Finite Group Databasebeta

← C101×#19010 #38801161

Subgroups — C101×#19010 #38801161

Order 25856.

920 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3529C211yesmaximal, characteristic, complemented
2C101×#3219C211yesmaximal, characteristic, complemented
3C101×#3214C211yesmaximal, characteristic, complemented
4C101×#3180C211yesmaximal, characteristic, complemented
5C101×#1664C211yesmaximal, characteristic, complemented
6C101×#1662C211yesmaximal, characteristic, complemented
7C101×#1661C211yesmaximal, characteristic, complemented
8C101×#1659C211yesmaximal, characteristic, complemented
9C101×#1657C211yesmaximal, characteristic, complemented
10C101×#1656C211yesmaximal, characteristic, complemented
11C101×#1656C211yesmaximal, characteristic, complemented
12C101×#1655C211yesmaximal, characteristic, complemented
13C101×#1535C211yesmaximal, characteristic, complemented
14C101×#1532C211yesmaximal, characteristic, complemented
15C101×#1530C211yesmaximal, characteristic, complemented
16#563×C101—21no—
17#563×C101C2211yescharacteristic
18#562×C101—21no—
19#562×C101—21no—
20#562×C101C2211yescharacteristic
21#562×C101C2211yescharacteristic
22H(3,𝔽4)×C101C2211yescharacteristic
23#560×C101—21no—
24#560×C101—21no—
25#560×C101—21no—
26#532×C101—21no—
27#532×C101C2211yescharacteristic
28#532×C101C2211yescharacteristic, complemented
29#529×C101—21no—
30#529×C101—21no—
31#529×C101C2211yescharacteristic
32#529×C101C2211yescharacteristic
33#525×C101—21no—
34#525×C101—21no—
35#525×C101—21no—
36#501×C101C2211yescharacteristic, complemented
37#497×C101C2211yescharacteristic
38#496×C101C2211yescharacteristic
39#496×C101C2211yescharacteristic
40#496×C101C2211yescharacteristic
41#496×C101C2211yescharacteristic, complemented
42#491×C101C2211yescharacteristic, complemented
43#490×C101C2211yescharacteristic, complemented
44#490×C101C2211yescharacteristic, complemented
45#489×C101C2211yescharacteristic
46#489×C101C2211yescharacteristic
47#489×C101C2211yescharacteristic, complemented
48#466×C101—21no—
49#465×C101—21no—
50#464×C101—21no—
51#463×C101—21no—
52#461×C101—21no—
53#459×C101—21no—
54#452×C101—21no—
55#449×C101—21no—
56#449×C101—21no—
57#449×C101—21no—
58#442×C101—21no—
59#440×C101—21no—
60#432×C101C2211yescharacteristic, complemented
61#432×C101C2211yescharacteristic, complemented
62C2×#97×C101C2211yescharacteristic, complemented
63#330×C101C2211yescharacteristic, complemented
64#330×C101C2211yescharacteristic, complemented
65#330×C101C2211yescharacteristic, complemented
66#330×C101C2211yescharacteristic, complemented
67#329×C101C2211yescharacteristic
68#329×C101C2211yescharacteristic
69#329×C101C2211yescharacteristic
70#329×C101C2211yescharacteristic
71#329×C101C2211yescharacteristic
72#329×C101C2211yescharacteristic
73#329×C101C2211yescharacteristic, complemented
74#329×C101C2211yescharacteristic, complemented
75C2×#41×C101—21no—
76C2×#41×C101—21no—
77C2×#41×C101D411yescharacteristic
78C2×#41×C101D411yescharacteristic
79C23×C4×C101—21no—
80C2×Q16×C101—21no—
81C2×SD16×C101—21no—
82C2×SD16×C101—21no—
83C2×SD16×C101—21no—
84C2×SD16×C101—21no—
85C2×SD16×C101—21no—
86C2×D8×C101—21no—
87C2×D8×C101—21no—
88C2×D8×C101—21no—
89C2×D8×C101—21no—
90C22×C8×C101—21no—
91C4⋊Q8×C101—21no—
92C4⋊Q8×C101D411yescharacteristic
93C4⋊Q8×C101C2311yescharacteristic
94#127×C101—21no—
95#127×C101D411yescharacteristic
96#127×C101C2311yescharacteristic
97#126×C101—21no—
98#126×C101—21no—
99#126×C101—21no—
100#126×C101—21no—
101#126×C101—21no—
102#126×C101—21no—
103#125×C101—21no—
104#125×C101—21no—
105#125×C101C2311yescharacteristic
106#125×C101C2311yescharacteristic
107#124×C101—21no—
108#124×C101—21no—
109#124×C101—21no—
110#124×C101—21no—
111#124×C101—21no—
112#124×C101C2311yescharacteristic
113#124×C101C2311yescharacteristic
114#124×C101C2311yescharacteristic
115#124×C101C2311yescharacteristic
116#123×C101—21no—
117#123×C101—21no—
118#123×C101—21no—
119#123×C101—21no—
120#123×C101—21no—
121#123×C101—21no—
122#123×C101—21no—
123#123×C101—21no—
124#123×C101—21no—
125#123×C101—21no—
126#123×C101—21no—
127#123×C101—21no—
128C22⋊Q8×C101—21no—
129C22⋊Q8×C101—21no—
130C22⋊Q8×C101—21no—
131C22⋊Q8×C101—21no—
132C22⋊Q8×C101—21no—
133C22⋊Q8×C101—21no—
134C22⋊Q8×C101—21no—
135C22⋊Q8×C101—21no—
136C22⋊Q8×C101D411yescharacteristic
137C22⋊Q8×C101D411yescharacteristic
138#121×C101—21no—
139#121×C101—21no—
140#121×C101—21no—
141#121×C101—21no—
142#121×C101—21no—
143#121×C101—21no—
144#121×C101—21no—
145#121×C101—21no—
146#121×C101—21no—
147#121×C101—21no—
148#121×C101—21no—
149#121×C101—21no—
150#121×C101—21no—
151#121×C101—21no—
152#121×C101—21no—
153#121×C101—21no—
154#121×C101D411yescharacteristic
155#121×C101D411yescharacteristic
156#120×C101—21no—
157#120×C101—21no—
158#120×C101—21no—
159#120×C101—21no—
160#120×C101—21no—
161#120×C101—21no—
162C4×Q8×C101D411yescharacteristic
163C4×Q8×C101D411yescharacteristic
164C4×D4×C101—21no—
165C4×D4×C101—21no—
166C4×D4×C101—21no—
167C4×D4×C101—21no—
168C4×D4×C101—21no—
169C4×D4×C101—21no—
170C4×D4×C101—21no—
171C4×D4×C101—21no—
172C4×D4×C101—21no—
173C4×D4×C101—21no—
174C4×D4×C101D411yescharacteristic
175C4×D4×C101D411yescharacteristic
176#117×C101—21no—
177#117×C101—21no—
178#117×C101—21no—
179C2×C42×C101—21no—
180C2×C42×C101C2311yescharacteristic
181#107×C101—21no—
182#106×C101—21no—
183C4⋊C8×C101—21no—
184C4⋊C8×C101—21no—
185#103×C101—21no—
186#103×C101—21no—
187#103×C101—21no—
188#103×C101—21no—
189#103×C101—21no—
190#102×C101—21no—
191#102×C101—21no—
192#102×C101—21no—
193#102×C101—21no—
194#102×C101—21no—
195#102×C101—21no—
196#102×C101—21no—
197C22⋊C8×C101—21no—
198C22⋊C8×C101—21no—
199#97×C101—21no—
200#97×C101C2311yescharacteristic
201#97×C101C2311yescharacteristic
202#97×C101C2311yescharacteristic
203#97×C101C2311yescharacteristic
204#97×C101C2311yescharacteristic
205#97×C101C2311yescharacteristic
206C24×C101—21no—
207#41×C101—81no—
208#41×C101—81no—
209#41×C101—82no—
210#41×C101—81no—
211#41×C101—81no—
212C2×Q8×C101—21no—
213C2×Q8×C101—21no—
214C2×Q8×C101C2×D411yescharacteristic
215C2×Q8×C101C2×D411yescharacteristic
216C2×Q8×C101C2×D411yescharacteristic
217C2×Q8×C101C2×D411yescharacteristic
218C2×D4×C101—21no—
219C2×D4×C101—21no—
220C2×D4×C101—21no—
221C2×D4×C101—21no—
222C2×D4×C101—21no—
223C2×D4×C101—21no—
224C2×D4×C101—21no—
225C2×D4×C101—21no—
226C2×D4×C101—21no—
227C2×D4×C101—21no—
228C2×D4×C101—21no—
229C2×D4×C101—21no—
230C2×D4×C101—21no—
231C2×D4×C101—21no—
232C2×D4×C101—21no—
233C2×D4×C101—21no—
234C2×D4×C101—41no—
235C2×D4×C101C2×D411yescharacteristic
236C2×D4×C101C2×D411yescharacteristic
237C2×D4×C101C2×D411yescharacteristic
238C2×D4×C101C2×D411yescharacteristic
239C22×C4×C101—21no—
240C22×C4×C101—21no—
241C22×C4×C101—21no—
242C22×C4×C101—21no—
243C22×C4×C101—21no—
244C22×C4×C101—21no—
245C22×C4×C101—21no—
246C22×C4×C101—21no—
247C22×C4×C101—21no—
248C22×C4×C101—41no—
249C22×C4×C101—82no—
250C22×C4×C101C2×D411yescharacteristic
251C22×C4×C101C2×D411yescharacteristic
252C22×C4×C101C2×D411yescharacteristic
253Q16×C101—81no—
254SD16×C101—42no—
255SD16×C101—81no—
256SD16×C101—81no—
257SD16×C101—81no—
258SD16×C101—81no—
259D8×C101—42no—
260D8×C101—81no—
261D8×C101—81no—
262D8×C101—81no—
263C2×C8×C101—21no—
264C2×C8×C101—21no—
265C2×C8×C101—21no—
266C2×C8×C101—21no—
267C2×C8×C101—21no—
268C2×C8×C101—21no—
269C2×C8×C101—42no—
270C4⋊C4×C101—21no—
271C4⋊C4×C101—21no—
272C4⋊C4×C101—21no—
273C4⋊C4×C101—21no—
274C4⋊C4×C101—21no—
275C4⋊C4×C101—21no—
276C4⋊C4×C101—21no—
277C4⋊C4×C101—21no—
278C4⋊C4×C101—21no—
279C4⋊C4×C101—21no—
280C4⋊C4×C101—21no—
281C4⋊C4×C101—21no—
282C4⋊C4×C101—21no—
283C4⋊C4×C101—21no—
284C4⋊C4×C101—21no—
285C4⋊C4×C101—21no—
286C4⋊C4×C101—21no—
287C4⋊C4×C101—21no—
288C4⋊C4×C101C2×D411yescharacteristic
289C4⋊C4×C101C2×D411yescharacteristic
290C4⋊C4×C101C2×D411yescharacteristic
291C4⋊C4×C101C2×D411yescharacteristic
292C22⋊C4×C101—21no—
293C22⋊C4×C101—21no—
294C22⋊C4×C101—21no—
295C22⋊C4×C101—21no—
296C22⋊C4×C101—21no—
297C22⋊C4×C101—21no—
298C22⋊C4×C101—21no—
299C22⋊C4×C101—21no—
300C22⋊C4×C101—21no—
301C22⋊C4×C101—21no—
302C22⋊C4×C101—21no—
303C22⋊C4×C101—21no—
304C22⋊C4×C101—21no—
305C22⋊C4×C101—21no—
306C22⋊C4×C101—21no—
307C22⋊C4×C101—21no—
308C22⋊C4×C101—21no—
309C22⋊C4×C101—21no—
310C22⋊C4×C101—21no—
311C22⋊C4×C101—21no—
312C22⋊C4×C101—21no—
313C22⋊C4×C101—21no—
314C22⋊C4×C101—21no—
315C22⋊C4×C101—21no—
316C22⋊C4×C101—41no—
317C22⋊C4×C101—41no—
318C42×C101—21no—
319C42×C101—21no—
320C42×C101—21no—
321C42×C101—21no—
322C42×C101C2×D411yescharacteristic
323C42×C101C2×D411yescharacteristic
324C42×C101C2×D411yescharacteristic
325C42×C101C2411yescharacteristic
326C23×C101—21no—
327C23×C101—21no—
328C23×C101—21no—
329C23×C101—21no—
330C23×C101—41no—
331C23×C101—81no—
332C23×C101—81no—
333C23×C101—81no—
334C23×C101#12011yescharacteristic
335Q8×C101—41no—
336Q8×C101—41no—
337Q8×C101—41no—
338Q8×C101—41no—
339Q8×C101—41no—
340Q8×C101—41no—
341Q8×C101—81no—
342D4×C101—41no—
343D4×C101—41no—
344D4×C101—41no—
345D4×C101—41no—
346D4×C101—41no—
347D4×C101—41no—
348D4×C101—41no—
349D4×C101—41no—
350D4×C101—41no—
351D4×C101—41no—
352D4×C101—81no—
353D4×C101—81no—
354D4×C101—81no—
355D4×C101—81no—
356D4×C101—81no—
357D4×C101—81no—
358D4×C101—81no—
359D4×C101—81no—
360D4×C101—81no—
361D4×C101—81no—
362D4×C101—81no—
363D4×C101—81no—
364D4×C101—81no—
365D4×C101—82no—
366C2×C4×C101—21no—
367C2×C4×C101—21no—
368C2×C4×C101—21no—
369C2×C4×C101—21no—
370C2×C4×C101—21no—
371C2×C4×C101—21no—
372C2×C4×C101—21no—
373C2×C4×C101—21no—
374C2×C4×C101—41no—
375C2×C4×C101—41no—
376C2×C4×C101—41no—
377C2×C4×C101—42no—
378C2×C4×C101—42no—
379C2×C4×C101—42no—
380C2×C4×C101—42no—
381C2×C4×C101—41no—
382C2×C4×C101—82no—
383C2×C4×C101—81no—
384C2×C4×C101—81no—
385C2×C4×C101—81no—
386C2×C4×C101—81no—
387C2×C4×C101—81no—
388C2×C4×C101#12011yescharacteristic
389C2×C4×C101#12011yescharacteristic
390C2×C4×C101#12011yescharacteristic
391C2×C4×C101C22×D411yescharacteristic
392C2×C4×C101C22×D411yescharacteristic
393C2×C4×C101C22×D411yescharacteristic
394C8×C101—22no—
395C8×C101—41no—
396C8×C101—41no—
397C8×C101—41no—
398C8×C101—41no—
399C8×C101—41no—
400C22×C101—21no—
401C22×C101—21no—
402C22×C101—21no—
403C22×C101—41no—
404C22×C101—41no—
405C22×C101—41no—
406C22×C101—41no—
407C22×C101—41no—
408C22×C101—41no—
409C22×C101—41no—
410C22×C101—41no—
411C22×C101—41no—
412C22×C101—41no—
413C22×C101—41no—
414C22×C101—41no—
415C22×C101—84no—
416C22×C101—81no—
417C22×C101—81no—
418C22×C101—81no—
419C22×C101C2×#12011yescharacteristic
420C4×C101—21no—
421C4×C101—21no—
422C4×C101—21no—
423C4×C101—21no—
424C4×C101—21no—
425C4×C101—21no—
426C4×C101—41no—
427C4×C101—41no—
428C4×C101—41no—
429C4×C101—41no—
430C4×C101—41no—
431C4×C101—41no—
432C4×C101—41no—
433C4×C101—41no—
434C4×C101—81no—
435#19010C10111yesmaximal, characteristic, direct product factor, Sylow
436C2×C101—41no—
437C2×C101—81no—
438C2×C101—81no—
439C2×C101—81no—
440C2×C101—81no—
441C2×C101—161no—
442C2×C101#301811yescharacteristic
443C2×C101#301911yescharacteristic
444C2×C101#302111yescharacteristic
445#3529C2×C10111yescharacteristic, complemented
446#3219C2×C10111yescharacteristic, complemented
447#3214C2×C10111yescharacteristic, complemented
448#3180C2×C10111yescharacteristic, complemented
449#1664C2×C10111yescharacteristic, complemented
450#1662C2×C10111yescharacteristic, complemented
451#1661C2×C10111yescharacteristic, complemented
452#1659C2×C10111yescharacteristic, complemented
453#1657C2×C10111yescharacteristic, complemented
454#1656C2×C10111yescharacteristic, complemented
455#1656C2×C10111yescharacteristic, complemented
456#1655C2×C10111yescharacteristic, complemented
457#1535C2×C10111yescharacteristic, complemented
458#1532C2×C10111yescharacteristic, complemented
459#1530C2×C10111yescharacteristic, complemented
460C101#1901011yescharacteristic, direct product factor, Sylow
461#563—21no—
462#563C22×C10111yescharacteristic
463#562—21no—
464#562—21no—
465#562C22×C10111yescharacteristic
466#562C22×C10111yescharacteristic
467H(3,𝔽4)C22×C10111yescharacteristic
468#560—21no—
469#560—21no—
470#560—21no—
471#532—21no—
472#532C22×C10111yescharacteristic
473#532C22×C10111yescharacteristic, complemented
474#529—21no—
475#529—21no—
476#529C22×C10111yescharacteristic
477#529C22×C10111yescharacteristic
478#525—21no—
479#525—21no—
480#525—21no—
481#501C22×C10111yescharacteristic, complemented
482#497C22×C10111yescharacteristic
483#496C22×C10111yescharacteristic
484#496C22×C10111yescharacteristic
485#496C22×C10111yescharacteristic
486#496C22×C10111yescharacteristic, complemented
487#491C22×C10111yescharacteristic, complemented
488#490C22×C10111yescharacteristic, complemented
489#490C22×C10111yescharacteristic, complemented
490#489C22×C10111yescharacteristic
491#489C22×C10111yescharacteristic
492#489C22×C10111yescharacteristic, complemented
493#466—21no—
494#465—21no—
495#464—21no—
496#463—21no—
497#461—21no—
498#459—21no—
499#452—21no—
500#449—21no—
501#449—21no—
502#449—21no—
503#442—21no—
504#440—21no—
505#432C22×C10111yescharacteristic, complemented
506#432C22×C10111yescharacteristic, complemented
507C2×#97C22×C10111yescharacteristic, complemented
508#330C22×C10111yescharacteristic, complemented
509#330C22×C10111yescharacteristic, complemented
510#330C22×C10111yescharacteristic, complemented
511#330C22×C10111yescharacteristic, complemented
512#329C22×C10111yescharacteristic
513#329C22×C10111yescharacteristic
514#329C22×C10111yescharacteristic
515#329C22×C10111yescharacteristic
516#329C22×C10111yescharacteristic
517#329C22×C10111yescharacteristic
518#329C22×C10111yescharacteristic, complemented
519#329C22×C10111yescharacteristic, complemented
520C2×#41—21no—
521C2×#41—21no—
522C2×#41D4×C10111yescharacteristic
523C2×#41D4×C10111yescharacteristic
524C23×C4—21no—
525C2×Q16—21no—
526C2×SD16—21no—
527C2×SD16—21no—
528C2×SD16—21no—
529C2×SD16—21no—
530C2×SD16—21no—
531C2×D8—21no—
532C2×D8—21no—
533C2×D8—21no—
534C2×D8—21no—
535C22×C8—21no—
536C4⋊Q8—21no—
537C4⋊Q8D4×C10111yescharacteristic
538C4⋊Q8C23×C10111yescharacteristic
539#127—21no—
540#127D4×C10111yescharacteristic
541#127C23×C10111yescharacteristic
542#126—21no—
543#126—21no—
544#126—21no—
545#126—21no—
546#126—21no—
547#126—21no—
548#125—21no—
549#125—21no—
550#125C23×C10111yescharacteristic
551#125C23×C10111yescharacteristic
552#124—21no—
553#124—21no—
554#124—21no—
555#124—21no—
556#124—21no—
557#124C23×C10111yescharacteristic
558#124C23×C10111yescharacteristic
559#124C23×C10111yescharacteristic
560#124C23×C10111yescharacteristic
561#123—21no—
562#123—21no—
563#123—21no—
564#123—21no—
565#123—21no—
566#123—21no—
567#123—21no—
568#123—21no—
569#123—21no—
570#123—21no—
571#123—21no—
572#123—21no—
573C22⋊Q8—21no—
574C22⋊Q8—21no—
575C22⋊Q8—21no—
576C22⋊Q8—21no—
577C22⋊Q8—21no—
578C22⋊Q8—21no—
579C22⋊Q8—21no—
580C22⋊Q8—21no—
581C22⋊Q8D4×C10111yescharacteristic
582C22⋊Q8D4×C10111yescharacteristic
583#121—21no—
584#121—21no—
585#121—21no—
586#121—21no—
587#121—21no—
588#121—21no—
589#121—21no—
590#121—21no—
591#121—21no—
592#121—21no—
593#121—21no—
594#121—21no—
595#121—21no—
596#121—21no—
597#121—21no—
598#121—21no—
599#121D4×C10111yescharacteristic
600#121D4×C10111yescharacteristic
601#120—21no—
602#120—21no—
603#120—21no—
604#120—21no—
605#120—21no—
606#120—21no—
607C4×Q8D4×C10111yescharacteristic
608C4×Q8D4×C10111yescharacteristic
609C4×D4—21no—
610C4×D4—21no—
611C4×D4—21no—
612C4×D4—21no—
613C4×D4—21no—
614C4×D4—21no—
615C4×D4—21no—
616C4×D4—21no—
617C4×D4—21no—
618C4×D4—21no—
619C4×D4D4×C10111yescharacteristic
620C4×D4D4×C10111yescharacteristic
621#117—21no—
622#117—21no—
623#117—21no—
624C2×C42—21no—
625C2×C42C23×C10111yescharacteristic
626#107—21no—
627#106—21no—
628C4⋊C8—21no—
629C4⋊C8—21no—
630#103—21no—
631#103—21no—
632#103—21no—
633#103—21no—
634#103—21no—
635#102—21no—
636#102—21no—
637#102—21no—
638#102—21no—
639#102—21no—
640#102—21no—
641#102—21no—
642C22⋊C8—21no—
643C22⋊C8—21no—
644#97—21no—
645#97C23×C10111yescharacteristic
646#97C23×C10111yescharacteristic
647#97C23×C10111yescharacteristic
648#97C23×C10111yescharacteristic
649#97C23×C10111yescharacteristic
650#97C23×C10111yescharacteristic
651C24—21no—
652#41—81no—
653#41—81no—
654#41—82no—
655#41—81no—
656#41—81no—
657C2×Q8—21no—
658C2×Q8—21no—
659C2×Q8C2×D4×C10111yescharacteristic
660C2×Q8C2×D4×C10111yescharacteristic
661C2×Q8C2×D4×C10111yescharacteristic
662C2×Q8C2×D4×C10111yescharacteristic
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—41no—
680C2×D4C2×D4×C10111yescharacteristic
681C2×D4C2×D4×C10111yescharacteristic
682C2×D4C2×D4×C10111yescharacteristic
683C2×D4C2×D4×C10111yescharacteristic
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—41no—
694C22×C4—82no—
695C22×C4C2×D4×C10111yescharacteristic
696C22×C4C2×D4×C10111yescharacteristic
697C22×C4C2×D4×C10111yescharacteristic
698Q16—81no—
699SD16—42no—
700SD16—81no—
701SD16—81no—
702SD16—81no—
703SD16—81no—
704D8—42no—
705D8—81no—
706D8—81no—
707D8—81no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—21no—
714C2×C8—42no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4C2×D4×C10111yescharacteristic
734C4⋊C4C2×D4×C10111yescharacteristic
735C4⋊C4C2×D4×C10111yescharacteristic
736C4⋊C4C2×D4×C10111yescharacteristic
737C22⋊C4—21no—
738C22⋊C4—21no—
739C22⋊C4—21no—
740C22⋊C4—21no—
741C22⋊C4—21no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—21no—
745C22⋊C4—21no—
746C22⋊C4—21no—
747C22⋊C4—21no—
748C22⋊C4—21no—
749C22⋊C4—21no—
750C22⋊C4—21no—
751C22⋊C4—21no—
752C22⋊C4—21no—
753C22⋊C4—21no—
754C22⋊C4—21no—
755C22⋊C4—21no—
756C22⋊C4—21no—
757C22⋊C4—21no—
758C22⋊C4—21no—
759C22⋊C4—21no—
760C22⋊C4—21no—
761C22⋊C4—41no—
762C22⋊C4—41no—
763C42—21no—
764C42—21no—
765C42—21no—
766C42—21no—
767C42C2×D4×C10111yescharacteristic
768C42C2×D4×C10111yescharacteristic
769C42C2×D4×C10111yescharacteristic
770C42C24×C10111yescharacteristic
771C23—21no—
772C23—21no—
773C23—21no—
774C23—21no—
775C23—41no—
776C23—81no—
777C23—81no—
778C23—81no—
779C23#120×C10111yescharacteristic
780Q8—41no—
781Q8—41no—
782Q8—41no—
783Q8—41no—
784Q8—41no—
785Q8—41no—
786Q8—81no—
787D4—41no—
788D4—41no—
789D4—41no—
790D4—41no—
791D4—41no—
792D4—41no—
793D4—41no—
794D4—41no—
795D4—41no—
796D4—41no—
797D4—81no—
798D4—81no—
799D4—81no—
800D4—81no—
801D4—81no—
802D4—81no—
803D4—81no—
804D4—81no—
805D4—81no—
806D4—81no—
807D4—81no—
808D4—81no—
809D4—81no—
810D4—82no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—41no—
827C2×C4—82no—
828C2×C4—81no—
829C2×C4—81no—
830C2×C4—81no—
831C2×C4—81no—
832C2×C4—81no—
833C2×C4#120×C10111yescharacteristic
834C2×C4#120×C10111yescharacteristic
835C2×C4#120×C10111yescharacteristic
836C2×C4C22×D4×C10111yescharacteristic
837C2×C4C22×D4×C10111yescharacteristic
838C2×C4C22×D4×C10111yescharacteristic
839C8—22no—
840C8—41no—
841C8—41no—
842C8—41no—
843C8—41no—
844C8—41no—
845C22—21no—
846C22—21no—
847C22—21no—
848C22—41no—
849C22—41no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—84no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22C2×#120×C10111yescharacteristic
865C4—21no—
866C4—21no—
867C4—21no—
868C4—21no—
869C4—21no—
870C4—21no—
871C4—41no—
872C4—41no—
873C4—41no—
874C4—41no—
875C4—41no—
876C4—41no—
877C4—41no—
878C4—41no—
879C4—81no—
880C2—41no—
881C2—81no—
882C2—81no—
883C2—81no—
884C2—81no—
885C2—161no—
886C2C101×#301811yescharacteristic
887C2C101×#301911yescharacteristic
888C2C101×#302111yescharacteristic
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×#3529C2semidirect
2. C101×#3219C2semidirect
3. C101×#3214C2semidirect
4. C101×#3180C2semidirect
5. C101×#1664C2semidirect
6. C101×#1662C2semidirect
7. C101×#1661C2semidirect
8. C101×#1659C2semidirect
9. C101×#1657C2semidirect
10. C101×#1656C2semidirect
11. C101×#1656C2semidirect
12. C101×#1655C2semidirect
13. C101×#1535C2semidirect
14. C101×#1532C2semidirect
15. C101×#1530C2semidirect
28. #532×C101C22semidirect
36. #501×C101C22semidirect
41. #496×C101C22semidirect
42. #491×C101C22semidirect
43. #490×C101C22semidirect
44. #490×C101C22semidirect
47. #489×C101C22semidirect
60. #432×C101C22semidirect
61. #432×C101C22semidirect
62. C2×#97×C101C22semidirect
63. #330×C101C22semidirect
64. #330×C101C22semidirect
65. #330×C101C22semidirect
66. #330×C101C22semidirect
73. #329×C101C22semidirect
74. #329×C101C22semidirect
435. #19010C101direct (N × H)
445. #3529C2×C101semidirect
446. #3219C2×C101semidirect
447. #3214C2×C101semidirect
448. #3180C2×C101semidirect
449. #1664C2×C101semidirect
450. #1662C2×C101semidirect
451. #1661C2×C101semidirect
452. #1659C2×C101semidirect
453. #1657C2×C101semidirect
454. #1656C2×C101semidirect
455. #1656C2×C101semidirect
456. #1655C2×C101semidirect
457. #1535C2×C101semidirect
458. #1532C2×C101semidirect
459. #1530C2×C101semidirect
460. C101#19010direct (N × H)
473. #532C22×C101semidirect
481. #501C22×C101semidirect
486. #496C22×C101semidirect
487. #491C22×C101semidirect
488. #490C22×C101semidirect
489. #490C22×C101semidirect
492. #489C22×C101semidirect
505. #432C22×C101semidirect
506. #432C22×C101semidirect
507. C2×#97C22×C101semidirect
508. #330C22×C101semidirect
509. #330C22×C101semidirect
510. #330C22×C101semidirect
511. #330C22×C101semidirect
518. #329C22×C101semidirect
519. #329C22×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#35292
C101×#32192
C101×#32142
C101×#31802
C101×#16642
C101×#16622
C101×#16612
C101×#16592
C101×#16572
C101×#16562
C101×#16552
C101×#15352
C101×#15322
C101×#15302
#19010101