22no—
533#120—22no—
534C4×Q8—21no—
535C4×Q8C23×C7911yescharacteristic
536C4×D4—22no—
537C4×D4—21no—
538C4×D4—21no—
539C4×D4—21no—
540C4×D4—21no—
541C4×D4—21no—
542C4×D4—21no—
543C4×D4D4×C7912yes—
544C4×D4C23×C7911yescharacteristic
545C4×D4C23×C7911yescharacteristic
546C4×D4C23×C7911yescharacteristic
547#117—21no—
548#117—21no—
549C2×C4⋊C4—21no—
550C2×C22⋊C4—22no—
551C2×C42C23×C7911yescharacteristic
552#107—21no—
553#106—21no—
554#106—21no—
555#106—21no—
556C4⋊C8—21no—
557C4⋊C8—21no—
558C4⋊C8—21no—
559C4⋊C8C23×C7911yescharacteristic
560C4⋊C8C23×C7911yescharacteristic
561C4⋊C8C23×C7911yescharacteristic
562C4⋊C8C23×C7911yescharacteristic
563#103—21no—
564#103—22no—
565#102—21no—
566#102—21no—
567#102—21no—
568#102—22no—
569#102—21no—
570#102—21no—
571#102—21no—
572#102—21no—
573C22⋊C8—21no—
574C4×C8C23×C7911yescharacteristic
575C4×C8C23×C7911yescharacteristic
576C24—22no—
577#41—81no—
578#41—81no—
579#41—81no—
580#41—81no—
581#41—81no—
582#41—81no—
583#41—81no—
584#41—81no—
585#41—82no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8C2×D4×C7911yescharacteristic
590C2×D4—22no—
591C2×D4—22no—
592C2×D4—22no—
593C2×D4—22no—
594C2×D4—22no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—22no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—41no—
607C2×D4—81no—
608C2×D4—81no—
609C2×D4—81no—
610C2×D4—81no—
611C2×D4C2×D4×C7911yescharacteristic
612C2×D4C2×D4×C7911yescharacteristic
613C2×D4C2×D4×C7911yescharacteristic
614C2×D4C2×D4×C7912yes—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—22no—
621C22×C4—41no—
622C22×C4C2×D4×C7911yescharacteristic
623C22×C4C2×D4×C7911yescharacteristic
624C22×C4C2×D4×C7911yescharacteristic
625SD16—81no—
626SD16—82no—
627D8—81no—
628D8—81no—
629D8—81no—
630D8—82no—
631M16—81no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—81no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4C2×D4×C7912yes—
650C4⋊C4C2×D4×C7911yescharacteristic
651C4⋊C4C2×D4×C7911yescharacteristic
652C4⋊C4C2×D4×C7911yescharacteristic
653C4⋊C4C2×D4×C7911yescharacteristic
654C22⋊C4—22no—
655C22⋊C4—22no—
656C22⋊C4—22no—
657C22⋊C4—22no—
658C22⋊C4—22no—
659C22⋊C4—21no—
660C22⋊C4—21no—
661C22⋊C4—21no—
662C22⋊C4—21no—
663C22⋊C4—21no—
664C22⋊C4—21no—
665C22⋊C4—22no—
666C22⋊C4—22no—
667C22⋊C4—21no—
668C22⋊C4—21no—
669C22⋊C4—21no—
670C22⋊C4—41no—
671C22⋊C4—41no—
672C42—22no—
673C42—21no—
674C42C2×D4×C7911yescharacteristic
675C42C2×D4×C7911yescharacteristic
676C42C2×D4×C7911yescharacteristic
677C42C24×C7911yescharacteristic
678C23—21no—
679C23—21no—
680C23—22no—
681C23—21no—
682C23—41no—
683C23—82no—
684C23—82no—
685C23—82no—
686C23#120×C7911yescharacteristic
687Q8—21no—
688Q8—21no—
689Q8—42no—
690Q8—41no—
691Q8—41no—
692Q8—81no—
693D4—21no—
694D4—21no—
695D4—21no—
696D4—21no—
697D4—21no—
698D4—21no—
699D4—42no—
700D4—42no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—41no—
708D4—41no—
709D4—81no—
710D4—81no—
711D4—81no—
712D4—81no—
713D4—81no—
714D4—82no—
715D4—82no—
716D4—82no—
717D4—82no—
718D4—82no—
719D4—82no—
720D4—82no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—82no—
740C2×C4—82no—
741C2×C4—82no—
742C2×C4—82no—
743C2×C4#120×C7911yescharacteristic
744C2×C4#120×C7911yescharacteristic
745C2×C4#120×C7911yescharacteristic
746C2×C4C22×D4×C7911yescharacteristic
747C2×C4C22×D4×C7911yescharacteristic
748C2×C4C22×D4×C7911yescharacteristic
749C8—41no—
750C8—41no—
751C8—41no—
752C8—41no—
753C8—41no—
754C8—41no—
755C22—21no—
756C22—21no—
757C22—21no—
758C22—42no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—42no—
767C22—42no—
768C22—41no—
769C22—41no—
770C22—81no—
771C22—81no—
772C22—81no—
773C22—164no—
774C22C2×#120×C7911yescharacteristic
775C4—21no—
776C4—21no—
777C4—21no—
778C4—21no—
779C4—41no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—41no—
784C4—42no—
785C4—81no—
786C4#576×C7911yescharacteristic
787C4#576×C7911yescharacteristic
788C4#577×C7911yescharacteristic
789C4#577×C7911yescharacteristic
790C2—41no—
791C2—81no—
792C2—81no—
793C2—82no—
794C2—81no—
795C2—161no—
796C2C79×#301211yescharacteristic
797C2C79×#301211yescharacteristic
798C2C79×#302111yescharacteristic
subgroupG/H
center, socleC22×C79C2×#120
commutator, Frattini, cosocleC42C24×C79
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C79 ◁ C2×C42×C79 ◁ G

Complements

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

NH ≅ G/Ntype
1. C79×#3546C2semidirect
2. C79×#3253C2semidirect
3. C79×#3247C2semidirect
4. C79×#3207C2semidirect
5. C79×#1638C2semidirect
6. C79×#1635C2semidirect
7. C79×#1631C2semidirect
8. C79×#1629C2semidirect
9. C79×#1628C2semidirect
10. C79×#1625C2semidirect
11. C79×#1621C2semidirect
12. C79×#1619C2semidirect
13. C79×#1547C2semidirect
14. C79×#1495C2semidirect
15. C79×#1480C2semidirect
32. #532×C79C22semidirect
36. #487×C79C22semidirect
37. #486×C79C22semidirect
39. #477×C79C22semidirect
43. #476×C79C22semidirect
50. #460×C79C22semidirect
54. #459×C79C22semidirect
56. #431×C79C22semidirect
57. #423×C79C22semidirect
58. C2×C4⋊C8×C79C22semidirect
59. #332×C79C22semidirect
60. #332×C79C22semidirect
63. Q8⋊C8×C79C22semidirect
64. Q8⋊C8×C79C22semidirect
69. D4⋊C8×C79C22semidirect
70. D4⋊C8×C79C22semidirect
390. #18962C79direct (N × H)
400. #3546C2×C79semidirect
401. #3253C2×C79semidirect
402. #3247C2×C79semidirect
403. #3207C2×C79semidirect
404. #1638C2×C79semidirect
405. #1635C2×C79semidirect
406. #1631C2×C79semidirect
407. #1629C2×C79semidirect
408. #1628C2×C79semidirect
409. #1625C2×C79semidirect
410. #1621C2×C79semidirect
411. #1619C2×C79semidirect
412. #1547C2×C79semidirect
413. #1495C2×C79semidirect
414. #1480C2×C79semidirect
415. C79#18962direct (N × H)
432. #532C22×C79semidirect
436. #487C22×C79semidirect
437. #486C22×C79semidirect
439. #477C22×C79semidirect
443. #476C22×C79semidirect
450. #460C22×C79semidirect
454. #459C22×C79semidirect
456. #431C22×C79semidirect
457. #423C22×C79semidirect
458. C2×C4⋊C8C22×C79semidirect
459. #332C22×C79semidirect
460. #332C22×C79semidirect
463. Q8⋊C8C22×C79semidirect
464. Q8⋊C8C22×C79semidirect
469. D4⋊C8C22×C79semidirect
470. D4⋊C8C22×C79semidirect

Maximal subgroups

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

subgroupindex
C79×#35462
C79×#32532
C79×#32472
C79×#32072
C79×#16382
C79×#16352
C79×#16312
C79×#16292
C79×#16282
C79×#16252
C79×#16212
C79×#16192
C79×#15472
C79×#14952
C79×#14802
#1896279