Finite Group Databasebeta

← C101×#24467 #38806618

Subgroups — C101×#24467 #38806618

Order 25856.

1486 conjugacy classes of subgroups.

The subgroup lattice has 1068 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3488C211yesmaximal, characteristic
2C101×#3056C211yesmaximal, characteristic, complemented
3C2×#455×C101C211yesmaximal, characteristic, complemented
4C101×#3007C211yesmaximal, characteristic, complemented
5C22×#104×C101C211yesmaximal, characteristic, complemented
6C101×#2850C211yesmaximal, characteristic, complemented
7C101×#2040C211yesmaximal, characteristic, complemented
8C101×#2037C211yesmaximal, characteristic, complemented
9C101×#2007C211yesmaximal, characteristic, complemented
10C101×#2004C211yesmaximal, characteristic, complemented
11C101×#1900C211yesmaximal, characteristic, complemented
12C101×#1896C211yesmaximal, characteristic, complemented
13C101×#1882C211yesmaximal, characteristic, complemented
14C101×#1860C211yesmaximal, characteristic, complemented
15C101×#1792C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C101C2211yescharacteristic
17C22×#41×C101C2211yescharacteristic
18C2×#137×C101C2211yescharacteristic
19C2×#137×C101C2211yescharacteristic, complemented
20C2×#137×C101C2211yescharacteristic, complemented
21C22×M16×C101C2211yescharacteristic, complemented
22#550×C101—21no—
23#548×C101—21no—
24#546×C101—21no—
25#546×C101—22no—
26D42×C101—22no—
27D42×C101—21no—
28#537×C101—21no—
29#537×C101C2211yescharacteristic
30#535×C101—21no—
31#535×C101C2211yescharacteristic
32C2×#124×C101C2211yescharacteristic, complemented
33#525×C101—21no—
34#525×C101C2211yescharacteristic
35C2×C22⋊Q8×C101C2211yescharacteristic, complemented
36C2×#121×C101—21no—
37C2×#121×C101C2211yescharacteristic
38#520×C101C2211yescharacteristic
39C22×C42×C101C2211yescharacteristic, complemented
40#470×C101—21no—
41#468×C101—21no—
42#467×C101—21no—
43#465×C101—21no—
44#455×C101—24no—
45#452×C101—21no—
46#452×C101—21no—
47#451×C101—21no—
48#450×C101—21no—
49#428×C101C2211yescharacteristic, complemented
50C2×#104×C101—24no—
51C2×#104×C101C2211yescharacteristic
52C2×#104×C101C2211yescharacteristic
53C2×#104×C101C2211yescharacteristic, complemented
54C2×#104×C101C2211yescharacteristic, complemented
55C2×#104×C101C2211yescharacteristic, complemented
56C2×#104×C101C2211yescharacteristic, complemented
57#419×C101C2211yescharacteristic, complemented
58#417×C101C2211yescharacteristic
59#417×C101C2211yescharacteristic, complemented
60#417×C101C2211yescharacteristic, complemented
61C2×#100×C101C2211yescharacteristic, complemented
62C2×#100×C101C2211yescharacteristic, complemented
63#407×C101C2211yescharacteristic, complemented
64#391×C101C2211yescharacteristic, complemented
65#390×C101C2211yescharacteristic, complemented
66#388×C101—22no—
67#386×C101—22no—
68#382×C101C2211yescharacteristic, complemented
69#343×C101C2211yescharacteristic, complemented
70#343×C101C2211yescharacteristic, complemented
71#339×C101C2211yescharacteristic, complemented
72#339×C101C2211yescharacteristic, complemented
73H(5,𝔽2)×C101—22no—
74H(5,𝔽2)×C101—22no—
75H(5,𝔽2)×C101—41no—
76H(5,𝔽2)×C101—41no—
77C2×#41×C101—21no—
78C2×#41×C101—21no—
79C2×#41×C101—21no—
80C2×#41×C101—21no—
81C2×#41×C101—22no—
82C2×#41×C101—22no—
83C2×#41×C101—41no—
84C2×#41×C101—41no—
85C2×#41×C101D411yescharacteristic
86C2×#41×C101D411yescharacteristic
87C2×#41×C101C2311yescharacteristic
88C2×#41×C101C2311yescharacteristic
89C2×#41×C101C2311yescharacteristic
90C22×Q8×C101D411yescharacteristic
91C22×Q8×C101C2311yescharacteristic
92C22×D4×C101—21no—
93C22×D4×C101—22no—
94C22×D4×C101—22no—
95C22×D4×C101—21no—
96C22×D4×C101—21no—
97C22×D4×C101D411yescharacteristic
98C22×D4×C101D412yes—
99C22×D4×C101C2311yescharacteristic
100C23×C4×C101—21no—
101C23×C4×C101—21no—
102C23×C4×C101C2311yescharacteristic
103#137×C101—22no—
104#137×C101—22no—
105#137×C101—22no—
106#137×C101—41no—
107#137×C101—41no—
108#137×C101—41no—
109C2×Q16×C101—21no—
110C2×Q16×C101—21no—
111C2×Q16×C101—21no—
112C2×SD16×C101—21no—
113C2×SD16×C101—21no—
114C2×SD16×C101—21no—
115C2×M16×C101—21no—
116C2×M16×C101—22no—
117C2×M16×C101—41no—
118C2×M16×C101C2311yescharacteristic
119C2×M16×C101C2311yescharacteristic
120C2×M16×C101C2311yescharacteristic
121C2×M16×C101C2311yescharacteristic
122C22×C8×C101—21no—
123#127×C101—22no—
124#127×C101—21no—
125#124×C101—22no—
126#124×C101—21no—
127#124×C101—22no—
128#124×C101—41no—
129#123×C101—22no—
130#123×C101—21no—
131C22⋊Q8×C101—22no—
132C22⋊Q8×C101—21no—
133C22⋊Q8×C101—21no—
134C22⋊Q8×C101—21no—
135C22⋊Q8×C101—21no—
136C22⋊Q8×C101—21no—
137C22⋊Q8×C101—21no—
138C22⋊Q8×C101D411yescharacteristic
139C22⋊Q8×C101D411yescharacteristic
140#121×C101—22no—
141#121×C101—22no—
142#121×C101—22no—
143#121×C101—22no—
144#121×C101—22no—
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—22no—
152#121×C101—21no—
153#121×C101—21no—
154#121×C101D411yescharacteristic
155#121×C101D411yescharacteristic
156#120×C101—22no—
157#120×C101—22no—
158#120×C101—22no—
159#120×C101—21no—
160#120×C101—22no—
161C4×Q8×C101—21no—
162C4×D4×C101—22no—
163C4×D4×C101—22no—
164C4×D4×C101—21no—
165C4×D4×C101—22no—
166C4×D4×C101—21no—
167C4×D4×C101—21no—
168#117×C101—21no—
169#117×C101C2311yescharacteristic
170C2×C4⋊C4×C101—21no—
171C2×C4⋊C4×C101—21no—
172C2×C4⋊C4×C101C2311yescharacteristic
173C2×C4⋊C4×C101C2311yescharacteristic
174C2×C22⋊C4×C101—22no—
175C2×C22⋊C4×C101—21no—
176C2×C22⋊C4×C101—22no—
177C2×C22⋊C4×C101—22no—
178C2×C22⋊C4×C101D412yes—
179C2×C42×C101—22no—
180C2×C42×C101—21no—
181C2×C42×C101—41no—
182C2×C42×C101C2311yescharacteristic
183C2×C42×C101C2311yescharacteristic
184#107×C101—21no—
185#106×C101—21no—
186#104×C101—22no—
187#104×C101—22no—
188#104×C101—22no—
189#104×C101—22no—
190#104×C101—41no—
191#104×C101D414yescomplemented
192#103×C101—21no—
193#103×C101—21no—
194#103×C101—21no—
195#103×C101—21no—
196#103×C101—21no—
197#102×C101—21no—
198#102×C101—21no—
199#102×C101—21no—
200#100×C101—22no—
201#100×C101—41no—
202C22⋊C8×C101—21no—
203C22⋊C8×C101—21no—
204#95×C101—22no—
205#95×C101—22no—
206C24×C101—22no—
207C24×C101—21no—
208C24×C101C2×D411yescharacteristic
209C24×C101C2×D412yes—
210#41×C101—21no—
211#41×C101—21no—
212#41×C101—22no—
213#41×C101—22no—
214#41×C101—21no—
215#41×C101—21no—
216#41×C101—21no—
217#41×C101—21no—
218#41×C101—21no—
219#41×C101—21no—
220#41×C101—21no—
221#41×C101—21no—
222#41×C101—42no—
223#41×C101—42no—
224#41×C101—41no—
225#41×C101—41no—
226#41×C101—42no—
227#41×C101—42no—
228#41×C101—42no—
229#41×C101—42no—
230#41×C101—42no—
231#41×C101—42no—
232#41×C101C2×D412yes—
233#41×C101#4112yes—
234C2×Q8×C101—21no—
235C2×Q8×C101—22no—
236C2×Q8×C101—21no—
237C2×Q8×C101—21no—
238C2×Q8×C101—21no—
239C2×Q8×C101—21no—
240C2×Q8×C101—21no—
241C2×Q8×C101—21no—
242C2×Q8×C101—41no—
243C2×Q8×C101C2×D411yescharacteristic
244C2×Q8×C101C2×D411yescharacteristic
245C2×Q8×C101C2×D411yescharacteristic
246C2×D4×C101—21no—
247C2×D4×C101—22no—
248C2×D4×C101—22no—
249C2×D4×C101—22no—
250C2×D4×C101—22no—
251C2×D4×C101—21no—
252C2×D4×C101—21no—
253C2×D4×C101—21no—
254C2×D4×C101—21no—
255C2×D4×C101—21no—
256C2×D4×C101—22no—
257C2×D4×C101—22no—
258C2×D4×C101—22no—
259C2×D4×C101—21no—
260C2×D4×C101—22no—
261C2×D4×C101—21no—
262C2×D4×C101—21no—
263C2×D4×C101—21no—
264C2×D4×C101—21no—
265C2×D4×C101—21no—
266C2×D4×C101—21no—
267C2×D4×C101—21no—
268C2×D4×C101—41no—
269C2×D4×C101—42no—
270C2×D4×C101—42no—
271C2×D4×C101—42no—
272C2×D4×C101—42no—
273C2×D4×C101—44no—
274C2×D4×C101—44no—
275C2×D4×C101—42no—
276C2×D4×C101—42no—
277C2×D4×C101—44no—
278C2×D4×C101—84no—
279C2×D4×C101C2×D411yescharacteristic
280C2×D4×C101C2×D411yescharacteristic
281C2×D4×C101C2×D411yescharacteristic
282C22×C4×C101—21no—
283C22×C4×C101—21no—
284C22×C4×C101—21no—
285C22×C4×C101—21no—
286C22×C4×C101—21no—
287C22×C4×C101—22no—
288C22×C4×C101—21no—
289C22×C4×C101—21no—
290C22×C4×C101—21no—
291C22×C4×C101—22no—
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—42no—
299C22×C4×C101—42no—
300C22×C4×C101—42no—
301C22×C4×C101—42no—
302C22×C4×C101—42no—
303C22×C4×C101C2×D411yescharacteristic
304C22×C4×C101C2×D411yescharacteristic
305C22×C4×C101C2×D411yescharacteristic
306C22×C4×C101C2×D411yescharacteristic
307C22×C4×C101C2×D411yescharacteristic
308C22×C4×C101C2×D412yes—
309C22×C4×C101C2411yescharacteristic
310Q16×C101—42no—
311Q16×C101—42no—
312Q16×C101—42no—
313SD16×C101—42no—
314SD16×C101—42no—
315SD16×C101—42no—
316M16×C101—21no—
317M16×C101—21no—
318M16×C101—21no—
319M16×C101—21no—
320M16×C101—21no—
321M16×C101—21no—
322M16×C101—21no—
323M16×C101—42no—
324M16×C101C2×D412yescomplemented
325C2×C8×C101—21no—
326C2×C8×C101—21no—
327C2×C8×C101—21no—
328C2×C8×C101—21no—
329C2×C8×C101—42no—
330C4⋊C4×C101—22no—
331C4⋊C4×C101—22no—
332C4⋊C4×C101—21no—
333C4⋊C4×C101—21no—
334C4⋊C4×C101—21no—
335C4⋊C4×C101—21no—
336C4⋊C4×C101—21no—
337C4⋊C4×C101—21no—
338C4⋊C4×C101—41no—
339C4⋊C4×C101—41no—
340C4⋊C4×C101C2×D411yescharacteristic
341C4⋊C4×C101C2×D411yescharacteristic
342C22⋊C4×C101—22no—
343C22⋊C4×C101—22no—
344C22⋊C4×C101—22no—
345C22⋊C4×C101—22no—
346C22⋊C4×C101—22no—
347C22⋊C4×C101—21no—
348C22⋊C4×C101—21no—
349C22⋊C4×C101—21no—
350C22⋊C4×C101—21no—
351C22⋊C4×C101—22no—
352C22⋊C4×C101—22no—
353C22⋊C4×C101—21no—
354C22⋊C4×C101—44no—
355C22⋊C4×C101—44no—
356C22⋊C4×C101—41no—
357C22⋊C4×C101—41no—
358C42×C101—22no—
359C42×C101—21no—
360C42×C101—21no—
361C42×C101—21no—
362C42×C101—21no—
363C42×C101—42no—
364C42×C101C2×D412yescomplemented
365C23×C101—21no—
366C23×C101—21no—
367C23×C101—21no—
368C23×C101—22no—
369C23×C101—22no—
370C23×C101—21no—
371C23×C101—21no—
372C23×C101—22no—
373C23×C101—22no—
374C23×C101—41no—
375C23×C101—42no—
376C23×C101—44no—
377C23×C101—42no—
378C23×C101—42no—
379C23×C101—42no—
380C23×C101—81no—
381C23×C101—82no—
382C23×C101—82no—
383C23×C101#12011yescharacteristic
384C23×C101#12011yescharacteristic
385C23×C101C22×D411yescharacteristic
386Q8×C101—21no—
387Q8×C101—21no—
388Q8×C101—21no—
389Q8×C101—21no—
390Q8×C101—21no—
391Q8×C101—42no—
392Q8×C101—41no—
393Q8×C101—41no—
394Q8×C101—41no—
395Q8×C101—41no—
396Q8×C101#12112yes—
397D4×C101—22no—
398D4×C101—22no—
399D4×C101—21no—
400D4×C101—21no—
401D4×C101—21no—
402D4×C101—21no—
403D4×C101—21no—
404D4×C101—42no—
405D4×C101—42no—
406D4×C101—44no—
407D4×C101—42no—
408D4×C101—44no—
409D4×C101—41no—
410D4×C101—41no—
411D4×C101—41no—
412D4×C101—41no—
413D4×C101—44no—
414D4×C101—42no—
415D4×C101—41no—
416D4×C101—41no—
417D4×C101—41no—
418D4×C101—41no—
419D4×C101—81no—
420D4×C101—82no—
421D4×C101—82no—
422D4×C101—82no—
423D4×C101—82no—
424D4×C101#12112yes—
425C2×C4×C101—21no—
426C2×C4×C101—21no—
427C2×C4×C101—21no—
428C2×C4×C101—21no—
429C2×C4×C101—21no—
430C2×C4×C101—21no—
431C2×C4×C101—21no—
432C2×C4×C101—21no—
433C2×C4×C101—21no—
434C2×C4×C101—22no—
435C2×C4×C101—21no—
436C2×C4×C101—21no—
437C2×C4×C101—22no—
438C2×C4×C101—22no—
439C2×C4×C101—21no—
440C2×C4×C101—22no—
441C2×C4×C101—21no—
442C2×C4×C101—21no—
443C2×C4×C101—21no—
444C2×C4×C101—22no—
445C2×C4×C101—42no—
446C2×C4×C101—42no—
447C2×C4×C101—42no—
448C2×C4×C101—44no—
449C2×C4×C101—41no—
450C2×C4×C101—41no—
451C2×C4×C101—41no—
452C2×C4×C101—48no—
453C2×C4×C101—41no—
454C2×C4×C101—41no—
455C2×C4×C101—41no—
456C2×C4×C101—41no—
457C2×C4×C101—41no—
458C2×C4×C101—42no—
459C2×C4×C101—42no—
460C2×C4×C101—41no—
461C2×C4×C101—41no—
462C2×C4×C101—41no—
463C2×C4×C101—41no—
464C2×C4×C101—82no—
465C2×C4×C101#12011yescharacteristic
466C2×C4×C101#12011yescharacteristic
467C2×C4×C101C22×D411yescharacteristic
468C2×C4×C101C22×D411yescharacteristic
469C2×C4×C101C22×D411yescharacteristic
470C2×C4×C101C2×#4111yescharacteristic
471C2×C4×C101H(5,𝔽2)11yescharacteristic
472C2×C4×C101H(5,𝔽2)11yescharacteristic
473C8×C101—22no—
474C8×C101—41no—
475C8×C101—41no—
476C8×C101—41no—
477C22×C101—21no—
478C22×C101—21no—
479C22×C101—21no—
480C22×C101—21no—
481C22×C101—21no—
482C22×C101—22no—
483C22×C101—21no—
484C22×C101—21no—
485C22×C101—42no—
486C22×C101—42no—
487C22×C101—41no—
488C22×C101—41no—
489C22×C101—41no—
490C22×C101—41no—
491C22×C101—42no—
492C22×C101—42no—
493C22×C101—41no—
494C22×C101—41no—
495C22×C101—41no—
496C22×C101—42no—
497C22×C101—41no—
498C22×C101—84no—
499C22×C101—82no—
500C22×C101—82no—
501C22×C101—164no—
502C22×C101#45512yescomplemented
503C22×C101C2×#12011yescharacteristic
504C22×C101D4211yescharacteristic
505C22×C101#54611yescharacteristic
506C4×C101—21no—
507C4×C101—21no—
508C4×C101—22no—
509C4×C101—42no—
510C4×C101—42no—
511C4×C101—41no—
512C4×C101—41no—
513C4×C101—42no—
514C4×C101—41no—
515C4×C101—41no—
516C4×C101—81no—
517C4×C101—81no—
518C4×C101C2×#12111yescharacteristic
519C4×C101#53411yescharacteristic
520C4×C101D4211yescharacteristic
521C4×C101#54611yescharacteristic
522#24467C10111yesmaximal, characteristic, direct product factor, Sylow
523C2×C101—21no—
524C2×C101—21no—
525C2×C101—22no—
526C2×C101—41no—
527C2×C101—42no—
528C2×C101—81no—
529C2×C101—82no—
530C2×C101—81no—
531C2×C101#241011yescharacteristic
532C2×C101C2×#45511yescharacteristic
533C2×C101#301811yescharacteristic
534#3488C2×C10111yescharacteristic
535#3056C2×C10111yescharacteristic, complemented
536C2×#455C2×C10111yescharacteristic, complemented
537#3007C2×C10111yescharacteristic, complemented
538C22×#104C2×C10111yescharacteristic, complemented
539#2850C2×C10111yescharacteristic, complemented
540#2040C2×C10111yescharacteristic, complemented
541#2037C2×C10111yescharacteristic, complemented
542#2007C2×C10111yescharacteristic, complemented
543#2004C2×C10111yescharacteristic, complemented
544#1900C2×C10111yescharacteristic, complemented
545#1896C2×C10111yescharacteristic, complemented
546#1882C2×C10111yescharacteristic, complemented
547#1860C2×C10111yescharacteristic, complemented
548#1792C2×C10111yescharacteristic, complemented
549C101#2446711yescharacteristic, direct product factor, Sylow
550C2×H(5,𝔽2)C22×C10111yescharacteristic
551C22×#41C22×C10111yescharacteristic
552C2×#137C22×C10111yescharacteristic
553C2×#137C22×C10111yescharacteristic, complemented
554C2×#137C22×C10111yescharacteristic, complemented
555C22×M16C22×C10111yescharacteristic, complemented
556#550—21no—
557#548—21no—
558#546—21no—
559#546—22no—
560D42—22no—
561D42—21no—
562#537—21no—
563#537C22×C10111yescharacteristic
564#535—21no—
565#535C22×C10111yescharacteristic
566C2×#124C22×C10111yescharacteristic, complemented
567#525—21no—
568#525C22×C10111yescharacteristic
569C2×C22⋊Q8C22×C10111yescharacteristic, complemented
570C2×#121—21no—
571C2×#121C22×C10111yescharacteristic
572#520C22×C10111yescharacteristic
573C22×C42C22×C10111yescharacteristic, complemented
574#470—21no—
575#468—21no—
576#467—21no—
577#465—21no—
578#455—24no—
579#452—21no—
580#452—21no—
581#451—21no—
582#450—21no—
583#428C22×C10111yescharacteristic, complemented
584C2×#104—24no—
585C2×#104C22×C10111yescharacteristic
586C2×#104C22×C10111yescharacteristic
587C2×#104C22×C10111yescharacteristic, complemented
588C2×#104C22×C10111yescharacteristic, complemented
589C2×#104C22×C10111yescharacteristic, complemented
590C2×#104C22×C10111yescharacteristic, complemented
591#419C22×C10111yescharacteristic, complemented
592#417C22×C10111yescharacteristic
593#417C22×C10111yescharacteristic, complemented
594#417C22×C10111yescharacteristic, complemented
595C2×#100C22×C10111yescharacteristic, complemented
596C2×#100C22×C10111yescharacteristic, complemented
597#407C22×C10111yescharacteristic, complemented
598#391C22×C10111yescharacteristic, complemented
599#390C22×C10111yescharacteristic, complemented
600#388—22no—
601#386—22no—
602#382C22×C10111yescharacteristic, complemented
603#343C22×C10111yescharacteristic, complemented
604#343C22×C10111yescharacteristic, complemented
605#339C22×C10111yescharacteristic, complemented
606#339C22×C10111yescharacteristic, complemented
607H(5,𝔽2)—22no—
608H(5,𝔽2)—22no—
609H(5,𝔽2)—41no—
610H(5,𝔽2)—41no—
611C2×#41—21no—
612C2×#41—21no—
613C2×#41—21no—
614C2×#41—21no—
615C2×#41—22no—
616C2×#41—22no—
617C2×#41—41no—
618C2×#41—41no—
619C2×#41D4×C10111yescharacteristic
620C2×#41D4×C10111yescharacteristic
621C2×#41C23×C10111yescharacteristic
622C2×#41C23×C10111yescharacteristic
623C2×#41C23×C10111yescharacteristic
624C22×Q8D4×C10111yescharacteristic
625C22×Q8C23×C10111yescharacteristic
626C22×D4—21no—
627C22×D4—22no—
628C22×D4—22no—
629C22×D4—21no—
630C22×D4—21no—
631C22×D4D4×C10111yescharacteristic
632C22×D4D4×C10112yes—
633C22×D4C23×C10111yescharacteristic
634C23×C4—21no—
635C23×C4—21no—
636C23×C4C23×C10111yescharacteristic
637#137—22no—
638#137—22no—
639#137—22no—
640#137—41no—
641#137—41no—
642#137—41no—
643C2×Q16—21no—
644C2×Q16—21no—
645C2×Q16—21no—
646C2×SD16—21no—
647C2×SD16—21no—
648C2×SD16—21no—
649C2×M16—21no—
650C2×M16—22no—
651C2×M16—41no—
652C2×M16C23×C10111yescharacteristic
653C2×M16C23×C10111yescharacteristic
654C2×M16C23×C10111yescharacteristic
655C2×M16C23×C10111yescharacteristic
656C22×C8—21no—
657#127—22no—
658#127—21no—
659#124—22no—
660#124—21no—
661#124—22no—
662#124—41no—
663#123—22no—
664#123—21no—
665C22⋊Q8—22no—
666C22⋊Q8—21no—
667C22⋊Q8—21no—
668C22⋊Q8—21no—
669C22⋊Q8—21no—
670C22⋊Q8—21no—
671C22⋊Q8—21no—
672C22⋊Q8D4×C10111yescharacteristic
673C22⋊Q8D4×C10111yescharacteristic
674#121—22no—
675#121—22no—
676#121—22no—
677#121—22no—
678#121—22no—
679#121—21no—
680#121—21no—
681#121—21no—
682#121—21no—
683#121—21no—
684#121—21no—
685#121—22no—
686#121—21no—
687#121—21no—
688#121D4×C10111yescharacteristic
689#121D4×C10111yescharacteristic
690#120—22no—
691#120—22no—
692#120—22no—
693#120—21no—
694#120—22no—
695C4×Q8—21no—
696C4×D4—22no—
697C4×D4—22no—
698C4×D4—21no—
699C4×D4—22no—
700C4×D4—21no—
701C4×D4—21no—
702#117—21no—
703#117C23×C10111yescharacteristic
704C2×C4⋊C4—21no—
705C2×C4⋊C4—21no—
706C2×C4⋊C4C23×C10111yescharacteristic
707C2×C4⋊C4C23×C10111yescharacteristic
708C2×C22⋊C4—22no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—22no—
711C2×C22⋊C4—22no—
712C2×C22⋊C4D4×C10112yes—
713C2×C42—22no—
714C2×C42—21no—
715C2×C42—41no—
716C2×C42C23×C10111yescharacteristic
717C2×C42C23×C10111yescharacteristic
718#107—21no—
719#106—21no—
720#104—22no—
721#104—22no—
722#104—22no—
723#104—22no—
724#104—41no—
725#104D4×C10114yescomplemented
726#103—21no—
727#103—21no—
728#103—21no—
729#103—21no—
730#103—21no—
731#102—21no—
732#102—21no—
733#102—21no—
734#100—22no—
735#100—41no—
736C22⋊C8—21no—
737C22⋊C8—21no—
738#95—22no—
739#95—22no—
740C24—22no—
741C24—21no—
742C24C2×D4×C10111yescharacteristic
743C24C2×D4×C10112yes—
744#41—21no—
745#41—21no—
746#41—22no—
747#41—22no—
748#41—21no—
749#41—21no—
750#41—21no—
751#41—21no—
752#41—21no—
753#41—21no—
754#41—21no—
755#41—21no—
756#41—42no—
757#41—42no—
758#41—41no—
759#41—41no—
760#41—42no—
761#41—42no—
762#41—42no—
763#41—42no—
764#41—42no—
765#41—42no—
766#41C2×D4×C10112yes—
767#41#41×C10112yes—
768C2×Q8—21no—
769C2×Q8—22no—
770C2×Q8—21no—
771C2×Q8—21no—
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—21no—
775C2×Q8—21no—
776C2×Q8—41no—
777C2×Q8C2×D4×C10111yescharacteristic
778C2×Q8C2×D4×C10111yescharacteristic
779C2×Q8C2×D4×C10111yescharacteristic
780C2×D4—21no—
781C2×D4—22no—
782C2×D4—22no—
783C2×D4—22no—
784C2×D4—22no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—22no—
791C2×D4—22no—
792C2×D4—22no—
793C2×D4—21no—
794C2×D4—22no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—41no—
803C2×D4—42no—
804C2×D4—42no—
805C2×D4—42no—
806C2×D4—42no—
807C2×D4—44no—
808C2×D4—44no—
809C2×D4—42no—
810C2×D4—42no—
811C2×D4—44no—
812C2×D4—84no—
813C2×D4C2×D4×C10111yescharacteristic
814C2×D4C2×D4×C10111yescharacteristic
815C2×D4C2×D4×C10111yescharacteristic
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—22no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—22no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—42no—
833C22×C4—42no—
834C22×C4—42no—
835C22×C4—42no—
836C22×C4—42no—
837C22×C4C2×D4×C10111yescharacteristic
838C22×C4C2×D4×C10111yescharacteristic
839C22×C4C2×D4×C10111yescharacteristic
840C22×C4C2×D4×C10111yescharacteristic
841C22×C4C2×D4×C10111yescharacteristic
842C22×C4C2×D4×C10112yes—
843C22×C4C24×C10111yescharacteristic
844Q16—42no—
845Q16—42no—
846Q16—42no—
847SD16—42no—
848SD16—42no—
849SD16—42no—
850M16—21no—
851M16—21no—
852M16—21no—
853M16—21no—
854M16—21no—
855M16—21no—
856M16—21no—
857M16—42no—
858M16C2×D4×C10112yescomplemented
859C2×C8—21no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—21no—
863C2×C8—42no—
864C4⋊C4—22no—
865C4⋊C4—22no—
866C4⋊C4—21no—
867C4⋊C4—21no—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—21no—
871C4⋊C4—21no—
872C4⋊C4—41no—
873C4⋊C4—41no—
874C4⋊C4C2×D4×C10111yescharacteristic
875C4⋊C4C2×D4×C10111yescharacteristic
876C22⋊C4—22no—
877C22⋊C4—22no—
878C22⋊C4—22no—
879C22⋊C4—22no—
880C22⋊C4—22no—
881C22⋊C4—21no—
882C22⋊C4—21no—
883C22⋊C4—21no—
884C22⋊C4—21no—
885C22⋊C4—22no—
886C22⋊C4—22no—
887C22⋊C4—21no—
888C22⋊C4—44no—
889C22⋊C4—44no—
890C22⋊C4—41no—
891C22⋊C4—41no—
892C42—22no—
893C42—21no—
894C42—21no—
895C42—21no—
896C42—21no—
897C42—42no—
898C42C2×D4×C10112yescomplemented
899C23—22no—
900C23—21no—
901C23—21no—
902C23—21no—
903C23—22no—
904C23—21no—
905C23—21no—
906C23—22no—
907C23—22no—
908C23—41no—
909C23—42no—
910C23—44no—
911C23—42no—
912C23—42no—
913C23—42no—
914C23—81no—
915C23—82no—
916C23—82no—
917C23#120×C10111yescharacteristic
918C23#120×C10111yescharacteristic
919C23C22×D4×C10111yescharacteristic
920Q8—21no—
921Q8—21no—
922Q8—21no—
923Q8—21no—
924Q8—21no—
925Q8—42no—
926Q8—41no—
927Q8—41no—
928Q8—41no—
929Q8—41no—
930Q8#121×C10112yes—
931D4—22no—
932D4—22no—
933D4—21no—
934D4—21no—
935D4—21no—
936D4—21no—
937D4—21no—
938D4—42no—
939D4—42no—
940D4—44no—
941D4—42no—
942D4—44no—
943D4—44no—
944D4—42no—
945D4—41no—
946D4—41no—
947D4—41no—
948D4—41no—
949D4—41no—
950D4—41no—
951D4—41no—
952D4—41no—
953D4—82no—
954D4—81no—
955D4—82no—
956D4—82no—
957D4—82no—
958D4#121×C10112yes—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—22no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—21no—
974C2×C4—22no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—22no—
979C2×C4—42no—
980C2×C4—42no—
981C2×C4—42no—
982C2×C4—44no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—48no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—42no—
993C2×C4—42no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—82no—
999C2×C4#120×C10111yescharacteristic
1000C2×C4#120×C10111yescharacteristic
1001C2×C4C22×D4×C10111yescharacteristic
1002C2×C4C22×D4×C10111yescharacteristic
1003C2×C4C22×D4×C10111yescharacteristic
1004C2×C4C2×#41×C10111yescharacteristic
1005C2×C4H(5,𝔽2)×C10111yescharacteristic
1006C2×C4H(5,𝔽2)×C10111yescharacteristic
1007C8—22no—
1008C8—41no—
1009C8—41no—
1010C8—41no—
1011C22—21no—
1012C22—21no—
1013C22—21no—
1014C22—21no—
1015C22—21no—
1016C22—22no—
1017C22—21no—
1018C22—21no—
1019C22—42no—
1020C22—42no—
1021C22—41no—
1022C22—41no—
1023C22—41no—
1024C22—41no—
1025C22—42no—
1026C22—42no—
1027C22—41no—
1028C22—41no—
1029C22—41no—
1030C22—42no—
1031C22—41no—
1032C22—84no—
1033C22—82no—
1034C22—82no—
1035C22—164no—
1036C22#455×C10112yescomplemented
1037C22C2×#120×C10111yescharacteristic
1038C22D42×C10111yescharacteristic
1039C22#546×C10111yescharacteristic
1040C4—21no—
1041C4—21no—
1042C4—22no—
1043C4—42no—
1044C4—42no—
1045C4—41no—
1046C4—41no—
1047C4—42no—
1048C4—41no—
1049C4—41no—
1050C4—81no—
1051C4—81no—
1052C4C2×#121×C10111yescharacteristic
1053C4#534×C10111yescharacteristic
1054C4D42×C10111yescharacteristic
1055C4#546×C10111yescharacteristic
1056C2—21no—
1057C2—22no—
1058C2—21no—
1059C2—41no—
1060C2—42no—
1061C2—81no—
1062C2—82no—
1063C2—81no—
1064C2C101×#241011yescharacteristic
1065C2C2×#455×C10111yescharacteristic
1066C2C101×#301811yescharacteristic
subgroupG/H
center, socleC22×C101C2×#120
commutator, Frattini, cosocleC22×C4C24×C101
prime radicalC101×#3488C2
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
2. C101×#3056C2semidirect
3. C2×#455×C101C2semidirect
4. C101×#3007C2semidirect
5. C22×#104×C101C2semidirect
6. C101×#2850C2semidirect
7. C101×#2040C2semidirect
8. C101×#2037C2semidirect
9. C101×#2007C2semidirect
10. C101×#2004C2semidirect
11. C101×#1900C2semidirect
12. C101×#1896C2semidirect
13. C101×#1882C2semidirect
14. C101×#1860C2semidirect
15. C101×#1792C2semidirect
19. C2×#137×C101C22semidirect
20. C2×#137×C101C22semidirect
21. C22×M16×C101C22semidirect
32. C2×#124×C101C22semidirect
35. C2×C22⋊Q8×C101C22semidirect
39. C22×C42×C101C22semidirect
49. #428×C101C22semidirect
53. C2×#104×C101C22semidirect
54. C2×#104×C101C22semidirect
55. C2×#104×C101C22semidirect
56. C2×#104×C101C22semidirect
57. #419×C101C22semidirect
59. #417×C101C22semidirect
60. #417×C101C22semidirect
61. C2×#100×C101C22semidirect
62. C2×#100×C101C22semidirect
63. #407×C101C22semidirect
64. #391×C101C22semidirect
65. #390×C101C22semidirect
68. #382×C101C22semidirect
69. #343×C101C22semidirect
70. #343×C101C22semidirect
71. #339×C101C22semidirect
72. #339×C101C22semidirect
191. #104×C101D4semidirect
324. M16×C101C2×D4semidirect
364. C42×C101C2×D4semidirect
502. C22×C101#455semidirect
522. #24467C101direct (N × H)
535. #3056C2×C101semidirect
536. C2×#455C2×C101semidirect
537. #3007C2×C101semidirect
538. C22×#104C2×C101semidirect
539. #2850C2×C101semidirect
540. #2040C2×C101semidirect
541. #2037C2×C101semidirect
542. #2007C2×C101semidirect
543. #2004C2×C101semidirect
544. #1900C2×C101semidirect
545. #1896C2×C101semidirect
546. #1882C2×C101semidirect
547. #1860C2×C101semidirect
548. #1792C2×C101semidirect
549. C101#24467direct (N × H)
553. C2×#137C22×C101semidirect
554. C2×#137C22×C101semidirect
555. C22×M16C22×C101semidirect
566. C2×#124C22×C101semidirect
569. C2×C22⋊Q8C22×C101semidirect
573. C22×C42C22×C101semidirect
583. #428C22×C101semidirect
587. C2×#104C22×C101semidirect
588. C2×#104C22×C101semidirect
589. C2×#104C22×C101semidirect
590. C2×#104C22×C101semidirect
591. #419C22×C101semidirect
593. #417C22×C101semidirect
594. #417C22×C101semidirect
595. C2×#100C22×C101semidirect
596. C2×#100C22×C101semidirect
597. #407C22×C101semidirect
598. #391C22×C101semidirect
599. #390C22×C101semidirect
602. #382C22×C101semidirect
603. #343C22×C101semidirect
604. #343C22×C101semidirect
605. #339C22×C101semidirect
606. #339C22×C101semidirect
725. #104D4×C101semidirect
858. M16C2×D4×C101semidirect
898. C42C2×D4×C101semidirect
1036. C22#455×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#34882
C101×#30562
C2×#455×C1012
C101×#30072
C22×#104×C1012
C101×#28502
C101×#20402
C101×#20372
C101×#20072
C101×#20042
C101×#19002
C101×#18962
C101×#18822
C101×#18602
C101×#17922
#24467101