Finite Group Databasebeta

← C101×#24662 #38806813

Subgroups — C101×#24662 #38806813

Order 25856.

970 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#459×C101C211yesmaximal, characteristic, complemented
2C2×#433×C101C211yesmaximal, characteristic, complemented
3C101×#2619C211yesmaximal, characteristic, complemented
4C101×#2324C211yesmaximal, characteristic, complemented
5C101×#2034C211yesmaximal, characteristic, complemented
6C101×#2033C211yesmaximal, characteristic, complemented
7C101×#1999C211yesmaximal, characteristic, complemented
8C101×#1999C211yesmaximal, characteristic, complemented
9C101×#1982C211yesmaximal, characteristic, complemented
10C101×#1972C211yesmaximal, characteristic, complemented
11C101×#1970C211yesmaximal, characteristic, complemented
12C101×#1949C211yesmaximal, characteristic, complemented
13C101×#1936C211yesmaximal, characteristic, complemented
14C101×#1934C211yesmaximal, characteristic, complemented
15C101×#1804C211yesmaximal, characteristic, complemented
16C22×D8×C101C2211yescharacteristic
17C22×D8×C101C2211yescharacteristic
18C2×#127×C101C2211yescharacteristic
19C2×#121×C101C2211yescharacteristic
20C2×#121×C101C2211yescharacteristic
21C2×#121×C101C2211yescharacteristic
22C2×C4×D4×C101C2211yescharacteristic
23C2×#117×C101C2211yescharacteristic
24#459×C101—24no—
25#433×C101—24no—
26C2×#107×C101C2211yescharacteristic
27C2×#106×C101C2211yescharacteristic
28C2×C4⋊C8×C101C2211yescharacteristic
29C2×C4⋊C8×C101C2211yescharacteristic
30C2×#102×C101C2211yescharacteristic
31C2×#102×C101C2211yescharacteristic
32C2×#102×C101C2211yescharacteristic
33C2×#102×C101C2211yescharacteristic
34C2×#102×C101C2211yescharacteristic
35C2×#102×C101C2211yescharacteristic
36C2×#102×C101C2211yescharacteristic
37C2×#102×C101C2211yescharacteristic
38C2×C22⋊C8×C101C2211yescharacteristic
39C2×C22⋊C8×C101C2211yescharacteristic
40C2×#97×C101C2211yescharacteristic
41C2×C4×C8×C101C2211yescharacteristic
42#394×C101—21no—
43#394×C101—21no—
44#392×C101—21no—
45#392×C101—21no—
46#390×C101—21no—
47#390×C101C2211yescharacteristic
48#390×C101C2211yescharacteristic
49#390×C101C2211yescharacteristic
50#389×C101C2211yescharacteristic
51#388×C101—21no—
52#386×C101—21no—
53#385×C101—21no—
54#382×C101C2211yescharacteristic
55#380×C101C2211yescharacteristic
56C4×C4⋊C4×C101C2211yescharacteristic
57#340×C101C2211yescharacteristic
58#340×C101C2211yescharacteristic
59#340×C101C2211yescharacteristic
60#340×C101C2211yescharacteristic
61C22×D4×C101—21no—
62C22×D4×C101—21no—
63C22×D4×C101—21no—
64C22×D4×C101—21no—
65C22×D4×C101—21no—
66C22×D4×C101C2311yescharacteristic
67C22×D4×C101C2311yescharacteristic
68C22×D4×C101C2311yescharacteristic
69C23×C4×C101—21no—
70C23×C4×C101C2311yescharacteristic
71C2×D8×C101—22no—
72C2×D8×C101—22no—
73C2×D8×C101—22no—
74C2×D8×C101—22no—
75C2×D8×C101—41no—
76C2×D8×C101—41no—
77C22×C8×C101C2311yescharacteristic
78C22×C8×C101C2311yescharacteristic
79C22×C8×C101C2311yescharacteristic
80C22×C8×C101C2311yescharacteristic
81#127×C101—22no—
82#127×C101—22no—
83#121×C101—22no—
84#121×C101—22no—
85#121×C101—41no—
86#121×C101—41no—
87#121×C101—41no—
88#121×C101—41no—
89C4×D4×C101—22no—
90C4×D4×C101—22no—
91#117×C101—22no—
92#117×C101—22no—
93C2×C4⋊C4×C101—21no—
94C2×C4⋊C4×C101D411yescharacteristic
95C2×C4⋊C4×C101D411yescharacteristic
96C2×C4⋊C4×C101C2311yescharacteristic
97C2×C4⋊C4×C101C2311yescharacteristic
98C2×C4⋊C4×C101C2311yescharacteristic
99C2×C4⋊C4×C101C2311yescharacteristic
100C2×C4⋊C4×C101C2311yescharacteristic
101C2×C22⋊C4×C101—21no—
102C2×C22⋊C4×C101—21no—
103C2×C22⋊C4×C101—21no—
104C2×C22⋊C4×C101—21no—
105C2×C22⋊C4×C101—21no—
106C2×C22⋊C4×C101—21no—
107C2×C22⋊C4×C101—21no—
108C2×C22⋊C4×C101—21no—
109C2×C22⋊C4×C101—21no—
110C2×C22⋊C4×C101—21no—
111C2×C22⋊C4×C101—21no—
112C2×C22⋊C4×C101D411yescharacteristic
113C2×C22⋊C4×C101D411yescharacteristic
114C2×C42×C101—21no—
115C2×C42×C101C2311yescharacteristic
116C2×C42×C101C2311yescharacteristic
117#107×C101—41no—
118#106×C101—41no—
119C4⋊C8×C101—22no—
120C4⋊C8×C101D414yescomplemented
121#102×C101—22no—
122#102×C101—22no—
123#102×C101—22no—
124#102×C101—22no—
125#102×C101—41no—
126#102×C101—41no—
127#102×C101—41no—
128#102×C101—41no—
129C22⋊C8×C101—22no—
130C22⋊C8×C101—22no—
131#97×C101—22no—
132C4×C8×C101—22no—
133#95×C101—21no—
134#95×C101—21no—
135#95×C101—21no—
136#95×C101—21no—
137#95×C101—21no—
138C24×C101—21no—
139C24×C101—21no—
140C24×C101—21no—
141C24×C101C2×D411yescharacteristic
142C2×D4×C101—24no—
143C2×D4×C101—21no—
144C2×D4×C101—21no—
145C2×D4×C101—21no—
146C2×D4×C101—21no—
147C2×D4×C101—21no—
148C2×D4×C101—21no—
149C2×D4×C101—21no—
150C2×D4×C101—21no—
151C2×D4×C101—21no—
152C2×D4×C101—21no—
153C2×D4×C101—21no—
154C2×D4×C101—21no—
155C2×D4×C101—21no—
156C2×D4×C101—21no—
157C2×D4×C101—21no—
158C2×D4×C101—21no—
159C2×D4×C101—21no—
160C2×D4×C101—42no—
161C2×D4×C101—42no—
162C2×D4×C101—42no—
163C2×D4×C101—42no—
164C2×D4×C101—81no—
165C2×D4×C101—81no—
166C2×D4×C101—81no—
167C2×D4×C101—81no—
168C2×D4×C101—81no—
169C2×D4×C101—81no—
170C2×D4×C101—81no—
171C2×D4×C101—81no—
172C2×D4×C101—81no—
173C2×D4×C101—81no—
174C2×D4×C101#4112yes—
175C22×C4×C101—21no—
176C22×C4×C101—21no—
177C22×C4×C101—21no—
178C22×C4×C101—21no—
179C22×C4×C101—21no—
180C22×C4×C101—21no—
181C22×C4×C101—21no—
182C22×C4×C101—21no—
183C22×C4×C101—21no—
184C22×C4×C101—21no—
185C22×C4×C101—21no—
186C22×C4×C101—42no—
187C22×C4×C101—81no—
188C22×C4×C101—81no—
189C22×C4×C101C2×D411yescharacteristic
190C22×C4×C101C2×D411yescharacteristic
191C22×C4×C101C2×D411yescharacteristic
192C22×C4×C101C2×D411yescharacteristic
193C22×C4×C101C2×D411yescharacteristic
194C22×C4×C101C2411yescharacteristic
195D8×C101—44no—
196D8×C101—44no—
197C2×C8×C101—21no—
198C2×C8×C101—21no—
199C2×C8×C101—21no—
200C2×C8×C101—21no—
201C2×C8×C101—21no—
202C2×C8×C101—21no—
203C2×C8×C101—21no—
204C2×C8×C101—21no—
205C2×C8×C101—21no—
206C2×C8×C101—21no—
207C2×C8×C101C2×D412yes—
208C2×C8×C101C2×D412yes—
209C4⋊C4×C101—22no—
210C4⋊C4×C101—22no—
211C4⋊C4×C101—21no—
212C4⋊C4×C101—21no—
213C4⋊C4×C101—21no—
214C4⋊C4×C101—21no—
215C4⋊C4×C101—21no—
216C4⋊C4×C101—21no—
217C4⋊C4×C101—21no—
218C4⋊C4×C101—21no—
219C4⋊C4×C101—21no—
220C4⋊C4×C101—81no—
221C4⋊C4×C101#4112yes—
222C22⋊C4×C101—24no—
223C22⋊C4×C101—22no—
224C22⋊C4×C101—22no—
225C22⋊C4×C101—42no—
226C22⋊C4×C101—42no—
227C22⋊C4×C101—42no—
228C22⋊C4×C101—81no—
229C22⋊C4×C101—81no—
230C22⋊C4×C101—81no—
231C22⋊C4×C101—81no—
232C22⋊C4×C101—81no—
233C22⋊C4×C101—81no—
234C22⋊C4×C101—81no—
235C42×C101—21no—
236C42×C101—21no—
237C42×C101—81no—
238C42×C101C2×D412yes—
239C42×C101#4112yes—
240C23×C101—21no—
241C23×C101—22no—
242C23×C101—21no—
243C23×C101—21no—
244C23×C101—21no—
245C23×C101—21no—
246C23×C101—21no—
247C23×C101—21no—
248C23×C101—41no—
249C23×C101—41no—
250C23×C101—41no—
251C23×C101—41no—
252C23×C101—41no—
253C23×C101—41no—
254C23×C101—41no—
255C23×C101—41no—
256C23×C101—41no—
257C23×C101—41no—
258C23×C101—41no—
259C23×C101—41no—
260C23×C101—41no—
261C23×C101—41no—
262C23×C101—41no—
263C23×C101—41no—
264C23×C101—41no—
265C23×C101—41no—
266C23×C101—41no—
267C23×C101—41no—
268C23×C101C22×D411yescharacteristic
269D4×C101—22no—
270D4×C101—22no—
271D4×C101—41no—
272D4×C101—41no—
273D4×C101—41no—
274D4×C101—41no—
275D4×C101—41no—
276D4×C101—41no—
277D4×C101—41no—
278D4×C101—41no—
279D4×C101—41no—
280D4×C101—41no—
281D4×C101—84no—
282D4×C101—84no—
283D4×C101—84no—
284D4×C101—84no—
285D4×C101—84no—
286C2×C4×C101—21no—
287C2×C4×C101—21no—
288C2×C4×C101—21no—
289C2×C4×C101—21no—
290C2×C4×C101—21no—
291C2×C4×C101—21no—
292C2×C4×C101—21no—
293C2×C4×C101—21no—
294C2×C4×C101—22no—
295C2×C4×C101—21no—
296C2×C4×C101—21no—
297C2×C4×C101—21no—
298C2×C4×C101—21no—
299C2×C4×C101—21no—
300C2×C4×C101—41no—
301C2×C4×C101—41no—
302C2×C4×C101—41no—
303C2×C4×C101—41no—
304C2×C4×C101—41no—
305C2×C4×C101—41no—
306C2×C4×C101—41no—
307C2×C4×C101—41no—
308C2×C4×C101—41no—
309C2×C4×C101—41no—
310C2×C4×C101—41no—
311C2×C4×C101—41no—
312C2×C4×C101—41no—
313C2×C4×C101—41no—
314C2×C4×C101—41no—
315C2×C4×C101—41no—
316C2×C4×C101—41no—
317C2×C4×C101—41no—
318C2×C4×C101—84no—
319C2×C4×C101#12112yes—
320C2×C4×C101#12112yes—
321C2×C4×C101C22×D411yescharacteristic
322C2×C4×C101C2×#4111yescharacteristic
323C2×C4×C101C2×#4111yescharacteristic
324C2×C4×C101C2×#4111yescharacteristic
325C2×C4×C101H(5,𝔽2)11yescharacteristic
326C2×C4×C101H(5,𝔽2)11yescharacteristic
327C8×C101—22no—
328C8×C101—22no—
329C8×C101—41no—
330C8×C101—41no—
331C22×C101—41no—
332C22×C101—42no—
333C22×C101—41no—
334C22×C101—42no—
335C22×C101—41no—
336C22×C101—42no—
337C22×C101—41no—
338C22×C101—41no—
339C22×C101—41no—
340C22×C101—41no—
341C22×C101—81no—
342C22×C101—81no—
343C22×C101—81no—
344C22×C101—81no—
345C22×C101—81no—
346C22×C101—81no—
347C22×C101—81no—
348C22×C101—81no—
349C22×C101—81no—
350C22×C101—81no—
351C22×C101—81no—
352C22×C101—81no—
353C22×C101—81no—
354C22×C101—81no—
355C22×C101—81no—
356C22×C101—81no—
357C22×C101—81no—
358C22×C101—81no—
359C22×C101C2×#12111yescharacteristic
360C22×C101#52511yescharacteristic
361C22×C101#53511yescharacteristic
362C22×C101#57611yescharacteristic
363C22×C101#57611yescharacteristic
364C22×C101#57611yescharacteristic
365C22×C101#57711yescharacteristic
366C4×C101—22no—
367C4×C101—22no—
368C4×C101—42no—
369C4×C101—41no—
370C4×C101—41no—
371C4×C101—41no—
372C4×C101—81no—
373C4×C101—81no—
374C4×C101—81no—
375C4×C101—81no—
376C4×C101#54611yescharacteristic
377C4×C101#55011yescharacteristic
378C4×C101#55311yescharacteristic
379C4×C101#55511yescharacteristic
380#24662C10111yesmaximal, characteristic, direct product factor, Sylow
381C2×C101—81no—
382C2×C101—82no—
383C2×C101—161no—
384C2×C101—161no—
385C2×C101#241411yescharacteristic
386C2×C101#305811yescharacteristic
387C2×C101#306211yescharacteristic
388C2×C101#311911yescharacteristic
389C2×C101#312211yescharacteristic
390C2×C101#322011yescharacteristic
391C2×C101#322411yescharacteristic
392C2×#459C2×C10111yescharacteristic, complemented
393C2×#433C2×C10111yescharacteristic, complemented
394#2619C2×C10111yescharacteristic, complemented
395#2324C2×C10111yescharacteristic, complemented
396#2034C2×C10111yescharacteristic, complemented
397#2033C2×C10111yescharacteristic, complemented
398#1999C2×C10111yescharacteristic, complemented
399#1999C2×C10111yescharacteristic, complemented
400#1982C2×C10111yescharacteristic, complemented
401#1972C2×C10111yescharacteristic, complemented
402#1970C2×C10111yescharacteristic, complemented
403#1949C2×C10111yescharacteristic, complemented
404#1936C2×C10111yescharacteristic, complemented
405#1934C2×C10111yescharacteristic, complemented
406#1804C2×C10111yescharacteristic, complemented
407C101#2466211yescharacteristic, direct product factor, Sylow
408C22×D8C22×C10111yescharacteristic
409C22×D8C22×C10111yescharacteristic
410C2×#127C22×C10111yescharacteristic
411C2×#121C22×C10111yescharacteristic
412C2×#121C22×C10111yescharacteristic
413C2×#121C22×C10111yescharacteristic
414C2×C4×D4C22×C10111yescharacteristic
415C2×#117C22×C10111yescharacteristic
416#459—24no—
417#433—24no—
418C2×#107C22×C10111yescharacteristic
419C2×#106C22×C10111yescharacteristic
420C2×C4⋊C8C22×C10111yescharacteristic
421C2×C4⋊C8C22×C10111yescharacteristic
422C2×#102C22×C10111yescharacteristic
423C2×#102C22×C10111yescharacteristic
424C2×#102C22×C10111yescharacteristic
425C2×#102C22×C10111yescharacteristic
426C2×#102C22×C10111yescharacteristic
427C2×#102C22×C10111yescharacteristic
428C2×#102C22×C10111yescharacteristic
429C2×#102C22×C10111yescharacteristic
430C2×C22⋊C8C22×C10111yescharacteristic
431C2×C22⋊C8C22×C10111yescharacteristic
432C2×#97C22×C10111yescharacteristic
433C2×C4×C8C22×C10111yescharacteristic
434#394—21no—
435#394—21no—
436#392—21no—
437#392—21no—
438#390—21no—
439#390C22×C10111yescharacteristic
440#390C22×C10111yescharacteristic
441#390C22×C10111yescharacteristic
442#389C22×C10111yescharacteristic
443#388—21no—
444#386—21no—
445#385—21no—
446#382C22×C10111yescharacteristic
447#380C22×C10111yescharacteristic
448C4×C4⋊C4C22×C10111yescharacteristic
449#340C22×C10111yescharacteristic
450#340C22×C10111yescharacteristic
451#340C22×C10111yescharacteristic
452#340C22×C10111yescharacteristic
453C22×D4—21no—
454C22×D4—21no—
455C22×D4—21no—
456C22×D4—21no—
457C22×D4—21no—
458C22×D4C23×C10111yescharacteristic
459C22×D4C23×C10111yescharacteristic
460C22×D4C23×C10111yescharacteristic
461C23×C4—21no—
462C23×C4C23×C10111yescharacteristic
463C2×D8—22no—
464C2×D8—22no—
465C2×D8—22no—
466C2×D8—22no—
467C2×D8—41no—
468C2×D8—41no—
469C22×C8C23×C10111yescharacteristic
470C22×C8C23×C10111yescharacteristic
471C22×C8C23×C10111yescharacteristic
472C22×C8C23×C10111yescharacteristic
473#127—22no—
474#127—22no—
475#121—22no—
476#121—22no—
477#121—41no—
478#121—41no—
479#121—41no—
480#121—41no—
481C4×D4—22no—
482C4×D4—22no—
483#117—22no—
484#117—22no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4D4×C10111yescharacteristic
487C2×C4⋊C4D4×C10111yescharacteristic
488C2×C4⋊C4C23×C10111yescharacteristic
489C2×C4⋊C4C23×C10111yescharacteristic
490C2×C4⋊C4C23×C10111yescharacteristic
491C2×C4⋊C4C23×C10111yescharacteristic
492C2×C4⋊C4C23×C10111yescharacteristic
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4D4×C10111yescharacteristic
505C2×C22⋊C4D4×C10111yescharacteristic
506C2×C42—21no—
507C2×C42C23×C10111yescharacteristic
508C2×C42C23×C10111yescharacteristic
509#107—41no—
510#106—41no—
511C4⋊C8—22no—
512C4⋊C8D4×C10114yescomplemented
513#102—22no—
514#102—22no—
515#102—22no—
516#102—22no—
517#102—41no—
518#102—41no—
519#102—41no—
520#102—41no—
521C22⋊C8—22no—
522C22⋊C8—22no—
523#97—22no—
524C4×C8—22no—
525#95—21no—
526#95—21no—
527#95—21no—
528#95—21no—
529#95—21no—
530C24—21no—
531C24—21no—
532C24—21no—
533C24C2×D4×C10111yescharacteristic
534C2×D4—24no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—42no—
553C2×D4—42no—
554C2×D4—42no—
555C2×D4—42no—
556C2×D4—81no—
557C2×D4—81no—
558C2×D4—81no—
559C2×D4—81no—
560C2×D4—81no—
561C2×D4—81no—
562C2×D4—81no—
563C2×D4—81no—
564C2×D4—81no—
565C2×D4—81no—
566C2×D4#41×C10112yes—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—42no—
579C22×C4—81no—
580C22×C4—81no—
581C22×C4C2×D4×C10111yescharacteristic
582C22×C4C2×D4×C10111yescharacteristic
583C22×C4C2×D4×C10111yescharacteristic
584C22×C4C2×D4×C10111yescharacteristic
585C22×C4C2×D4×C10111yescharacteristic
586C22×C4C24×C10111yescharacteristic
587D8—44no—
588D8—44no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8C2×D4×C10112yes—
600C2×C8C2×D4×C10112yes—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—81no—
613C4⋊C4#41×C10112yes—
614C22⋊C4—24no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—42no—
618C22⋊C4—42no—
619C22⋊C4—42no—
620C22⋊C4—81no—
621C22⋊C4—81no—
622C22⋊C4—81no—
623C22⋊C4—81no—
624C22⋊C4—81no—
625C22⋊C4—81no—
626C22⋊C4—81no—
627C42—21no—
628C42—21no—
629C42—81no—
630C42C2×D4×C10112yes—
631C42#41×C10112yes—
632C23—21no—
633C23—22no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23C22×D4×C10111yescharacteristic
661D4—22no—
662D4—22no—
663D4—41no—
664D4—41no—
665D4—41no—
666D4—41no—
667D4—41no—
668D4—41no—
669D4—41no—
670D4—41no—
671D4—41no—
672D4—41no—
673D4—84no—
674D4—84no—
675D4—84no—
676D4—84no—
677D4—84no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—22no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—84no—
711C2×C4#121×C10112yes—
712C2×C4#121×C10112yes—
713C2×C4C22×D4×C10111yescharacteristic
714C2×C4C2×#41×C10111yescharacteristic
715C2×C4C2×#41×C10111yescharacteristic
716C2×C4C2×#41×C10111yescharacteristic
717C2×C4H(5,𝔽2)×C10111yescharacteristic
718C2×C4H(5,𝔽2)×C10111yescharacteristic
719C8—22no—
720C8—22no—
721C8—41no—
722C8—41no—
723C22—41no—
724C22—42no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—42no—
731C22—41no—
732C22—42no—
733C22—81no—
734C22—81no—
735C22—81no—
736C22—81no—
737C22—81no—
738C22—81no—
739C22—81no—
740C22—81no—
741C22—81no—
742C22—81no—
743C22—81no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22C2×#121×C10111yescharacteristic
752C22#525×C10111yescharacteristic
753C22#535×C10111yescharacteristic
754C22#576×C10111yescharacteristic
755C22#576×C10111yescharacteristic
756C22#576×C10111yescharacteristic
757C22#577×C10111yescharacteristic
758C4—22no—
759C4—22no—
760C4—41no—
761C4—41no—
762C4—41no—
763C4—42no—
764C4—81no—
765C4—81no—
766C4—81no—
767C4—81no—
768C4#546×C10111yescharacteristic
769C4#550×C10111yescharacteristic
770C4#553×C10111yescharacteristic
771C4#555×C10111yescharacteristic
772C2—81no—
773C2—82no—
774C2—161no—
775C2—161no—
776C2C101×#241411yescharacteristic
777C2C101×#305811yescharacteristic
778C2C101×#306211yescharacteristic
779C2C101×#311911yescharacteristic
780C2C101×#312211yescharacteristic
781C2C101×#322011yescharacteristic
782C2C101×#322411yescharacteristic
subgroupG/H
center, socleC23×C101C22×D4
commutator, Frattini, cosocleC22×C4C24×C101
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C101 ◁ C2×#117×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#459×C101C2semidirect
2. C2×#433×C101C2semidirect
3. C101×#2619C2semidirect
4. C101×#2324C2semidirect
5. C101×#2034C2semidirect
6. C101×#2033C2semidirect
7. C101×#1999C2semidirect
8. C101×#1999C2semidirect
9. C101×#1982C2semidirect
10. C101×#1972C2semidirect
11. C101×#1970C2semidirect
12. C101×#1949C2semidirect
13. C101×#1936C2semidirect
14. C101×#1934C2semidirect
15. C101×#1804C2semidirect
120. C4⋊C8×C101D4semidirect
380. #24662C101direct (N × H)
392. C2×#459C2×C101semidirect
393. C2×#433C2×C101semidirect
394. #2619C2×C101semidirect
395. #2324C2×C101semidirect
396. #2034C2×C101semidirect
397. #2033C2×C101semidirect
398. #1999C2×C101semidirect
399. #1999C2×C101semidirect
400. #1982C2×C101semidirect
401. #1972C2×C101semidirect
402. #1970C2×C101semidirect
403. #1949C2×C101semidirect
404. #1936C2×C101semidirect
405. #1934C2×C101semidirect
406. #1804C2×C101semidirect
407. C101#24662direct (N × H)
512. C4⋊C8D4×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#459×C1012
C2×#433×C1012
C101×#26192
C101×#23242
C101×#20342
C101×#20332
C101×#19992
C101×#19822
C101×#19722
C101×#19702
C101×#19492
C101×#19362
C101×#19342
C101×#18042
#24662101