Finite Group Databasebeta

← C101×#24524 #38806675

Subgroups — C101×#24524 #38806675

Order 25856.

884 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3094C211yesmaximal, characteristic, complemented
2C2×#449×C101C211yesmaximal, characteristic
3C101×#2924C211yesmaximal, characteristic, complemented
4C101×#2896C211yesmaximal, characteristic, complemented
5C101×#2064C211yesmaximal, characteristic, complemented
6C101×#2063C211yesmaximal, characteristic, complemented
7C101×#2046C211yesmaximal, characteristic, complemented
8C101×#2045C211yesmaximal, characteristic, complemented
9C101×#1978C211yesmaximal, characteristic, complemented
10C101×#1977C211yesmaximal, characteristic, complemented
11C101×#1931C211yesmaximal, characteristic, complemented
12C101×#1930C211yesmaximal, characteristic, complemented
13C101×#1900C211yesmaximal, characteristic, complemented
14C101×#1855C211yesmaximal, characteristic, complemented
15C101×#1785C211yesmaximal, characteristic, complemented
16C22×#41×C101C2211yescharacteristic
17C22×SD16×C101C2211yescharacteristic
18C22×D8×C101C2211yescharacteristic
19C22×M16×C101C2211yescharacteristic
20C2×#121×C101C2211yescharacteristic
21C2×#117×C101C2211yescharacteristic
22#482×C101—21no—
23#482×C101—21no—
24#481×C101—21no—
25#480×C101—21no—
26#449×C101—21no—
27#449×C101—21no—
28#449×C101—21no—
29#449×C101—21no—
30#433×C101—21no—
31#433×C101—21no—
32#432×C101—21no—
33#431×C101—21no—
34C2×#108×C101C2211yescharacteristic
35C2×#108×C101C2211yescharacteristic
36#428×C101C2211yescharacteristic
37#428×C101C2211yescharacteristic
38#424×C101C2211yescharacteristic
39#424×C101C2211yescharacteristic
40#419×C101C2211yescharacteristic
41#419×C101C2211yescharacteristic
42#418×C101C2211yescharacteristic
43#418×C101C2211yescharacteristic
44#418×C101C2211yescharacteristic
45#418×C101C2211yescharacteristic
46#417×C101—21no—
47#417×C101—21no—
48#416×C101—21no—
49#416×C101—21no—
50C2×#103×C101C2211yescharacteristic
51C2×#102×C101C2211yescharacteristic
52C2×#101×C101C2211yescharacteristic
53C2×#101×C101C2211yescharacteristic
54C2×#100×C101C2211yescharacteristic
55C2×#100×C101C2211yescharacteristic
56C2×#100×C101C2211yescharacteristic
57C2×#100×C101C2211yescharacteristic
58#407×C101C2211yescharacteristic
59#407×C101C2211yescharacteristic
60C2×C22⋊C8×C101C2211yescharacteristic
61#405×C101C2211yescharacteristic
62#405×C101C2211yescharacteristic
63#343×C101C2211yescharacteristic
64#343×C101C2211yescharacteristic
65#341×C101C2211yescharacteristic
66#341×C101C2211yescharacteristic
67C2×#41×C101—22no—
68C2×#41×C101—22no—
69C2×#41×C101—21no—
70C2×#41×C101—21no—
71C2×#41×C101—21no—
72C2×#41×C101—21no—
73C2×#41×C101—41no—
74C2×#41×C101—41no—
75C22×Q8×C101C2311yescharacteristic
76C22×D4×C101—21no—
77C22×D4×C101—21no—
78C22×D4×C101C2311yescharacteristic
79C22×D4×C101C2311yescharacteristic
80C23×C4×C101—21no—
81C23×C4×C101C2311yescharacteristic
82C2×SD16×C101—22no—
83C2×SD16×C101—21no—
84C2×SD16×C101—21no—
85C2×SD16×C101—41no—
86C2×D8×C101—22no—
87C2×D8×C101—21no—
88C2×D8×C101—21no—
89C2×D8×C101—41no—
90C2×M16×C101—21no—
91C2×M16×C101—41no—
92C2×M16×C101—41no—
93C2×M16×C101C2311yescharacteristic
94C2×M16×C101C2311yescharacteristic
95C2×M16×C101C2311yescharacteristic
96C2×M16×C101C2311yescharacteristic
97C2×M16×C101C2311yescharacteristic
98C2×M16×C101C2311yescharacteristic
99C22×C8×C101—21no—
100C22×C8×C101C2311yescharacteristic
101C22×C8×C101C2311yescharacteristic
102#121×C101—21no—
103#121×C101—21no—
104#121×C101—21no—
105#121×C101—21no—
106#117×C101—21no—
107#117×C101—21no—
108#117×C101D411yescharacteristic
109#117×C101D411yescharacteristic
110#117×C101C2311yescharacteristic
111#117×C101C2311yescharacteristic
112C2×C4⋊C4×C101D411yescharacteristic
113C2×C4⋊C4×C101D411yescharacteristic
114C2×C4⋊C4×C101C2311yescharacteristic
115C2×C22⋊C4×C101—21no—
116C2×C22⋊C4×C101—21no—
117C2×C42×C101—21no—
118#108×C101—41no—
119#108×C101—41no—
120#107×C101—21no—
121#107×C101—21no—
122#106×C101—21no—
123#106×C101—21no—
124C4⋊C8×C101—21no—
125C4⋊C8×C101—21no—
126C4⋊C8×C101—21no—
127C4⋊C8×C101—21no—
128#103×C101—21no—
129#103×C101—21no—
130#103×C101—21no—
131#103×C101—21no—
132#103×C101—21no—
133#103×C101—21no—
134#102×C101—21no—
135#102×C101—21no—
136#102×C101—21no—
137#102×C101—21no—
138#102×C101—21no—
139#102×C101—21no—
140#102×C101—21no—
141#102×C101—21no—
142#102×C101—21no—
143#102×C101—21no—
144#101×C101—22no—
145#101×C101—41no—
146#100×C101—22no—
147#100×C101—41no—
148#100×C101—41no—
149#100×C101—41no—
150C22⋊C8×C101—21no—
151C22⋊C8×C101—21no—
152C22⋊C8×C101—21no—
153C22⋊C8×C101—21no—
154C22⋊C8×C101D411yescharacteristic
155C22⋊C8×C101D411yescharacteristic
156C22⋊C8×C101D411yescharacteristic
157C22⋊C8×C101D411yescharacteristic
158#97×C101—21no—
159#97×C101—21no—
160C4×C8×C101—21no—
161C4×C8×C101—21no—
162C24×C101—21no—
163C24×C101—21no—
164C24×C101#4111yescharacteristic
165#41×C101—24no—
166#41×C101—24no—
167#41×C101—42no—
168#41×C101—42no—
169#41×C101—42no—
170#41×C101—42no—
171#41×C101—42no—
172#41×C101—42no—
173C2×Q8×C101—21no—
174C2×Q8×C101—21no—
175C2×Q8×C101—21no—
176C2×Q8×C101—21no—
177C2×Q8×C101—21no—
178C2×Q8×C101#4112yes—
179C2×D4×C101—21no—
180C2×D4×C101—21no—
181C2×D4×C101—21no—
182C2×D4×C101—21no—
183C2×D4×C101—21no—
184C2×D4×C101—21no—
185C2×D4×C101—21no—
186C2×D4×C101—21no—
187C2×D4×C101—21no—
188C2×D4×C101—21no—
189C2×D4×C101—21no—
190C2×D4×C101—42no—
191C2×D4×C101—42no—
192C2×D4×C101—41no—
193C2×D4×C101—41no—
194C2×D4×C101—41no—
195C2×D4×C101—41no—
196C2×D4×C101—82no—
197C2×D4×C101#4112yes—
198C22×C4×C101—21no—
199C22×C4×C101—21no—
200C22×C4×C101—21no—
201C22×C4×C101—21no—
202C22×C4×C101—21no—
203C22×C4×C101—21no—
204C22×C4×C101—21no—
205C22×C4×C101—21no—
206C22×C4×C101—42no—
207C22×C4×C101—42no—
208C22×C4×C101—41no—
209C22×C4×C101—41no—
210C22×C4×C101C2×D411yescharacteristic
211C22×C4×C101C2×D411yescharacteristic
212C22×C4×C101C2×D411yescharacteristic
213C22×C4×C101C2×D411yescharacteristic
214C22×C4×C101#4111yescharacteristic
215C22×C4×C101C2411yescharacteristic
216SD16×C101—42no—
217SD16×C101—42no—
218D8×C101—42no—
219D8×C101—42no—
220M16×C101—21no—
221M16×C101—21no—
222M16×C101—21no—
223M16×C101—21no—
224M16×C101—21no—
225M16×C101—21no—
226M16×C101—21no—
227M16×C101—21no—
228M16×C101—21no—
229M16×C101—21no—
230M16×C101—21no—
231M16×C101—21no—
232M16×C101—42no—
233C2×C8×C101—21no—
234C2×C8×C101—21no—
235C2×C8×C101—21no—
236C2×C8×C101—21no—
237C2×C8×C101—21no—
238C2×C8×C101—21no—
239C2×C8×C101—21no—
240C2×C8×C101—21no—
241C2×C8×C101—21no—
242C2×C8×C101—21no—
243C2×C8×C101—42no—
244C2×C8×C101C2×D411yescharacteristic
245C2×C8×C101C2×D411yescharacteristic
246C2×C8×C101C2×D411yescharacteristic
247C2×C8×C101C2×D411yescharacteristic
248C4⋊C4×C101—21no—
249C4⋊C4×C101—21no—
250C4⋊C4×C101—21no—
251C4⋊C4×C101—21no—
252C4⋊C4×C101C2×D411yescharacteristic
253C4⋊C4×C101C2×D411yescharacteristic
254C4⋊C4×C101C2×D411yescharacteristic
255C4⋊C4×C101C2×D411yescharacteristic
256C22⋊C4×C101—21no—
257C22⋊C4×C101—21no—
258C22⋊C4×C101—21no—
259C22⋊C4×C101—21no—
260C22⋊C4×C101—41no—
261C22⋊C4×C101—41no—
262C42×C101—21no—
263C42×C101—21no—
264C42×C101—21no—
265C42×C101—21no—
266C23×C101—21no—
267C23×C101—21no—
268C23×C101—22no—
269C23×C101—41no—
270C23×C101—41no—
271C23×C101—41no—
272C23×C101—41no—
273C23×C101—41no—
274C23×C101—41no—
275C23×C101—41no—
276C23×C101—81no—
277C23×C101—81no—
278C23×C101—81no—
279C23×C101—81no—
280C23×C101#12111yescharacteristic
281C23×C101#12111yescharacteristic
282C23×C101C2×#4111yescharacteristic
283Q8×C101—22no—
284Q8×C101—22no—
285Q8×C101—41no—
286Q8×C101—41no—
287D4×C101—22no—
288D4×C101—22no—
289D4×C101—44no—
290D4×C101—44no—
291D4×C101—41no—
292D4×C101—41no—
293D4×C101—41no—
294D4×C101—41no—
295D4×C101—41no—
296D4×C101—41no—
297D4×C101—82no—
298D4×C101—82no—
299C2×C4×C101—21no—
300C2×C4×C101—21no—
301C2×C4×C101—21no—
302C2×C4×C101—21no—
303C2×C4×C101—21no—
304C2×C4×C101—21no—
305C2×C4×C101—21no—
306C2×C4×C101—21no—
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—22no—
314C2×C4×C101—44no—
315C2×C4×C101—44no—
316C2×C4×C101—42no—
317C2×C4×C101—41no—
318C2×C4×C101—41no—
319C2×C4×C101—41no—
320C2×C4×C101—81no—
321C2×C4×C101—81no—
322C2×C4×C101#12111yescharacteristic
323C2×C4×C101#12111yescharacteristic
324C2×C4×C101C22×D411yescharacteristic
325C2×C4×C101C22×D411yescharacteristic
326C2×C4×C101C2×#4111yescharacteristic
327C2×C4×C101C2×#4111yescharacteristic
328C2×C4×C101H(5,𝔽2)11yescharacteristic
329C2×C4×C101H(5,𝔽2)11yescharacteristic
330C8×C101—21no—
331C8×C101—21no—
332C8×C101—21no—
333C8×C101—21no—
334C8×C101—41no—
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—21no—
344C22×C101—21no—
345C22×C101—21no—
346C22×C101—21no—
347C22×C101—21no—
348C22×C101—42no—
349C22×C101—81no—
350C22×C101—81no—
351C22×C101—82no—
352C22×C101—82no—
353C22×C101—81no—
354C22×C101—81no—
355C22×C101—81no—
356C22×C101—81no—
357C22×C101—81no—
358C22×C101—161no—
359C22×C101—161no—
360C22×C101C2×#12111yescharacteristic
361C22×C101#55111yescharacteristic
362C22×C101#55111yescharacteristic
363C4×C101—21no—
364C4×C101—21no—
365C4×C101—42no—
366C4×C101—41no—
367C4×C101—41no—
368C4×C101—41no—
369C4×C101—41no—
370C4×C101—81no—
371C4×C101#52511yescharacteristic
372C4×C101#53511yescharacteristic
373C4×C101#54611yescharacteristic
374C4×C101#54611yescharacteristic
375#24524C10111yesmaximal, characteristic, direct product factor, Sylow
376C2×C101—21no—
377C2×C101—21no—
378C2×C101—41no—
379C2×C101—41no—
380C2×C101—82no—
381C2×C101—161no—
382C2×C101#241111yescharacteristic
383C2×C101#306711yescharacteristic
384C2×C101#306811yescharacteristic
385#3094C2×C10111yescharacteristic, complemented
386C2×#449C2×C10111yescharacteristic
387#2924C2×C10111yescharacteristic, complemented
388#2896C2×C10111yescharacteristic, complemented
389#2064C2×C10111yescharacteristic, complemented
390#2063C2×C10111yescharacteristic, complemented
391#2046C2×C10111yescharacteristic, complemented
392#2045C2×C10111yescharacteristic, complemented
393#1978C2×C10111yescharacteristic, complemented
394#1977C2×C10111yescharacteristic, complemented
395#1931C2×C10111yescharacteristic, complemented
396#1930C2×C10111yescharacteristic, complemented
397#1900C2×C10111yescharacteristic, complemented
398#1855C2×C10111yescharacteristic, complemented
399#1785C2×C10111yescharacteristic, complemented
400C101#2452411yescharacteristic, direct product factor, Sylow
401C22×#41C22×C10111yescharacteristic
402C22×SD16C22×C10111yescharacteristic
403C22×D8C22×C10111yescharacteristic
404C22×M16C22×C10111yescharacteristic
405C2×#121C22×C10111yescharacteristic
406C2×#117C22×C10111yescharacteristic
407#482—21no—
408#482—21no—
409#481—21no—
410#480—21no—
411#449—21no—
412#449—21no—
413#449—21no—
414#449—21no—
415#433—21no—
416#433—21no—
417#432—21no—
418#431—21no—
419C2×#108C22×C10111yescharacteristic
420C2×#108C22×C10111yescharacteristic
421#428C22×C10111yescharacteristic
422#428C22×C10111yescharacteristic
423#424C22×C10111yescharacteristic
424#424C22×C10111yescharacteristic
425#419C22×C10111yescharacteristic
426#419C22×C10111yescharacteristic
427#418C22×C10111yescharacteristic
428#418C22×C10111yescharacteristic
429#418C22×C10111yescharacteristic
430#418C22×C10111yescharacteristic
431#417—21no—
432#417—21no—
433#416—21no—
434#416—21no—
435C2×#103C22×C10111yescharacteristic
436C2×#102C22×C10111yescharacteristic
437C2×#101C22×C10111yescharacteristic
438C2×#101C22×C10111yescharacteristic
439C2×#100C22×C10111yescharacteristic
440C2×#100C22×C10111yescharacteristic
441C2×#100C22×C10111yescharacteristic
442C2×#100C22×C10111yescharacteristic
443#407C22×C10111yescharacteristic
444#407C22×C10111yescharacteristic
445C2×C22⋊C8C22×C10111yescharacteristic
446#405C22×C10111yescharacteristic
447#405C22×C10111yescharacteristic
448#343C22×C10111yescharacteristic
449#343C22×C10111yescharacteristic
450#341C22×C10111yescharacteristic
451#341C22×C10111yescharacteristic
452C2×#41—22no—
453C2×#41—22no—
454C2×#41—21no—
455C2×#41—21no—
456C2×#41—21no—
457C2×#41—21no—
458C2×#41—41no—
459C2×#41—41no—
460C22×Q8C23×C10111yescharacteristic
461C22×D4—21no—
462C22×D4—21no—
463C22×D4C23×C10111yescharacteristic
464C22×D4C23×C10111yescharacteristic
465C23×C4—21no—
466C23×C4C23×C10111yescharacteristic
467C2×SD16—22no—
468C2×SD16—21no—
469C2×SD16—21no—
470C2×SD16—41no—
471C2×D8—22no—
472C2×D8—21no—
473C2×D8—21no—
474C2×D8—41no—
475C2×M16—21no—
476C2×M16—41no—
477C2×M16—41no—
478C2×M16C23×C10111yescharacteristic
479C2×M16C23×C10111yescharacteristic
480C2×M16C23×C10111yescharacteristic
481C2×M16C23×C10111yescharacteristic
482C2×M16C23×C10111yescharacteristic
483C2×M16C23×C10111yescharacteristic
484C22×C8—21no—
485C22×C8C23×C10111yescharacteristic
486C22×C8C23×C10111yescharacteristic
487#121—21no—
488#121—21no—
489#121—21no—
490#121—21no—
491#117—21no—
492#117—21no—
493#117D4×C10111yescharacteristic
494#117D4×C10111yescharacteristic
495#117C23×C10111yescharacteristic
496#117C23×C10111yescharacteristic
497C2×C4⋊C4D4×C10111yescharacteristic
498C2×C4⋊C4D4×C10111yescharacteristic
499C2×C4⋊C4C23×C10111yescharacteristic
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C42—21no—
503#108—41no—
504#108—41no—
505#107—21no—
506#107—21no—
507#106—21no—
508#106—21no—
509C4⋊C8—21no—
510C4⋊C8—21no—
511C4⋊C8—21no—
512C4⋊C8—21no—
513#103—21no—
514#103—21no—
515#103—21no—
516#103—21no—
517#103—21no—
518#103—21no—
519#102—21no—
520#102—21no—
521#102—21no—
522#102—21no—
523#102—21no—
524#102—21no—
525#102—21no—
526#102—21no—
527#102—21no—
528#102—21no—
529#101—22no—
530#101—41no—
531#100—22no—
532#100—41no—
533#100—41no—
534#100—41no—
535C22⋊C8—21no—
536C22⋊C8—21no—
537C22⋊C8—21no—
538C22⋊C8—21no—
539C22⋊C8D4×C10111yescharacteristic
540C22⋊C8D4×C10111yescharacteristic
541C22⋊C8D4×C10111yescharacteristic
542C22⋊C8D4×C10111yescharacteristic
543#97—21no—
544#97—21no—
545C4×C8—21no—
546C4×C8—21no—
547C24—21no—
548C24—21no—
549C24#41×C10111yescharacteristic
550#41—24no—
551#41—24no—
552#41—42no—
553#41—42no—
554#41—42no—
555#41—42no—
556#41—42no—
557#41—42no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8#41×C10112yes—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—42no—
576C2×D4—42no—
577C2×D4—41no—
578C2×D4—41no—
579C2×D4—41no—
580C2×D4—41no—
581C2×D4—82no—
582C2×D4#41×C10112yes—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—41no—
594C22×C4—41no—
595C22×C4C2×D4×C10111yescharacteristic
596C22×C4C2×D4×C10111yescharacteristic
597C22×C4C2×D4×C10111yescharacteristic
598C22×C4C2×D4×C10111yescharacteristic
599C22×C4#41×C10111yescharacteristic
600C22×C4C24×C10111yescharacteristic
601SD16—42no—
602SD16—42no—
603D8—42no—
604D8—42no—
605M16—21no—
606M16—21no—
607M16—21no—
608M16—21no—
609M16—21no—
610M16—21no—
611M16—21no—
612M16—21no—
613M16—21no—
614M16—21no—
615M16—21no—
616M16—21no—
617M16—42no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—42no—
629C2×C8C2×D4×C10111yescharacteristic
630C2×C8C2×D4×C10111yescharacteristic
631C2×C8C2×D4×C10111yescharacteristic
632C2×C8C2×D4×C10111yescharacteristic
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4C2×D4×C10111yescharacteristic
638C4⋊C4C2×D4×C10111yescharacteristic
639C4⋊C4C2×D4×C10111yescharacteristic
640C4⋊C4C2×D4×C10111yescharacteristic
641C22⋊C4—21no—
642C22⋊C4—21no—
643C22⋊C4—21no—
644C22⋊C4—21no—
645C22⋊C4—41no—
646C22⋊C4—41no—
647C42—21no—
648C42—21no—
649C42—21no—
650C42—21no—
651C23—21no—
652C23—21no—
653C23—22no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—81no—
662C23—81no—
663C23—81no—
664C23—81no—
665C23#121×C10111yescharacteristic
666C23#121×C10111yescharacteristic
667C23C2×#41×C10111yescharacteristic
668Q8—22no—
669Q8—22no—
670Q8—41no—
671Q8—41no—
672D4—22no—
673D4—22no—
674D4—44no—
675D4—44no—
676D4—41no—
677D4—41no—
678D4—41no—
679D4—41no—
680D4—41no—
681D4—41no—
682D4—82no—
683D4—82no—
684C2×C4—21no—
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—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—22no—
699C2×C4—44no—
700C2×C4—44no—
701C2×C4—42no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—81no—
706C2×C4—81no—
707C2×C4#121×C10111yescharacteristic
708C2×C4#121×C10111yescharacteristic
709C2×C4C22×D4×C10111yescharacteristic
710C2×C4C22×D4×C10111yescharacteristic
711C2×C4C2×#41×C10111yescharacteristic
712C2×C4C2×#41×C10111yescharacteristic
713C2×C4H(5,𝔽2)×C10111yescharacteristic
714C2×C4H(5,𝔽2)×C10111yescharacteristic
715C8—21no—
716C8—21no—
717C8—21no—
718C8—21no—
719C8—41no—
720C8—41no—
721C8—41no—
722C8—41no—
723C8—41no—
724C8—41no—
725C22—21no—
726C22—21no—
727C22—21no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—42no—
734C22—81no—
735C22—81no—
736C22—82no—
737C22—82no—
738C22—81no—
739C22—81no—
740C22—81no—
741C22—81no—
742C22—81no—
743C22—161no—
744C22—161no—
745C22C2×#121×C10111yescharacteristic
746C22#551×C10111yescharacteristic
747C22#551×C10111yescharacteristic
748C4—21no—
749C4—21no—
750C4—42no—
751C4—41no—
752C4—41no—
753C4—41no—
754C4—41no—
755C4—81no—
756C4#525×C10111yescharacteristic
757C4#535×C10111yescharacteristic
758C4#546×C10111yescharacteristic
759C4#546×C10111yescharacteristic
760C2—21no—
761C2—21no—
762C2—41no—
763C2—41no—
764C2—82no—
765C2—161no—
766C2C101×#241111yescharacteristic
767C2C101×#306711yescharacteristic
768C2C101×#306811yescharacteristic
subgroupG/H
center, socleC22×C101C2×#121
commutator, Frattini, cosocleC22×C4C24×C101
prime radicalC2×#449×C101C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C101 ◁ C23×C4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C101×#3094C2semidirect
3. C101×#2924C2semidirect
4. C101×#2896C2semidirect
5. C101×#2064C2semidirect
6. C101×#2063C2semidirect
7. C101×#2046C2semidirect
8. C101×#2045C2semidirect
9. C101×#1978C2semidirect
10. C101×#1977C2semidirect
11. C101×#1931C2semidirect
12. C101×#1930C2semidirect
13. C101×#1900C2semidirect
14. C101×#1855C2semidirect
15. C101×#1785C2semidirect
375. #24524C101direct (N × H)
385. #3094C2×C101semidirect
387. #2924C2×C101semidirect
388. #2896C2×C101semidirect
389. #2064C2×C101semidirect
390. #2063C2×C101semidirect
391. #2046C2×C101semidirect
392. #2045C2×C101semidirect
393. #1978C2×C101semidirect
394. #1977C2×C101semidirect
395. #1931C2×C101semidirect
396. #1930C2×C101semidirect
397. #1900C2×C101semidirect
398. #1855C2×C101semidirect
399. #1785C2×C101semidirect
400. C101#24524direct (N × H)

Maximal subgroups

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

subgroupindex
C101×#30942
C2×#449×C1012
C101×#29242
C101×#28962
C101×#20642
C101×#20632
C101×#20462
C101×#20452
C101×#19782
C101×#19772
C101×#19312
C101×#19302
C101×#19002
C101×#18552
C101×#17852
#24524101