Finite Group Databasebeta

← C101×#18742 #38800893

Subgroups — C101×#18742 #38800893

Order 25856.

908 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3554C211yesmaximal, characteristic, complemented
2C101×#3246C211yesmaximal, characteristic, complemented
3C101×#3212C211yesmaximal, characteristic, complemented
4C101×#3184C211yesmaximal, characteristic, complemented
5C101×#1653C211yesmaximal, characteristic, complemented
6C101×#1651C211yesmaximal, characteristic, complemented
7C101×#1642C211yesmaximal, characteristic, complemented
8C101×#1640C211yesmaximal, characteristic, complemented
9C101×#1627C211yesmaximal, characteristic, complemented
10C101×#1626C211yesmaximal, characteristic, complemented
11C101×#1621C211yesmaximal, characteristic, complemented
12C101×#1620C211yesmaximal, characteristic, complemented
13C101×#1540C211yesmaximal, characteristic, complemented
14C101×#1485C211yesmaximal, characteristic, complemented
15C101×#1483C211yesmaximal, characteristic, complemented
16#562×C101—22no—
17#559×C101—21no—
18#559×C101C2211yescharacteristic
19#557×C101C2211yescharacteristic
20#554×C101—21no—
21#550×C101C2211yescharacteristic
22D4×Q8×C101C2211yescharacteristic
23#548×C101—21no—
24#547×C101—21no—
25#542×C101—21no—
26#542×C101—21no—
27#540×C101—21no—
28#539×C101—22no—
29#536×C101—21no—
30#533×C101C2211yescharacteristic
31#532×C101C2211yescharacteristic
32#532×C101C2211yescharacteristic
33#529×C101C2211yescharacteristic
34#498×C101C2211yescharacteristic
35#495×C101—21no—
36#493×C101C2211yescharacteristic
37#488×C101—21no—
38#486×C101C2211yescharacteristic
39#486×C101C2211yescharacteristic
40#476×C101—21no—
41#475×C101C2211yescharacteristic
42#475×C101C2211yescharacteristic
43#469×C101—22no—
44#465×C101—21no—
45#465×C101—21no—
46#462×C101C2211yescharacteristic
47#461×C101—21no—
48#461×C101C2211yescharacteristic
49#460×C101C2211yescharacteristic
50#460×C101C2211yescharacteristic
51#460×C101C2211yescharacteristic
52#459×C101C2211yescharacteristic
53#452×C101—21no—
54#449×C101—21no—
55#442×C101—22no—
56#431×C101C2211yescharacteristic
57C2×C4⋊C8×C101C2211yescharacteristic
58C4×M16×C101C2211yescharacteristic
59#332×C101C2211yescharacteristic
60#332×C101C2211yescharacteristic
61#331×C101C2211yescharacteristic
62#331×C101C2211yescharacteristic
63Q8⋊C8×C101C2211yescharacteristic
64Q8⋊C8×C101C2211yescharacteristic
65Q8⋊C8×C101C2211yescharacteristic
66Q8⋊C8×C101C2211yescharacteristic
67Q8⋊C8×C101C2211yescharacteristic
68Q8⋊C8×C101C2211yescharacteristic
69D4⋊C8×C101C2211yescharacteristic
70D4⋊C8×C101C2211yescharacteristic
71C2×#41×C101—21no—
72C2×#41×C101—21no—
73C2×#41×C101—21no—
74C22×Q8×C101—21no—
75C2×Q16×C101—21no—
76C2×SD16×C101—21no—
77C2×SD16×C101—21no—
78C2×SD16×C101—21no—
79C2×SD16×C101—21no—
80C2×D8×C101—22no—
81C2×D8×C101—21no—
82C2×M16×C101—21no—
83C22×C8×C101—21no—
84C4⋊Q8×C101—21no—
85C4⋊Q8×C101—21no—
86C4⋊Q8×C101D411yescharacteristic
87C4⋊Q8×C101D411yescharacteristic
88C4⋊Q8×C101C2311yescharacteristic
89C4⋊Q8×C101C2311yescharacteristic
90#127×C101—21no—
91#127×C101C2311yescharacteristic
92#127×C101C2311yescharacteristic
93#126×C101—22no—
94#126×C101—21no—
95#125×C101—22no—
96#125×C101—21no—
97#125×C101—21no—
98#125×C101D411yescharacteristic
99#124×C101—22no—
100#124×C101—22no—
101#124×C101—21no—
102#124×C101—21no—
103#124×C101—21no—
104#124×C101—21no—
105#124×C101D411yescharacteristic
106#123×C101—22no—
107#123×C101—22no—
108#123×C101—22no—
109#123×C101—22no—
110#123×C101—22no—
111#123×C101—22no—
112#123×C101—21no—
113C22⋊Q8×C101—22no—
114C22⋊Q8×C101—22no—
115C22⋊Q8×C101—22no—
116C22⋊Q8×C101—22no—
117C22⋊Q8×C101—21no—
118C22⋊Q8×C101—22no—
119C22⋊Q8×C101—21no—
120C22⋊Q8×C101D411yescharacteristic
121C22⋊Q8×C101D411yescharacteristic
122C22⋊Q8×C101D411yescharacteristic
123#121×C101—22no—
124#121×C101—22no—
125#121×C101—22no—
126#121×C101—21no—
127#121×C101—21no—
128#121×C101—21no—
129#121×C101—21no—
130#121×C101D411yescharacteristic
131#121×C101D412yes—
132C4×Q8×C101—21no—
133C4×Q8×C101—21no—
134C4×Q8×C101—21no—
135C4×Q8×C101C2311yescharacteristic
136C4×Q8×C101C2311yescharacteristic
137C4×Q8×C101C2311yescharacteristic
138C4×D4×C101—22no—
139C4×D4×C101—21no—
140C4×D4×C101—21no—
141C4×D4×C101—21no—
142C4×D4×C101—21no—
143C4×D4×C101—21no—
144C4×D4×C101—21no—
145C4×D4×C101—21no—
146C4×D4×C101—21no—
147C4×D4×C101D412yes—
148C4×D4×C101C2311yescharacteristic
149#117×C101—21no—
150#117×C101—21no—
151C2×C4⋊C4×C101—22no—
152C2×C42×C101C2311yescharacteristic
153#106×C101—22no—
154#106×C101—21no—
155#106×C101—21no—
156C4⋊C8×C101—21no—
157C4⋊C8×C101C2311yescharacteristic
158C4⋊C8×C101C2311yescharacteristic
159C4⋊C8×C101C2311yescharacteristic
160C4⋊C8×C101C2311yescharacteristic
161#103×C101—21no—
162#103×C101—21no—
163#103×C101—21no—
164#103×C101—21no—
165#102×C101—22no—
166#102×C101—22no—
167#102×C101—21no—
168#102×C101—21no—
169#102×C101—21no—
170#102×C101—21no—
171C22⋊C8×C101—21no—
172#97×C101—21no—
173C4×C8×C101—21no—
174C4×C8×C101C2311yescharacteristic
175C4×C8×C101C2311yescharacteristic
176#41×C101—81no—
177#41×C101—81no—
178#41×C101—81no—
179#41×C101—81no—
180#41×C101—81no—
181#41×C101—81no—
182C2×Q8×C101—22no—
183C2×Q8×C101—21no—
184C2×Q8×C101—21no—
185C2×Q8×C101—21no—
186C2×Q8×C101—81no—
187C2×Q8×C101—81no—
188C2×Q8×C101C2×D411yescharacteristic
189C2×Q8×C101C2×D411yescharacteristic
190C2×Q8×C101C2×D411yescharacteristic
191C2×D4×C101—22no—
192C2×D4×C101—22no—
193C2×D4×C101—21no—
194C2×D4×C101—22no—
195C2×D4×C101—21no—
196C2×D4×C101—21no—
197C2×D4×C101—21no—
198C2×D4×C101—21no—
199C2×D4×C101—21no—
200C2×D4×C101—41no—
201C2×D4×C101C2×D411yescharacteristic
202C2×D4×C101C2×D412yes—
203C22×C4×C101—22no—
204C22×C4×C101—22no—
205C22×C4×C101—22no—
206C22×C4×C101—21no—
207C22×C4×C101—22no—
208C22×C4×C101—41no—
209C22×C4×C101C2×D411yescharacteristic
210C22×C4×C101C2×D411yescharacteristic
211C22×C4×C101C2×D411yescharacteristic
212Q16×C101—81no—
213SD16×C101—81no—
214SD16×C101—81no—
215SD16×C101—81no—
216SD16×C101—81no—
217D8×C101—44no—
218D8×C101—81no—
219M16×C101—42no—
220C2×C8×C101—21no—
221C2×C8×C101—21no—
222C2×C8×C101—21no—
223C2×C8×C101—21no—
224C2×C8×C101—21no—
225C2×C8×C101—21no—
226C2×C8×C101—81no—
227C4⋊C4×C101—22no—
228C4⋊C4×C101—22no—
229C4⋊C4×C101—22no—
230C4⋊C4×C101—22no—
231C4⋊C4×C101—21no—
232C4⋊C4×C101—21no—
233C4⋊C4×C101—21no—
234C4⋊C4×C101—21no—
235C4⋊C4×C101—21no—
236C4⋊C4×C101—21no—
237C4⋊C4×C101—21no—
238C4⋊C4×C101—21no—
239C4⋊C4×C101—21no—
240C4⋊C4×C101—21no—
241C4⋊C4×C101—21no—
242C4⋊C4×C101—21no—
243C4⋊C4×C101—21no—
244C4⋊C4×C101—21no—
245C4⋊C4×C101C2×D411yescharacteristic
246C4⋊C4×C101C2×D411yescharacteristic
247C4⋊C4×C101C2×D411yescharacteristic
248C4⋊C4×C101C2×D412yes—
249C4⋊C4×C101C2×D411yescharacteristic
250C22⋊C4×C101—22no—
251C22⋊C4×C101—22no—
252C22⋊C4×C101—22no—
253C22⋊C4×C101—22no—
254C22⋊C4×C101—22no—
255C22⋊C4×C101—21no—
256C22⋊C4×C101—21no—
257C22⋊C4×C101—21no—
258C22⋊C4×C101—21no—
259C22⋊C4×C101—21no—
260C22⋊C4×C101—21no—
261C22⋊C4×C101—22no—
262C22⋊C4×C101—22no—
263C22⋊C4×C101—21no—
264C22⋊C4×C101—41no—
265C22⋊C4×C101—41no—
266C42×C101—22no—
267C42×C101—21no—
268C42×C101—21no—
269C42×C101—21no—
270C42×C101C2×D411yescharacteristic
271C42×C101C2×D411yescharacteristic
272C42×C101C2×D411yescharacteristic
273C42×C101C2411yescharacteristic
274C23×C101—21no—
275C23×C101—22no—
276C23×C101—41no—
277C23×C101#12011yescharacteristic
278Q8×C101—21no—
279Q8×C101—21no—
280Q8×C101—21no—
281Q8×C101—21no—
282Q8×C101—21no—
283Q8×C101—21no—
284Q8×C101—41no—
285Q8×C101—41no—
286Q8×C101—41no—
287Q8×C101—41no—
288Q8×C101—81no—
289Q8×C101—82no—
290D4×C101—21no—
291D4×C101—21no—
292D4×C101—42no—
293D4×C101—42no—
294D4×C101—41no—
295D4×C101—41no—
296D4×C101—41no—
297D4×C101—41no—
298D4×C101—41no—
299D4×C101—41no—
300D4×C101—41no—
301D4×C101—41no—
302D4×C101—81no—
303D4×C101—82no—
304D4×C101—82no—
305D4×C101—82no—
306D4×C101—82no—
307C2×C4×C101—21no—
308C2×C4×C101—21no—
309C2×C4×C101—21no—
310C2×C4×C101—21no—
311C2×C4×C101—21no—
312C2×C4×C101—21no—
313C2×C4×C101—21no—
314C2×C4×C101—21no—
315C2×C4×C101—21no—
316C2×C4×C101—22no—
317C2×C4×C101—21no—
318C2×C4×C101—21no—
319C2×C4×C101—41no—
320C2×C4×C101—41no—
321C2×C4×C101—41no—
322C2×C4×C101—41no—
323C2×C4×C101—82no—
324C2×C4×C101—82no—
325C2×C4×C101—82no—
326C2×C4×C101—82no—
327C2×C4×C101—82no—
328C2×C4×C101#12011yescharacteristic
329C2×C4×C101#12011yescharacteristic
330C2×C4×C101#12011yescharacteristic
331C2×C4×C101C22×D411yescharacteristic
332C2×C4×C101C22×D411yescharacteristic
333C2×C4×C101C22×D411yescharacteristic
334C8×C101—22no—
335C8×C101—41no—
336C8×C101—41no—
337C8×C101—41no—
338C8×C101—41no—
339C8×C101—41no—
340C22×C101—21no—
341C22×C101—21no—
342C22×C101—21no—
343C22×C101—41no—
344C22×C101—42no—
345C22×C101—41no—
346C22×C101—42no—
347C22×C101—42no—
348C22×C101—41no—
349C22×C101—81no—
350C22×C101—81no—
351C22×C101—81no—
352C22×C101C2×#12011yescharacteristic
353C4×C101—21no—
354C4×C101—21no—
355C4×C101—21no—
356C4×C101—21no—
357C4×C101—41no—
358C4×C101—41no—
359C4×C101—41no—
360C4×C101—42no—
361C4×C101—41no—
362C4×C101—41no—
363C4×C101—41no—
364C4×C101—41no—
365C4×C101—81no—
366C4×C101#57611yescharacteristic
367C4×C101#57711yescharacteristic
368C4×C101#57711yescharacteristic
369C4×C101#57711yescharacteristic
370#18742C10111yesmaximal, characteristic, direct product factor, Sylow
371C2×C101—41no—
372C2×C101—81no—
373C2×C101—82no—
374C2×C101—161no—
375C2×C101#301011yescharacteristic
376C2×C101#301211yescharacteristic
377C2×C101#301811yescharacteristic
378#3554C2×C10111yescharacteristic, complemented
379#3246C2×C10111yescharacteristic, complemented
380#3212C2×C10111yescharacteristic, complemented
381#3184C2×C10111yescharacteristic, complemented
382#1653C2×C10111yescharacteristic, complemented
383#1651C2×C10111yescharacteristic, complemented
384#1642C2×C10111yescharacteristic, complemented
385#1640C2×C10111yescharacteristic, complemented
386#1627C2×C10111yescharacteristic, complemented
387#1626C2×C10111yescharacteristic, complemented
388#1621C2×C10111yescharacteristic, complemented
389#1620C2×C10111yescharacteristic, complemented
390#1540C2×C10111yescharacteristic, complemented
391#1485C2×C10111yescharacteristic, complemented
392#1483C2×C10111yescharacteristic, complemented
393C101#1874211yescharacteristic, direct product factor, Sylow
394#562—22no—
395#559—21no—
396#559C22×C10111yescharacteristic
397#557C22×C10111yescharacteristic
398#554—21no—
399#550C22×C10111yescharacteristic
400D4×Q8C22×C10111yescharacteristic
401#548—21no—
402#547—21no—
403#542—21no—
404#542—21no—
405#540—21no—
406#539—22no—
407#536—21no—
408#533C22×C10111yescharacteristic
409#532C22×C10111yescharacteristic
410#532C22×C10111yescharacteristic
411#529C22×C10111yescharacteristic
412#498C22×C10111yescharacteristic
413#495—21no—
414#493C22×C10111yescharacteristic
415#488—21no—
416#486C22×C10111yescharacteristic
417#486C22×C10111yescharacteristic
418#476—21no—
419#475C22×C10111yescharacteristic
420#475C22×C10111yescharacteristic
421#469—22no—
422#465—21no—
423#465—21no—
424#462C22×C10111yescharacteristic
425#461—21no—
426#461C22×C10111yescharacteristic
427#460C22×C10111yescharacteristic
428#460C22×C10111yescharacteristic
429#460C22×C10111yescharacteristic
430#459C22×C10111yescharacteristic
431#452—21no—
432#449—21no—
433#442—22no—
434#431C22×C10111yescharacteristic
435C2×C4⋊C8C22×C10111yescharacteristic
436C4×M16C22×C10111yescharacteristic
437#332C22×C10111yescharacteristic
438#332C22×C10111yescharacteristic
439#331C22×C10111yescharacteristic
440#331C22×C10111yescharacteristic
441Q8⋊C8C22×C10111yescharacteristic
442Q8⋊C8C22×C10111yescharacteristic
443Q8⋊C8C22×C10111yescharacteristic
444Q8⋊C8C22×C10111yescharacteristic
445Q8⋊C8C22×C10111yescharacteristic
446Q8⋊C8C22×C10111yescharacteristic
447D4⋊C8C22×C10111yescharacteristic
448D4⋊C8C22×C10111yescharacteristic
449C2×#41—21no—
450C2×#41—21no—
451C2×#41—21no—
452C22×Q8—21no—
453C2×Q16—21no—
454C2×SD16—21no—
455C2×SD16—21no—
456C2×SD16—21no—
457C2×SD16—21no—
458C2×D8—22no—
459C2×D8—21no—
460C2×M16—21no—
461C22×C8—21no—
462C4⋊Q8—21no—
463C4⋊Q8—21no—
464C4⋊Q8D4×C10111yescharacteristic
465C4⋊Q8D4×C10111yescharacteristic
466C4⋊Q8C23×C10111yescharacteristic
467C4⋊Q8C23×C10111yescharacteristic
468#127—21no—
469#127C23×C10111yescharacteristic
470#127C23×C10111yescharacteristic
471#126—22no—
472#126—21no—
473#125—22no—
474#125—21no—
475#125—21no—
476#125D4×C10111yescharacteristic
477#124—22no—
478#124—22no—
479#124—21no—
480#124—21no—
481#124—21no—
482#124—21no—
483#124D4×C10111yescharacteristic
484#123—22no—
485#123—22no—
486#123—22no—
487#123—22no—
488#123—22no—
489#123—22no—
490#123—21no—
491C22⋊Q8—22no—
492C22⋊Q8—22no—
493C22⋊Q8—22no—
494C22⋊Q8—22no—
495C22⋊Q8—21no—
496C22⋊Q8—22no—
497C22⋊Q8—21no—
498C22⋊Q8D4×C10111yescharacteristic
499C22⋊Q8D4×C10111yescharacteristic
500C22⋊Q8D4×C10111yescharacteristic
501#121—22no—
502#121—22no—
503#121—22no—
504#121—21no—
505#121—21no—
506#121—21no—
507#121—21no—
508#121D4×C10111yescharacteristic
509#121D4×C10112yes—
510C4×Q8—21no—
511C4×Q8—21no—
512C4×Q8—21no—
513C4×Q8C23×C10111yescharacteristic
514C4×Q8C23×C10111yescharacteristic
515C4×Q8C23×C10111yescharacteristic
516C4×D4—22no—
517C4×D4—21no—
518C4×D4—21no—
519C4×D4—21no—
520C4×D4—21no—
521C4×D4—21no—
522C4×D4—21no—
523C4×D4—21no—
524C4×D4—21no—
525C4×D4D4×C10112yes—
526C4×D4C23×C10111yescharacteristic
527#117—21no—
528#117—21no—
529C2×C4⋊C4—22no—
530C2×C42C23×C10111yescharacteristic
531#106—22no—
532#106—21no—
533#106—21no—
534C4⋊C8—21no—
535C4⋊C8C23×C10111yescharacteristic
536C4⋊C8C23×C10111yescharacteristic
537C4⋊C8C23×C10111yescharacteristic
538C4⋊C8C23×C10111yescharacteristic
539#103—21no—
540#103—21no—
541#103—21no—
542#103—21no—
543#102—22no—
544#102—22no—
545#102—21no—
546#102—21no—
547#102—21no—
548#102—21no—
549C22⋊C8—21no—
550#97—21no—
551C4×C8—21no—
552C4×C8C23×C10111yescharacteristic
553C4×C8C23×C10111yescharacteristic
554#41—81no—
555#41—81no—
556#41—81no—
557#41—81no—
558#41—81no—
559#41—81no—
560C2×Q8—22no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—81no—
565C2×Q8—81no—
566C2×Q8C2×D4×C10111yescharacteristic
567C2×Q8C2×D4×C10111yescharacteristic
568C2×Q8C2×D4×C10111yescharacteristic
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—21no—
572C2×D4—22no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—41no—
579C2×D4C2×D4×C10111yescharacteristic
580C2×D4C2×D4×C10112yes—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—41no—
587C22×C4C2×D4×C10111yescharacteristic
588C22×C4C2×D4×C10111yescharacteristic
589C22×C4C2×D4×C10111yescharacteristic
590Q16—81no—
591SD16—81no—
592SD16—81no—
593SD16—81no—
594SD16—81no—
595D8—44no—
596D8—81no—
597M16—42no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—81no—
605C4⋊C4—22no—
606C4⋊C4—22no—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4C2×D4×C10111yescharacteristic
624C4⋊C4C2×D4×C10111yescharacteristic
625C4⋊C4C2×D4×C10111yescharacteristic
626C4⋊C4C2×D4×C10112yes—
627C4⋊C4C2×D4×C10111yescharacteristic
628C22⋊C4—22no—
629C22⋊C4—22no—
630C22⋊C4—22no—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—21no—
634C22⋊C4—21no—
635C22⋊C4—21no—
636C22⋊C4—21no—
637C22⋊C4—21no—
638C22⋊C4—21no—
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—21no—
642C22⋊C4—41no—
643C22⋊C4—41no—
644C42—22no—
645C42—21no—
646C42—21no—
647C42—21no—
648C42C2×D4×C10111yescharacteristic
649C42C2×D4×C10111yescharacteristic
650C42C2×D4×C10111yescharacteristic
651C42C24×C10111yescharacteristic
652C23—21no—
653C23—22no—
654C23—41no—
655C23#120×C10111yescharacteristic
656Q8—21no—
657Q8—21no—
658Q8—21no—
659Q8—21no—
660Q8—21no—
661Q8—21no—
662Q8—41no—
663Q8—41no—
664Q8—41no—
665Q8—41no—
666Q8—81no—
667Q8—82no—
668D4—21no—
669D4—21no—
670D4—42no—
671D4—42no—
672D4—41no—
673D4—41no—
674D4—41no—
675D4—41no—
676D4—41no—
677D4—41no—
678D4—41no—
679D4—41no—
680D4—82no—
681D4—81no—
682D4—82no—
683D4—82no—
684D4—82no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—22no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—82no—
702C2×C4—82no—
703C2×C4—82no—
704C2×C4—82no—
705C2×C4—82no—
706C2×C4#120×C10111yescharacteristic
707C2×C4#120×C10111yescharacteristic
708C2×C4#120×C10111yescharacteristic
709C2×C4C22×D4×C10111yescharacteristic
710C2×C4C22×D4×C10111yescharacteristic
711C2×C4C22×D4×C10111yescharacteristic
712C8—22no—
713C8—41no—
714C8—41no—
715C8—41no—
716C8—41no—
717C8—41no—
718C22—21no—
719C22—21no—
720C22—21no—
721C22—41no—
722C22—42no—
723C22—41no—
724C22—42no—
725C22—42no—
726C22—41no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22C2×#120×C10111yescharacteristic
731C4—21no—
732C4—21no—
733C4—21no—
734C4—21no—
735C4—41no—
736C4—41no—
737C4—41no—
738C4—42no—
739C4—41no—
740C4—41no—
741C4—41no—
742C4—41no—
743C4—81no—
744C4#576×C10111yescharacteristic
745C4#577×C10111yescharacteristic
746C4#577×C10111yescharacteristic
747C4#577×C10111yescharacteristic
748C2—41no—
749C2—81no—
750C2—82no—
751C2—161no—
752C2C101×#301011yescharacteristic
753C2C101×#301211yescharacteristic
754C2C101×#301811yescharacteristic
subgroupG/H
center, socleC22×C101C2×#120
commutator, Frattini, cosocleC42C24×C101
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C101 ◁ C2×C42×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C101×#3554C2semidirect
2. C101×#3246C2semidirect
3. C101×#3212C2semidirect
4. C101×#3184C2semidirect
5. C101×#1653C2semidirect
6. C101×#1651C2semidirect
7. C101×#1642C2semidirect
8. C101×#1640C2semidirect
9. C101×#1627C2semidirect
10. C101×#1626C2semidirect
11. C101×#1621C2semidirect
12. C101×#1620C2semidirect
13. C101×#1540C2semidirect
14. C101×#1485C2semidirect
15. C101×#1483C2semidirect
370. #18742C101direct (N × H)
378. #3554C2×C101semidirect
379. #3246C2×C101semidirect
380. #3212C2×C101semidirect
381. #3184C2×C101semidirect
382. #1653C2×C101semidirect
383. #1651C2×C101semidirect
384. #1642C2×C101semidirect
385. #1640C2×C101semidirect
386. #1627C2×C101semidirect
387. #1626C2×C101semidirect
388. #1621C2×C101semidirect
389. #1620C2×C101semidirect
390. #1540C2×C101semidirect
391. #1485C2×C101semidirect
392. #1483C2×C101semidirect
393. C101#18742direct (N × H)

Maximal subgroups

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

subgroupindex
C101×#35542
C101×#32462
C101×#32122
C101×#31842
C101×#16532
C101×#16512
C101×#16422
C101×#16402
C101×#16272
C101×#16262
C101×#16212
C101×#16202
C101×#15402
C101×#14852
C101×#14832
#18742101