Finite Group Databasebeta

← C101×#25443 #38807594

Subgroups — C101×#25443 #38807594

Order 25856.

910 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3154C211yesmaximal, characteristic, complemented
2C2×#471×C101C211yesmaximal, characteristic, complemented
3C101×#3063C211yesmaximal, characteristic, complemented
4C101×#3062C211yesmaximal, characteristic, complemented
5C101×#3061C211yesmaximal, characteristic, complemented
6C2×#444×C101C211yesmaximal, characteristic, complemented
7C101×#2038C211yesmaximal, characteristic, complemented
8C101×#2037C211yesmaximal, characteristic, complemented
9C101×#2007C211yesmaximal, characteristic, complemented
10C101×#2006C211yesmaximal, characteristic, complemented
11C101×#1973C211yesmaximal, characteristic, complemented
12C101×#1952C211yesmaximal, characteristic, complemented
13C101×#1908C211yesmaximal, characteristic, complemented
14C101×#1907C211yesmaximal, characteristic, complemented
15C101×#1765C211yesmaximal, characteristic, complemented
16C2×#137×C101C2211yescharacteristic
17C2×#137×C101C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C101C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C101C2211yescharacteristic
20C2×#135×C101C2211yescharacteristic
21C22×SD16×C101C2211yescharacteristic
22C2×#131×C101C2211yescharacteristic
23C2×#131×C101C2211yescharacteristic
24C2×#131×C101C2211yescharacteristic
25#537×C101C2211yescharacteristic
26#537×C101C2211yescharacteristic
27#536×C101C2211yescharacteristic
28#535×C101C2211yescharacteristic
29#497×C101—21no—
30#496×C101—21no—
31#495×C101—21no—
32#492×C101—21no—
33#471×C101—24no—
34#470×C101—21no—
35#469×C101—21no—
36#468×C101—21no—
37#468×C101—21no—
38#468×C101—21no—
39#468×C101—21no—
40#467×C101—21no—
41#467×C101—21no—
42#466×C101—21no—
43#466×C101—21no—
44#465×C101—21no—
45#465×C101—21no—
46#444×C101—24no—
47C2×#108×C101C2211yescharacteristic
48#428×C101C2211yescharacteristic
49#428×C101C2211yescharacteristic
50C2×#107×C101C2211yescharacteristic
51C2×#104×C101C2211yescharacteristic
52C2×#104×C101C2211yescharacteristic
53C2×#104×C101C2211yescharacteristic
54#417×C101C2211yescharacteristic
55#417×C101C2211yescharacteristic
56#416×C101C2211yescharacteristic
57C2×#103×C101C2211yescharacteristic
58C2×#102×C101C2211yescharacteristic
59C2×#101×C101C2211yescharacteristic
60C2×#100×C101C2211yescharacteristic
61#405×C101C2211yescharacteristic
62C2×#97×C101C2211yescharacteristic
63#391×C101C2211yescharacteristic
64#390×C101C2211yescharacteristic
65#343×C101C2211yescharacteristic
66#343×C101C2211yescharacteristic
67#341×C101C2211yescharacteristic
68#339×C101C2211yescharacteristic
69C2×#41×C101C2311yescharacteristic
70C2×#41×C101C2311yescharacteristic
71C2×#41×C101C2311yescharacteristic
72C22×Q8×C101C2311yescharacteristic
73C22×D4×C101C2311yescharacteristic
74#137×C101—22no—
75#137×C101—22no—
76#137×C101—41no—
77#137×C101—41no—
78AGL(1,ℤ/8)×C101—22no—
79AGL(1,ℤ/8)×C101—22no—
80AGL(1,ℤ/8)×C101—41no—
81AGL(1,ℤ/8)×C101—41no—
82#135×C101—22no—
83#135×C101—22no—
84C2×Q16×C101—21no—
85C2×Q16×C101—21no—
86C2×Q16×C101D411yescharacteristic
87C2×SD16×C101—21no—
88C2×SD16×C101—21no—
89C2×SD16×C101—21no—
90C2×SD16×C101—21no—
91C2×SD16×C101—22no—
92C2×SD16×C101—21no—
93C2×SD16×C101—21no—
94C2×SD16×C101—22no—
95C2×SD16×C101D411yescharacteristic
96C2×SD16×C101D411yescharacteristic
97C2×D8×C101—21no—
98C2×D8×C101—21no—
99C2×D8×C101D411yescharacteristic
100#131×C101—22no—
101#131×C101—22no—
102#131×C101—22no—
103#131×C101—22no—
104#131×C101—41no—
105#131×C101—41no—
106C2×M16×C101—21no—
107C2×M16×C101—21no—
108C2×M16×C101—21no—
109C2×M16×C101C2311yescharacteristic
110C2×M16×C101C2311yescharacteristic
111C2×M16×C101C2311yescharacteristic
112C2×M16×C101C2311yescharacteristic
113C22×C8×C101—21no—
114C22×C8×C101—21no—
115C22×C8×C101—21no—
116C22×C8×C101C2311yescharacteristic
117C22×C8×C101C2311yescharacteristic
118C4⋊Q8×C101—21no—
119#127×C101—21no—
120#124×C101—21no—
121#124×C101—21no—
122#123×C101—41no—
123C22⋊Q8×C101—21no—
124C22⋊Q8×C101—21no—
125C22⋊Q8×C101—21no—
126C22⋊Q8×C101—21no—
127C22⋊Q8×C101—21no—
128C22⋊Q8×C101—21no—
129#121×C101—21no—
130#121×C101—21no—
131#121×C101—21no—
132#121×C101—21no—
133#121×C101—21no—
134#121×C101—21no—
135#121×C101—41no—
136#121×C101—41no—
137#120×C101—41no—
138#117×C101C2311yescharacteristic
139C2×C4⋊C4×C101C2311yescharacteristic
140C2×C4⋊C4×C101C2311yescharacteristic
141C2×C22⋊C4×C101—41no—
142C2×C42×C101C2311yescharacteristic
143#108×C101D414yescomplemented
144#107×C101—21no—
145#107×C101—21no—
146#107×C101—21no—
147#107×C101—21no—
148#106×C101—21no—
149#106×C101—21no—
150#104×C101—22no—
151#104×C101—22no—
152#104×C101—22no—
153#103×C101—21no—
154#103×C101—21no—
155#103×C101—21no—
156#103×C101—21no—
157#103×C101D411yescharacteristic
158#103×C101D411yescharacteristic
159#102×C101—21no—
160#102×C101—21no—
161#102×C101—21no—
162#102×C101—21no—
163#102×C101D411yescharacteristic
164#102×C101D411yescharacteristic
165#101×C101—22no—
166#100×C101—22no—
167#97×C101—22no—
168#97×C101—21no—
169C4×C8×C101—21no—
170#95×C101—41no—
171C24×C101—21no—
172#41×C101—21no—
173#41×C101—21no—
174#41×C101—21no—
175#41×C101—21no—
176#41×C101—21no—
177#41×C101—21no—
178#41×C101—21no—
179#41×C101—21no—
180#41×C101—21no—
181#41×C101—21no—
182#41×C101—21no—
183#41×C101—21no—
184C2×Q8×C101—21no—
185C2×Q8×C101—21no—
186C2×Q8×C101—21no—
187C2×Q8×C101—21no—
188C2×Q8×C101—21no—
189C2×Q8×C101—21no—
190C2×Q8×C101C2×D411yescharacteristic
191C2×Q8×C101C2×D411yescharacteristic
192C2×Q8×C101C2×D411yescharacteristic
193C2×D4×C101—21no—
194C2×D4×C101—21no—
195C2×D4×C101—21no—
196C2×D4×C101—21no—
197C2×D4×C101—21no—
198C2×D4×C101—21no—
199C2×D4×C101—21no—
200C2×D4×C101—21no—
201C2×D4×C101—21no—
202C2×D4×C101—41no—
203C2×D4×C101—41no—
204C2×D4×C101—41no—
205C2×D4×C101—41no—
206C2×D4×C101C2×D411yescharacteristic
207C2×D4×C101C2×D411yescharacteristic
208C2×D4×C101C2×D411yescharacteristic
209C22×C4×C101—21no—
210C22×C4×C101—21no—
211C22×C4×C101—21no—
212C22×C4×C101—21no—
213C22×C4×C101—21no—
214C22×C4×C101—21no—
215C22×C4×C101—21no—
216C22×C4×C101C2411yescharacteristic
217Q16×C101—22no—
218Q16×C101—42no—
219Q16×C101—42no—
220SD16×C101—22no—
221SD16×C101—22no—
222SD16×C101—42no—
223SD16×C101—42no—
224SD16×C101—42no—
225SD16×C101—42no—
226SD16×C101—42no—
227SD16×C101—42no—
228D8×C101—22no—
229D8×C101—42no—
230D8×C101—42no—
231M16×C101—21no—
232M16×C101—21no—
233M16×C101—21no—
234M16×C101—21no—
235M16×C101—21no—
236M16×C101—42no—
237M16×C101—42no—
238M16×C101—42no—
239M16×C101C2×D412yes—
240M16×C101C2×D412yes—
241M16×C101#4112yes—
242C2×C8×C101—21no—
243C2×C8×C101—21no—
244C2×C8×C101—21no—
245C2×C8×C101—21no—
246C2×C8×C101—21no—
247C2×C8×C101—21no—
248C2×C8×C101—42no—
249C2×C8×C101—42no—
250C2×C8×C101—42no—
251C2×C8×C101C2×D411yescharacteristic
252C2×C8×C101C2×D411yescharacteristic
253C2×C8×C101C2×D411yescharacteristic
254C2×C8×C101C2×D411yescharacteristic
255C2×C8×C101C2×D412yes—
256C2×C8×C101#4112yes—
257C4⋊C4×C101—21no—
258C4⋊C4×C101—21no—
259C4⋊C4×C101—21no—
260C4⋊C4×C101—21no—
261C4⋊C4×C101—41no—
262C4⋊C4×C101—41no—
263C4⋊C4×C101—41no—
264C4⋊C4×C101—41no—
265C4⋊C4×C101C2×D411yescharacteristic
266C4⋊C4×C101C2×D411yescharacteristic
267C22⋊C4×C101—21no—
268C22⋊C4×C101—41no—
269C22⋊C4×C101—41no—
270C22⋊C4×C101—41no—
271C22⋊C4×C101—41no—
272C22⋊C4×C101—41no—
273C22⋊C4×C101—41no—
274C22⋊C4×C101—41no—
275C22⋊C4×C101—41no—
276C22⋊C4×C101—82no—
277C42×C101—21no—
278C42×C101—21no—
279C42×C101—21no—
280C23×C101—21no—
281C23×C101—21no—
282C23×C101—21no—
283C23×C101—41no—
284C23×C101—41no—
285C23×C101—41no—
286C23×C101—81no—
287C23×C101—81no—
288C23×C101H(5,𝔽2)11yescharacteristic
289Q8×C101—21no—
290Q8×C101—21no—
291Q8×C101—21no—
292Q8×C101—21no—
293Q8×C101—21no—
294Q8×C101—21no—
295Q8×C101—41no—
296Q8×C101—41no—
297Q8×C101—41no—
298Q8×C101—41no—
299D4×C101—21no—
300D4×C101—21no—
301D4×C101—21no—
302D4×C101—21no—
303D4×C101—21no—
304D4×C101—21no—
305D4×C101—41no—
306D4×C101—41no—
307D4×C101—41no—
308D4×C101—41no—
309D4×C101—41no—
310D4×C101—41no—
311D4×C101—41no—
312D4×C101—41no—
313D4×C101—41no—
314D4×C101—41no—
315D4×C101—161no—
316D4×C101—161no—
317D4×C101—161no—
318D4×C101—161no—
319C2×C4×C101—21no—
320C2×C4×C101—21no—
321C2×C4×C101—21no—
322C2×C4×C101—21no—
323C2×C4×C101—21no—
324C2×C4×C101—41no—
325C2×C4×C101—41no—
326C2×C4×C101—41no—
327C2×C4×C101—41no—
328C2×C4×C101—41no—
329C2×C4×C101—41no—
330C2×C4×C101—41no—
331C2×C4×C101—41no—
332C2×C4×C101—41no—
333C2×C4×C101—41no—
334C2×C4×C101—41no—
335C2×C4×C101—41no—
336C2×C4×C101—41no—
337C2×C4×C101—41no—
338C2×C4×C101—81no—
339C2×C4×C101—81no—
340C2×C4×C101C22×D411yescharacteristic
341C2×C4×C101C22×D411yescharacteristic
342C2×C4×C101C22×D411yescharacteristic
343C2×C4×C101C2×#4111yescharacteristic
344C2×C4×C101C2×#4111yescharacteristic
345C2×C4×C101H(5,𝔽2)11yescharacteristic
346C8×C101—21no—
347C8×C101—21no—
348C8×C101—22no—
349C8×C101—22no—
350C8×C101—22no—
351C8×C101—41no—
352C8×C101#12112yes—
353C8×C101#12112yes—
354C22×C101—21no—
355C22×C101—21no—
356C22×C101—41no—
357C22×C101—41no—
358C22×C101—41no—
359C22×C101—41no—
360C22×C101—41no—
361C22×C101—41no—
362C22×C101—41no—
363C22×C101—41no—
364C22×C101—41no—
365C22×C101—82no—
366C22×C101—81no—
367C22×C101—81no—
368C22×C101—81no—
369C22×C101—161no—
370C22×C101#54011yescharacteristic
371C22×C101D4211yescharacteristic
372C22×C101#55011yescharacteristic
373C4×C101—41no—
374C4×C101—41no—
375C4×C101—41no—
376C4×C101—41no—
377C4×C101—41no—
378C4×C101—81no—
379C4×C101—81no—
380C4×C101—81no—
381C4×C101—81no—
382C4×C101C2×#12111yescharacteristic
383C4×C101#53211yescharacteristic
384C4×C101D4211yescharacteristic
385C4×C101#54611yescharacteristic
386#25443C10111yesmaximal, characteristic, direct product factor, Sylow
387C2×C101—21no—
388C2×C101—21no—
389C2×C101—81no—
390C2×C101—81no—
391C2×C101—81no—
392C2×C101—161no—
393C2×C101#242811yescharacteristic
394C2×C101#328811yescharacteristic
395C2×C101#328911yescharacteristic
396#3154C2×C10111yescharacteristic, complemented
397C2×#471C2×C10111yescharacteristic, complemented
398#3063C2×C10111yescharacteristic, complemented
399#3062C2×C10111yescharacteristic, complemented
400#3061C2×C10111yescharacteristic, complemented
401C2×#444C2×C10111yescharacteristic, complemented
402#2038C2×C10111yescharacteristic, complemented
403#2037C2×C10111yescharacteristic, complemented
404#2007C2×C10111yescharacteristic, complemented
405#2006C2×C10111yescharacteristic, complemented
406#1973C2×C10111yescharacteristic, complemented
407#1952C2×C10111yescharacteristic, complemented
408#1908C2×C10111yescharacteristic, complemented
409#1907C2×C10111yescharacteristic, complemented
410#1765C2×C10111yescharacteristic, complemented
411C101#2544311yescharacteristic, direct product factor, Sylow
412C2×#137C22×C10111yescharacteristic
413C2×#137C22×C10111yescharacteristic
414C2×AGL(1,ℤ/8)C22×C10111yescharacteristic
415C2×AGL(1,ℤ/8)C22×C10111yescharacteristic
416C2×#135C22×C10111yescharacteristic
417C22×SD16C22×C10111yescharacteristic
418C2×#131C22×C10111yescharacteristic
419C2×#131C22×C10111yescharacteristic
420C2×#131C22×C10111yescharacteristic
421#537C22×C10111yescharacteristic
422#537C22×C10111yescharacteristic
423#536C22×C10111yescharacteristic
424#535C22×C10111yescharacteristic
425#497—21no—
426#496—21no—
427#495—21no—
428#492—21no—
429#471—24no—
430#470—21no—
431#469—21no—
432#468—21no—
433#468—21no—
434#468—21no—
435#468—21no—
436#467—21no—
437#467—21no—
438#466—21no—
439#466—21no—
440#465—21no—
441#465—21no—
442#444—24no—
443C2×#108C22×C10111yescharacteristic
444#428C22×C10111yescharacteristic
445#428C22×C10111yescharacteristic
446C2×#107C22×C10111yescharacteristic
447C2×#104C22×C10111yescharacteristic
448C2×#104C22×C10111yescharacteristic
449C2×#104C22×C10111yescharacteristic
450#417C22×C10111yescharacteristic
451#417C22×C10111yescharacteristic
452#416C22×C10111yescharacteristic
453C2×#103C22×C10111yescharacteristic
454C2×#102C22×C10111yescharacteristic
455C2×#101C22×C10111yescharacteristic
456C2×#100C22×C10111yescharacteristic
457#405C22×C10111yescharacteristic
458C2×#97C22×C10111yescharacteristic
459#391C22×C10111yescharacteristic
460#390C22×C10111yescharacteristic
461#343C22×C10111yescharacteristic
462#343C22×C10111yescharacteristic
463#341C22×C10111yescharacteristic
464#339C22×C10111yescharacteristic
465C2×#41C23×C10111yescharacteristic
466C2×#41C23×C10111yescharacteristic
467C2×#41C23×C10111yescharacteristic
468C22×Q8C23×C10111yescharacteristic
469C22×D4C23×C10111yescharacteristic
470#137—22no—
471#137—22no—
472#137—41no—
473#137—41no—
474AGL(1,ℤ/8)—22no—
475AGL(1,ℤ/8)—22no—
476AGL(1,ℤ/8)—41no—
477AGL(1,ℤ/8)—41no—
478#135—22no—
479#135—22no—
480C2×Q16—21no—
481C2×Q16—21no—
482C2×Q16D4×C10111yescharacteristic
483C2×SD16—21no—
484C2×SD16—21no—
485C2×SD16—21no—
486C2×SD16—21no—
487C2×SD16—22no—
488C2×SD16—21no—
489C2×SD16—21no—
490C2×SD16—22no—
491C2×SD16D4×C10111yescharacteristic
492C2×SD16D4×C10111yescharacteristic
493C2×D8—21no—
494C2×D8—21no—
495C2×D8D4×C10111yescharacteristic
496#131—22no—
497#131—22no—
498#131—22no—
499#131—22no—
500#131—41no—
501#131—41no—
502C2×M16—21no—
503C2×M16—21no—
504C2×M16—21no—
505C2×M16C23×C10111yescharacteristic
506C2×M16C23×C10111yescharacteristic
507C2×M16C23×C10111yescharacteristic
508C2×M16C23×C10111yescharacteristic
509C22×C8—21no—
510C22×C8—21no—
511C22×C8—21no—
512C22×C8C23×C10111yescharacteristic
513C22×C8C23×C10111yescharacteristic
514C4⋊Q8—21no—
515#127—21no—
516#124—21no—
517#124—21no—
518#123—41no—
519C22⋊Q8—21no—
520C22⋊Q8—21no—
521C22⋊Q8—21no—
522C22⋊Q8—21no—
523C22⋊Q8—21no—
524C22⋊Q8—21no—
525#121—21no—
526#121—21no—
527#121—21no—
528#121—21no—
529#121—21no—
530#121—21no—
531#121—41no—
532#121—41no—
533#120—41no—
534#117C23×C10111yescharacteristic
535C2×C4⋊C4C23×C10111yescharacteristic
536C2×C4⋊C4C23×C10111yescharacteristic
537C2×C22⋊C4—41no—
538C2×C42C23×C10111yescharacteristic
539#108D4×C10114yescomplemented
540#107—21no—
541#107—21no—
542#107—21no—
543#107—21no—
544#106—21no—
545#106—21no—
546#104—22no—
547#104—22no—
548#104—22no—
549#103—21no—
550#103—21no—
551#103—21no—
552#103—21no—
553#103D4×C10111yescharacteristic
554#103D4×C10111yescharacteristic
555#102—21no—
556#102—21no—
557#102—21no—
558#102—21no—
559#102D4×C10111yescharacteristic
560#102D4×C10111yescharacteristic
561#101—22no—
562#100—22no—
563#97—22no—
564#97—21no—
565C4×C8—21no—
566#95—41no—
567C24—21no—
568#41—21no—
569#41—21no—
570#41—21no—
571#41—21no—
572#41—21no—
573#41—21no—
574#41—21no—
575#41—21no—
576#41—21no—
577#41—21no—
578#41—21no—
579#41—21no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8C2×D4×C10111yescharacteristic
587C2×Q8C2×D4×C10111yescharacteristic
588C2×Q8C2×D4×C10111yescharacteristic
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—41no—
599C2×D4—41no—
600C2×D4—41no—
601C2×D4—41no—
602C2×D4C2×D4×C10111yescharacteristic
603C2×D4C2×D4×C10111yescharacteristic
604C2×D4C2×D4×C10111yescharacteristic
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4C24×C10111yescharacteristic
613Q16—22no—
614Q16—42no—
615Q16—42no—
616SD16—22no—
617SD16—22no—
618SD16—42no—
619SD16—42no—
620SD16—42no—
621SD16—42no—
622SD16—42no—
623SD16—42no—
624D8—22no—
625D8—42no—
626D8—42no—
627M16—21no—
628M16—21no—
629M16—21no—
630M16—21no—
631M16—21no—
632M16—42no—
633M16—42no—
634M16—42no—
635M16C2×D4×C10112yes—
636M16C2×D4×C10112yes—
637M16#41×C10112yes—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—42no—
645C2×C8—42no—
646C2×C8—42no—
647C2×C8C2×D4×C10111yescharacteristic
648C2×C8C2×D4×C10111yescharacteristic
649C2×C8C2×D4×C10111yescharacteristic
650C2×C8C2×D4×C10111yescharacteristic
651C2×C8C2×D4×C10112yes—
652C2×C8#41×C10112yes—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—41no—
658C4⋊C4—41no—
659C4⋊C4—41no—
660C4⋊C4—41no—
661C4⋊C4C2×D4×C10111yescharacteristic
662C4⋊C4C2×D4×C10111yescharacteristic
663C22⋊C4—21no—
664C22⋊C4—41no—
665C22⋊C4—41no—
666C22⋊C4—41no—
667C22⋊C4—41no—
668C22⋊C4—41no—
669C22⋊C4—41no—
670C22⋊C4—41no—
671C22⋊C4—41no—
672C22⋊C4—82no—
673C42—21no—
674C42—21no—
675C42—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—81no—
683C23—81no—
684C23H(5,𝔽2)×C10111yescharacteristic
685Q8—21no—
686Q8—21no—
687Q8—21no—
688Q8—21no—
689Q8—21no—
690Q8—21no—
691Q8—41no—
692Q8—41no—
693Q8—41no—
694Q8—41no—
695D4—21no—
696D4—21no—
697D4—21no—
698D4—21no—
699D4—21no—
700D4—21no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—41no—
708D4—41no—
709D4—41no—
710D4—41no—
711D4—161no—
712D4—161no—
713D4—161no—
714D4—161no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—81no—
735C2×C4—81no—
736C2×C4C22×D4×C10111yescharacteristic
737C2×C4C22×D4×C10111yescharacteristic
738C2×C4C22×D4×C10111yescharacteristic
739C2×C4C2×#41×C10111yescharacteristic
740C2×C4C2×#41×C10111yescharacteristic
741C2×C4H(5,𝔽2)×C10111yescharacteristic
742C8—21no—
743C8—21no—
744C8—22no—
745C8—22no—
746C8—22no—
747C8—41no—
748C8#121×C10112yes—
749C8#121×C10112yes—
750C22—21no—
751C22—21no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—82no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—161no—
766C22#540×C10111yescharacteristic
767C22D42×C10111yescharacteristic
768C22#550×C10111yescharacteristic
769C4—41no—
770C4—41no—
771C4—41no—
772C4—41no—
773C4—41no—
774C4—81no—
775C4—81no—
776C4—81no—
777C4—81no—
778C4C2×#121×C10111yescharacteristic
779C4#532×C10111yescharacteristic
780C4D42×C10111yescharacteristic
781C4#546×C10111yescharacteristic
782C2—21no—
783C2—21no—
784C2—81no—
785C2—81no—
786C2—81no—
787C2—161no—
788C2C101×#242811yescharacteristic
789C2C101×#328811yescharacteristic
790C2C101×#328911yescharacteristic
subgroupG/H
center, socleC22×C101D42
commutator, Frattini, cosocleC22×C4C24×C101
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C101 ◁ C22×C4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C101×#3154C2semidirect
2. C2×#471×C101C2semidirect
3. C101×#3063C2semidirect
4. C101×#3062C2semidirect
5. C101×#3061C2semidirect
6. C2×#444×C101C2semidirect
7. C101×#2038C2semidirect
8. C101×#2037C2semidirect
9. C101×#2007C2semidirect
10. C101×#2006C2semidirect
11. C101×#1973C2semidirect
12. C101×#1952C2semidirect
13. C101×#1908C2semidirect
14. C101×#1907C2semidirect
15. C101×#1765C2semidirect
143. #108×C101D4semidirect
386. #25443C101direct (N × H)
396. #3154C2×C101semidirect
397. C2×#471C2×C101semidirect
398. #3063C2×C101semidirect
399. #3062C2×C101semidirect
400. #3061C2×C101semidirect
401. C2×#444C2×C101semidirect
402. #2038C2×C101semidirect
403. #2037C2×C101semidirect
404. #2007C2×C101semidirect
405. #2006C2×C101semidirect
406. #1973C2×C101semidirect
407. #1952C2×C101semidirect
408. #1908C2×C101semidirect
409. #1907C2×C101semidirect
410. #1765C2×C101semidirect
411. C101#25443direct (N × H)
539. #108D4×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#31542
C2×#471×C1012
C101×#30632
C101×#30622
C101×#30612
C2×#444×C1012
C101×#20382
C101×#20372
C101×#20072
C101×#20062
C101×#19732
C101×#19522
C101×#19082
C101×#19072
C101×#17652
#25443101