Finite Group Databasebeta

← C101×#26246 #38808397

Subgroups — C101×#26246 #38808397

Order 25856.

1006 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
1C2×#481×C101C211yesmaximal, characteristic, complemented
2C2×#482×C101C211yesmaximal, characteristic, complemented
3C101×#2541C211yesmaximal, characteristic
4C101×#2352C211yesmaximal, characteristic, complemented
5C101×#2034C211yesmaximal, characteristic, complemented
6C101×#2033C211yesmaximal, characteristic, complemented
7C101×#2033C211yesmaximal, characteristic, complemented
8C101×#2033C211yesmaximal, characteristic, complemented
9C101×#1982C211yesmaximal, characteristic, complemented
10C101×#1961C211yesmaximal, characteristic, complemented
11C101×#1955C211yesmaximal, characteristic, complemented
12C101×#1949C211yesmaximal, characteristic, complemented
13C101×#1875C211yesmaximal, characteristic, complemented
14C101×#1874C211yesmaximal, characteristic, complemented
15C101×#1776C211yesmaximal, characteristic, complemented
16C2×#127×C101—21no—
17C2×#127×C101C2211yescharacteristic
18C2×#121×C101C2211yescharacteristic
19C2×#121×C101C2211yescharacteristic
20C2×#121×C101C2211yescharacteristic
21C2×#121×C101C2211yescharacteristic
22C2×C4×D4×C101C2211yescharacteristic
23C2×#117×C101C2211yescharacteristic
24C22×C4⋊C4×C101C2211yescharacteristic
25#482×C101—24no—
26#481×C101—24no—
27C2×#107×C101C2211yescharacteristic
28C2×#107×C101C2211yescharacteristic
29C2×#106×C101C2211yescharacteristic
30C2×#106×C101C2211yescharacteristic
31C2×C4⋊C8×C101C2211yescharacteristic
32C2×#102×C101C2211yescharacteristic
33C2×#102×C101C2211yescharacteristic
34C2×#102×C101C2211yescharacteristic
35C2×#102×C101C2211yescharacteristic
36C2×#102×C101C2211yescharacteristic
37C2×#102×C101C2211yescharacteristic
38C2×#102×C101C2211yescharacteristic
39C2×#102×C101C2211yescharacteristic
40C2×C22⋊C8×C101C2211yescharacteristic
41C2×C22⋊C8×C101C2211yescharacteristic
42C2×C22⋊C8×C101C2211yescharacteristic
43C2×C22⋊C8×C101C2211yescharacteristic
44C2×#97×C101C2211yescharacteristic
45#392×C101—21no—
46#392×C101—21no—
47#390×C101—21no—
48#388×C101—21no—
49#387×C101—21no—
50#386×C101—21no—
51#382×C101C2211yescharacteristic
52#380×C101C2211yescharacteristic
53#380×C101C2211yescharacteristic
54C4×C4⋊C4×C101C2211yescharacteristic
55C4×C4⋊C4×C101C2211yescharacteristic
56C4×C22⋊C4×C101—21no—
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×C101—21no—
67C22×D4×C101D411yescharacteristic
68C22×D4×C101C2311yescharacteristic
69C22×D4×C101C2311yescharacteristic
70C23×C4×C101—21no—
71C23×C4×C101C2311yescharacteristic
72C23×C4×C101C2311yescharacteristic
73C22×C8×C101C2311yescharacteristic
74C22×C8×C101C2311yescharacteristic
75C22×C8×C101C2311yescharacteristic
76C22×C8×C101C2311yescharacteristic
77#127×C101—22no—
78#127×C101—22no—
79#127×C101—44no—
80#121×C101—22no—
81#121×C101—22no—
82#121×C101—22no—
83#121×C101—22no—
84#121×C101—41no—
85#121×C101—41no—
86#121×C101—41no—
87#121×C101—41no—
88C4×D4×C101—22no—
89C4×D4×C101—22no—
90#117×C101—22no—
91#117×C101—41no—
92C2×C4⋊C4×C101—22no—
93C2×C4⋊C4×C101—21no—
94C2×C4⋊C4×C101—41no—
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×C4⋊C4×C101C2311yescharacteristic
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×C101D411yescharacteristic
110C2×C22⋊C4×C101D411yescharacteristic
111C2×C42×C101—21no—
112C2×C42×C101—21no—
113C2×C42×C101—21no—
114C2×C42×C101C2311yescharacteristic
115#107×C101—22no—
116#107×C101—22no—
117#106×C101—22no—
118#106×C101D414yescomplemented
119C4⋊C8×C101—22no—
120#102×C101—22no—
121#102×C101—22no—
122#102×C101—22no—
123#102×C101—22no—
124#102×C101—41no—
125#102×C101—41no—
126#102×C101—41no—
127#102×C101—41no—
128C22⋊C8×C101—22no—
129C22⋊C8×C101—22no—
130C22⋊C8×C101—41no—
131C22⋊C8×C101—41no—
132#97×C101—22no—
133#95×C101—21no—
134#95×C101—21no—
135#95×C101—21no—
136#95×C101—21no—
137#95×C101—21no—
138#95×C101—21no—
139C24×C101—21no—
140C24×C101—21no—
141C24×C101C2×D411yescharacteristic
142C24×C101C2×D411yescharacteristic
143C2×D4×C101—22no—
144C2×D4×C101—22no—
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—41no—
158C2×D4×C101—42no—
159C2×D4×C101—42no—
160C2×D4×C101—42no—
161C2×D4×C101—42no—
162C2×D4×C101—42no—
163C2×D4×C101—42no—
164C2×D4×C101—42no—
165C2×D4×C101—42no—
166C2×D4×C101—42no—
167C2×D4×C101—42no—
168C2×D4×C101—42no—
169C2×D4×C101—42no—
170C2×D4×C101—81no—
171C2×D4×C101—81no—
172C2×D4×C101—81no—
173C2×D4×C101—81no—
174C2×D4×C101—81no—
175C2×D4×C101—81no—
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—21no—
187C22×C4×C101—21no—
188C22×C4×C101—21no—
189C22×C4×C101—21no—
190C22×C4×C101—21no—
191C22×C4×C101—21no—
192C22×C4×C101—21no—
193C22×C4×C101—21no—
194C22×C4×C101—42no—
195C22×C4×C101—42no—
196C22×C4×C101—81no—
197C22×C4×C101C2×D411yescharacteristic
198C22×C4×C101C2×D411yescharacteristic
199C22×C4×C101C2×D411yescharacteristic
200C22×C4×C101C2×D411yescharacteristic
201C22×C4×C101C2411yescharacteristic
202C2×C8×C101—21no—
203C2×C8×C101—21no—
204C2×C8×C101—21no—
205C2×C8×C101—21no—
206C2×C8×C101—21no—
207C2×C8×C101—21no—
208C2×C8×C101—21no—
209C2×C8×C101—21no—
210C2×C8×C101—21no—
211C2×C8×C101—21no—
212C2×C8×C101—21no—
213C2×C8×C101C2×D412yes—
214C4⋊C4×C101—22no—
215C4⋊C4×C101—21no—
216C4⋊C4×C101—21no—
217C4⋊C4×C101—21no—
218C4⋊C4×C101—21no—
219C4⋊C4×C101—21no—
220C4⋊C4×C101—21no—
221C4⋊C4×C101—21no—
222C4⋊C4×C101—21no—
223C4⋊C4×C101—21no—
224C4⋊C4×C101—42no—
225C4⋊C4×C101C2×D412yes—
226C4⋊C4×C101C2×D412yes—
227C4⋊C4×C101#4112yes—
228C22⋊C4×C101—22no—
229C22⋊C4×C101—22no—
230C22⋊C4×C101—42no—
231C22⋊C4×C101—42no—
232C22⋊C4×C101—42no—
233C22⋊C4×C101—42no—
234C22⋊C4×C101—42no—
235C22⋊C4×C101—42no—
236C22⋊C4×C101—81no—
237C42×C101—42no—
238C42×C101—42no—
239C42×C101—81no—
240C42×C101#4112yes—
241C42×C101#4112yes—
242C23×C101—21no—
243C23×C101—21no—
244C23×C101—21no—
245C23×C101—21no—
246C23×C101—21no—
247C23×C101—21no—
248C23×C101—21no—
249C23×C101—21no—
250C23×C101—21no—
251C23×C101—21no—
252C23×C101—21no—
253C23×C101—21no—
254C23×C101—21no—
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×C101—41no—
269C23×C101AGL(1,ℤ/8)12yes—
270C23×C101C22×D411yescharacteristic
271D4×C101—44no—
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—84no—
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—22no—
294C2×C4×C101—22no—
295C2×C4×C101—21no—
296C2×C4×C101—22no—
297C2×C4×C101—21no—
298C2×C4×C101—21no—
299C2×C4×C101—41no—
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—41no—
319C2×C4×C101—41no—
320C2×C4×C101—41no—
321C2×C4×C101—41no—
322C2×C4×C101—84no—
323C2×C4×C101#12312yes—
324C2×C4×C101#12312yes—
325C2×C4×C101C22×D411yescharacteristic
326C2×C4×C101C2×#4111yescharacteristic
327C2×C4×C101C2×#4111yescharacteristic
328C2×C4×C101C2×#4111yescharacteristic
329C2×C4×C101H(5,𝔽2)11yescharacteristic
330C2×C4×C101H(5,𝔽2)11yescharacteristic
331C8×C101—22no—
332C8×C101—41no—
333C8×C101—41no—
334C8×C101—41no—
335C22×C101—22no—
336C22×C101—22no—
337C22×C101—22no—
338C22×C101—41no—
339C22×C101—41no—
340C22×C101—41no—
341C22×C101—41no—
342C22×C101—41no—
343C22×C101—41no—
344C22×C101—41no—
345C22×C101—41no—
346C22×C101—41no—
347C22×C101—41no—
348C22×C101—41no—
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×C101—81no—
360C22×C101—81no—
361C22×C101—81no—
362C22×C101—81no—
363C22×C101C2×#12311yescharacteristic
364C22×C101D4211yescharacteristic
365C22×C101#54611yescharacteristic
366C22×C101C2×AGL(1,ℤ/8)11yescharacteristic
367C22×C101#57511yescharacteristic
368C22×C101#57611yescharacteristic
369C22×C101#57711yescharacteristic
370C4×C101—22no—
371C4×C101—22no—
372C4×C101—41no—
373C4×C101—41no—
374C4×C101—42no—
375C4×C101—42no—
376C4×C101—42no—
377C4×C101—81no—
378C4×C101—81no—
379C4×C101—81no—
380C4×C101#53211yescharacteristic
381C4×C101#54011yescharacteristic
382C4×C101#55011yescharacteristic
383C4×C101#55911yescharacteristic
384#26246C10111yesmaximal, characteristic, direct product factor, Sylow
385C2×C101—42no—
386C2×C101—81no—
387C2×C101—161no—
388C2×C101—161no—
389C2×C101#244511yescharacteristic
390C2×C101#309411yescharacteristic
391C2×C101#309611yescharacteristic
392C2×C101#326511yescharacteristic
393C2×C101#326811yescharacteristic
394C2×C101#331711yescharacteristic
395C2×C101#331811yescharacteristic
396C2×#481C2×C10111yescharacteristic, complemented
397C2×#482C2×C10111yescharacteristic, complemented
398#2541C2×C10111yescharacteristic
399#2352C2×C10111yescharacteristic, complemented
400#2034C2×C10111yescharacteristic, complemented
401#2033C2×C10111yescharacteristic, complemented
402#2033C2×C10111yescharacteristic, complemented
403#2033C2×C10111yescharacteristic, complemented
404#1982C2×C10111yescharacteristic, complemented
405#1961C2×C10111yescharacteristic, complemented
406#1955C2×C10111yescharacteristic, complemented
407#1949C2×C10111yescharacteristic, complemented
408#1875C2×C10111yescharacteristic, complemented
409#1874C2×C10111yescharacteristic, complemented
410#1776C2×C10111yescharacteristic, complemented
411C101#2624611yescharacteristic, direct product factor, Sylow
412C2×#127—21no—
413C2×#127C22×C10111yescharacteristic
414C2×#121C22×C10111yescharacteristic
415C2×#121C22×C10111yescharacteristic
416C2×#121C22×C10111yescharacteristic
417C2×#121C22×C10111yescharacteristic
418C2×C4×D4C22×C10111yescharacteristic
419C2×#117C22×C10111yescharacteristic
420C22×C4⋊C4C22×C10111yescharacteristic
421#482—24no—
422#481—24no—
423C2×#107C22×C10111yescharacteristic
424C2×#107C22×C10111yescharacteristic
425C2×#106C22×C10111yescharacteristic
426C2×#106C22×C10111yescharacteristic
427C2×C4⋊C8C22×C10111yescharacteristic
428C2×#102C22×C10111yescharacteristic
429C2×#102C22×C10111yescharacteristic
430C2×#102C22×C10111yescharacteristic
431C2×#102C22×C10111yescharacteristic
432C2×#102C22×C10111yescharacteristic
433C2×#102C22×C10111yescharacteristic
434C2×#102C22×C10111yescharacteristic
435C2×#102C22×C10111yescharacteristic
436C2×C22⋊C8C22×C10111yescharacteristic
437C2×C22⋊C8C22×C10111yescharacteristic
438C2×C22⋊C8C22×C10111yescharacteristic
439C2×C22⋊C8C22×C10111yescharacteristic
440C2×#97C22×C10111yescharacteristic
441#392—21no—
442#392—21no—
443#390—21no—
444#388—21no—
445#387—21no—
446#386—21no—
447#382C22×C10111yescharacteristic
448#380C22×C10111yescharacteristic
449#380C22×C10111yescharacteristic
450C4×C4⋊C4C22×C10111yescharacteristic
451C4×C4⋊C4C22×C10111yescharacteristic
452C4×C22⋊C4—21no—
453#340C22×C10111yescharacteristic
454#340C22×C10111yescharacteristic
455#340C22×C10111yescharacteristic
456#340C22×C10111yescharacteristic
457C22×D4—21no—
458C22×D4—21no—
459C22×D4—21no—
460C22×D4—21no—
461C22×D4—21no—
462C22×D4—21no—
463C22×D4D4×C10111yescharacteristic
464C22×D4C23×C10111yescharacteristic
465C22×D4C23×C10111yescharacteristic
466C23×C4—21no—
467C23×C4C23×C10111yescharacteristic
468C23×C4C23×C10111yescharacteristic
469C22×C8C23×C10111yescharacteristic
470C22×C8C23×C10111yescharacteristic
471C22×C8C23×C10111yescharacteristic
472C22×C8C23×C10111yescharacteristic
473#127—22no—
474#127—22no—
475#127—44no—
476#121—22no—
477#121—22no—
478#121—22no—
479#121—22no—
480#121—41no—
481#121—41no—
482#121—41no—
483#121—41no—
484C4×D4—22no—
485C4×D4—22no—
486#117—22no—
487#117—41no—
488C2×C4⋊C4—22no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—41no—
491C2×C4⋊C4D4×C10111yescharacteristic
492C2×C4⋊C4C23×C10111yescharacteristic
493C2×C4⋊C4C23×C10111yescharacteristic
494C2×C4⋊C4C23×C10111yescharacteristic
495C2×C4⋊C4C23×C10111yescharacteristic
496C2×C4⋊C4C23×C10111yescharacteristic
497C2×C4⋊C4C23×C10111yescharacteristic
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⋊C4—21no—
505C2×C22⋊C4D4×C10111yescharacteristic
506C2×C22⋊C4D4×C10111yescharacteristic
507C2×C42—21no—
508C2×C42—21no—
509C2×C42—21no—
510C2×C42C23×C10111yescharacteristic
511#107—22no—
512#107—22no—
513#106—22no—
514#106D4×C10114yescomplemented
515C4⋊C8—22no—
516#102—22no—
517#102—22no—
518#102—22no—
519#102—22no—
520#102—41no—
521#102—41no—
522#102—41no—
523#102—41no—
524C22⋊C8—22no—
525C22⋊C8—22no—
526C22⋊C8—41no—
527C22⋊C8—41no—
528#97—22no—
529#95—21no—
530#95—21no—
531#95—21no—
532#95—21no—
533#95—21no—
534#95—21no—
535C24—21no—
536C24—21no—
537C24C2×D4×C10111yescharacteristic
538C24C2×D4×C10111yescharacteristic
539C2×D4—22no—
540C2×D4—22no—
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—21no—
553C2×D4—41no—
554C2×D4—42no—
555C2×D4—42no—
556C2×D4—42no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—81no—
567C2×D4—81no—
568C2×D4—81no—
569C2×D4—81no—
570C2×D4—81no—
571C2×D4—81no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—81no—
593C22×C4C2×D4×C10111yescharacteristic
594C22×C4C2×D4×C10111yescharacteristic
595C22×C4C2×D4×C10111yescharacteristic
596C22×C4C2×D4×C10111yescharacteristic
597C22×C4C24×C10111yescharacteristic
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8C2×D4×C10112yes—
610C4⋊C4—22no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—42no—
621C4⋊C4C2×D4×C10112yes—
622C4⋊C4C2×D4×C10112yes—
623C4⋊C4#41×C10112yes—
624C22⋊C4—22no—
625C22⋊C4—22no—
626C22⋊C4—42no—
627C22⋊C4—42no—
628C22⋊C4—42no—
629C22⋊C4—42no—
630C22⋊C4—42no—
631C22⋊C4—42no—
632C22⋊C4—81no—
633C42—42no—
634C42—42no—
635C42—81no—
636C42#41×C10112yes—
637C42#41×C10112yes—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23AGL(1,ℤ/8)×C10112yes—
666C23C22×D4×C10111yescharacteristic
667D4—44no—
668D4—41no—
669D4—41no—
670D4—41no—
671D4—41no—
672D4—41no—
673D4—41no—
674D4—41no—
675D4—41no—
676D4—84no—
677D4—84no—
678D4—84no—
679D4—84no—
680D4—84no—
681D4—84no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—21no—
692C2×C4—22no—
693C2×C4—21no—
694C2×C4—21no—
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—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—84no—
719C2×C4#123×C10112yes—
720C2×C4#123×C10112yes—
721C2×C4C22×D4×C10111yescharacteristic
722C2×C4C2×#41×C10111yescharacteristic
723C2×C4C2×#41×C10111yescharacteristic
724C2×C4C2×#41×C10111yescharacteristic
725C2×C4H(5,𝔽2)×C10111yescharacteristic
726C2×C4H(5,𝔽2)×C10111yescharacteristic
727C8—22no—
728C8—41no—
729C8—41no—
730C8—41no—
731C22—22no—
732C22—22no—
733C22—22no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22C2×#123×C10111yescharacteristic
760C22D42×C10111yescharacteristic
761C22#546×C10111yescharacteristic
762C22C2×AGL(1,ℤ/8)×C10111yescharacteristic
763C22#575×C10111yescharacteristic
764C22#576×C10111yescharacteristic
765C22#577×C10111yescharacteristic
766C4—22no—
767C4—22no—
768C4—41no—
769C4—41no—
770C4—42no—
771C4—42no—
772C4—42no—
773C4—81no—
774C4—81no—
775C4—81no—
776C4#532×C10111yescharacteristic
777C4#540×C10111yescharacteristic
778C4#550×C10111yescharacteristic
779C4#559×C10111yescharacteristic
780C2—42no—
781C2—81no—
782C2—161no—
783C2—161no—
784C2C101×#244511yescharacteristic
785C2C101×#309411yescharacteristic
786C2C101×#309611yescharacteristic
787C2C101×#326511yescharacteristic
788C2C101×#326811yescharacteristic
789C2C101×#331711yescharacteristic
790C2C101×#331811yescharacteristic
subgroupG/H
center, socleC23×C101C22×D4
commutator, Frattini, cosocleC22×C4C24×C101
prime radicalC101×#2541C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C101 ◁ C2×C4×D4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#481×C101C2semidirect
2. C2×#482×C101C2semidirect
4. C101×#2352C2semidirect
5. C101×#2034C2semidirect
6. C101×#2033C2semidirect
7. C101×#2033C2semidirect
8. C101×#2033C2semidirect
9. C101×#1982C2semidirect
10. C101×#1961C2semidirect
11. C101×#1955C2semidirect
12. C101×#1949C2semidirect
13. C101×#1875C2semidirect
14. C101×#1874C2semidirect
15. C101×#1776C2semidirect
118. #106×C101D4semidirect
384. #26246C101direct (N × H)
396. C2×#481C2×C101semidirect
397. C2×#482C2×C101semidirect
399. #2352C2×C101semidirect
400. #2034C2×C101semidirect
401. #2033C2×C101semidirect
402. #2033C2×C101semidirect
403. #2033C2×C101semidirect
404. #1982C2×C101semidirect
405. #1961C2×C101semidirect
406. #1955C2×C101semidirect
407. #1949C2×C101semidirect
408. #1875C2×C101semidirect
409. #1874C2×C101semidirect
410. #1776C2×C101semidirect
411. C101#26246direct (N × H)
514. #106D4×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#481×C1012
C2×#482×C1012
C101×#25412
C101×#23522
C101×#20342
C101×#20332
C101×#19822
C101×#19612
C101×#19552
C101×#19492
C101×#18752
C101×#18742
C101×#17762
#26246101