Finite Group Databasebeta

← C101×#26939 #38809090

Subgroups — C101×#26939 #38809090

Order 25856.

1032 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×#482×C101C211yesmaximal, characteristic, complemented
2C2×#459×C101C211yesmaximal, characteristic, complemented
3C101×#2428C211yesmaximal, characteristic, complemented
4C101×#2363C211yesmaximal, characteristic, complemented
5C101×#2087C211yesmaximal, characteristic, complemented
6C101×#2041C211yesmaximal, characteristic, complemented
7C101×#1999C211yesmaximal, characteristic, complemented
8C101×#1999C211yesmaximal, characteristic, complemented
9C101×#1970C211yesmaximal, characteristic, complemented
10C101×#1926C211yesmaximal, characteristic, complemented
11C101×#1923C211yesmaximal, characteristic, complemented
12C101×#1879C211yesmaximal, characteristic, complemented
13C101×#1875C211yesmaximal, characteristic, complemented
14C101×#1864C211yesmaximal, characteristic, complemented
15C4×#102×C101C211yesmaximal, characteristic, complemented
16C22×D8×C101C2211yescharacteristic
17C22×D8×C101C2211yescharacteristic
18C2×#127×C101C2211yescharacteristic
19C2×#121×C101—21no—
20C2×#121×C101C2211yescharacteristic
21C2×#121×C101C2211yescharacteristic
22C2×#121×C101C2211yescharacteristic
23C2×C4×D4×C101C2211yescharacteristic
24C2×C4×D4×C101C2211yescharacteristic
25C2×#117×C101C2211yescharacteristic
26#482×C101—24no—
27#459×C101—24no—
28C2×#107×C101C2211yescharacteristic
29C2×#106×C101C2211yescharacteristic
30C2×C4⋊C8×C101C2211yescharacteristic
31C2×#102×C101C2211yescharacteristic
32C2×#102×C101C2211yescharacteristic
33C2×#102×C101C2211yescharacteristic
34C2×#102×C101C2211yescharacteristic
35C2×#102×C101C2211yescharacteristic
36C2×#102×C101C2211yescharacteristic
37C2×#102×C101C2211yescharacteristic
38C2×#102×C101C2211yescharacteristic
39C2×C22⋊C8×C101C2211yescharacteristic
40C2×C22⋊C8×C101C2211yescharacteristic
41C2×C4×C8×C101C2211yescharacteristic
42#394×C101—21no—
43#392×C101—21no—
44#390×C101—21no—
45#390×C101C2211yescharacteristic
46#390×C101C2211yescharacteristic
47#389×C101C2211yescharacteristic
48#389×C101C2211yescharacteristic
49#388×C101—21no—
50#386×C101—21no—
51#386×C101—21no—
52C4×C4⋊C4×C101C2211yescharacteristic
53C4×C22⋊C4×C101—21no—
54C4×C22⋊C4×C101C2211yescharacteristic
55#340×C101C2211yescharacteristic
56#340×C101C2211yescharacteristic
57#340×C101C2211yescharacteristic
58#340×C101C2211yescharacteristic
59#336×C101C2211yescharacteristic
60#336×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×C101—21no—
71C23×C4×C101C2311yescharacteristic
72C2×D8×C101—22no—
73C2×D8×C101—22no—
74C2×D8×C101—22no—
75C2×D8×C101—22no—
76C2×D8×C101—41no—
77C2×D8×C101—41no—
78C22×C8×C101C2311yescharacteristic
79C22×C8×C101C2311yescharacteristic
80C22×C8×C101C2311yescharacteristic
81C22×C8×C101C2311yescharacteristic
82#127×C101—22no—
83#127×C101—41no—
84#121×C101—22no—
85#121×C101—22no—
86#121×C101—22no—
87#121×C101—22no—
88#121×C101—44no—
89#121×C101—41no—
90#121×C101—41no—
91C4×D4×C101—22no—
92C4×D4×C101—22no—
93C4×D4×C101—41no—
94C4×D4×C101—41no—
95#117×C101—22no—
96#117×C101—41no—
97C2×C4⋊C4×C101—21no—
98C2×C4⋊C4×C101—21no—
99C2×C4⋊C4×C101C2311yescharacteristic
100C2×C4⋊C4×C101C2311yescharacteristic
101C2×C4⋊C4×C101C2311yescharacteristic
102C2×C4⋊C4×C101C2311yescharacteristic
103C2×C4⋊C4×C101C2311yescharacteristic
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×C101—21no—
113C2×C22⋊C4×C101—21no—
114C2×C22⋊C4×C101D411yescharacteristic
115C2×C22⋊C4×C101D411yescharacteristic
116C2×C42×C101—21no—
117C2×C42×C101—21no—
118C2×C42×C101C2311yescharacteristic
119C2×C42×C101C2311yescharacteristic
120#107×C101—22no—
121#106×C101—22no—
122C4⋊C8×C101—22no—
123#102×C101—22no—
124#102×C101—22no—
125#102×C101—22no—
126#102×C101—22no—
127#102×C101—22no—
128#102×C101—41no—
129#102×C101—41no—
130#102×C101D414yescomplemented
131C22⋊C8×C101—22no—
132C22⋊C8×C101—41no—
133C4×C8×C101—41no—
134#95×C101—21no—
135#95×C101—21no—
136#95×C101—21no—
137#95×C101D411yescharacteristic
138#95×C101D411yescharacteristic
139C24×C101—21no—
140C24×C101—21no—
141C24×C101—21no—
142C24×C101C2×D411yescharacteristic
143C2×D4×C101—24no—
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—42no—
165C2×D4×C101—42no—
166C2×D4×C101—42no—
167C2×D4×C101—42no—
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×C101C2×D412yes—
175C2×D4×C101#4112yes—
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—42no—
188C22×C4×C101—42no—
189C22×C4×C101—42no—
190C22×C4×C101—42no—
191C22×C4×C101—81no—
192C22×C4×C101—81no—
193C22×C4×C101C2×D411yescharacteristic
194C22×C4×C101C2×D411yescharacteristic
195C22×C4×C101C2×D411yescharacteristic
196C22×C4×C101C2×D411yescharacteristic
197C22×C4×C101C2×D411yescharacteristic
198C22×C4×C101C2411yescharacteristic
199D8×C101—44no—
200D8×C101—44no—
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×C101—21no—
208C2×C8×C101—21no—
209C2×C8×C101—21no—
210C2×C8×C101—21no—
211C2×C8×C101—21no—
212C2×C8×C101C2×D412yes—
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—42no—
221C4⋊C4×C101—81no—
222C4⋊C4×C101C2×D412yes—
223C4⋊C4×C101#4112yes—
224C4⋊C4×C101#4112yes—
225C22⋊C4×C101—24no—
226C22⋊C4×C101—22no—
227C22⋊C4×C101—22no—
228C22⋊C4×C101—42no—
229C22⋊C4×C101—42no—
230C22⋊C4×C101—42no—
231C22⋊C4×C101—42no—
232C22⋊C4×C101—42no—
233C22⋊C4×C101—42no—
234C22⋊C4×C101—42no—
235C22⋊C4×C101—81no—
236C22⋊C4×C101—81no—
237C42×C101—21no—
238C42×C101—21no—
239C42×C101—21no—
240C42×C101—21no—
241C42×C101—42no—
242C42×C101—81no—
243C23×C101—22no—
244C23×C101—21no—
245C23×C101—21no—
246C23×C101—22no—
247C23×C101—21no—
248C23×C101—21no—
249C23×C101—21no—
250C23×C101—21no—
251C23×C101—21no—
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×C101—41no—
269C23×C101—41no—
270C23×C101—41no—
271C23×C101C22×D411yescharacteristic
272D4×C101—22no—
273D4×C101—22no—
274D4×C101—22no—
275D4×C101—22no—
276D4×C101—41no—
277D4×C101—41no—
278D4×C101—41no—
279D4×C101—41no—
280D4×C101—41no—
281D4×C101—41no—
282D4×C101—41no—
283D4×C101—41no—
284D4×C101—84no—
285D4×C101—84no—
286D4×C101—84no—
287D4×C101—84no—
288D4×C101—84no—
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—22no—
298C2×C4×C101—21no—
299C2×C4×C101—22no—
300C2×C4×C101—21no—
301C2×C4×C101—21no—
302C2×C4×C101—21no—
303C2×C4×C101—21no—
304C2×C4×C101—21no—
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—84no—
322C2×C4×C101—84no—
323C2×C4×C101#13512yes—
324C2×C4×C101AGL(1,ℤ/8)12yes—
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—41no—
336C22×C101—42no—
337C22×C101—41no—
338C22×C101—42no—
339C22×C101—41no—
340C22×C101—42no—
341C22×C101—42no—
342C22×C101—41no—
343C22×C101—42no—
344C22×C101—42no—
345C22×C101—41no—
346C22×C101—41no—
347C22×C101—41no—
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×C101—81no—
360C22×C101—81no—
361C22×C101—81no—
362C22×C101—81no—
363C22×C101#52511yescharacteristic
364C22×C101D4211yescharacteristic
365C22×C101#54611yescharacteristic
366C22×C101C2×#13511yescharacteristic
367C22×C101C2×AGL(1,ℤ/8)11yescharacteristic
368C22×C101#57611yescharacteristic
369C22×C101#57611yescharacteristic
370C4×C101—22no—
371C4×C101—22no—
372C4×C101—42no—
373C4×C101—41no—
374C4×C101—41no—
375C4×C101—42no—
376C4×C101—41no—
377C4×C101—42no—
378C4×C101—81no—
379C4×C101—81no—
380C4×C101#53211yescharacteristic
381C4×C101#54011yescharacteristic
382C4×C101#54611yescharacteristic
383C4×C101#55311yescharacteristic
384#26939C10111yesmaximal, characteristic, direct product factor, Sylow
385C2×C101—81no—
386C2×C101—82no—
387C2×C101—82no—
388C2×C101—161no—
389C2×C101#246411yescharacteristic
390C2×C101#310611yescharacteristic
391C2×C101#312211yescharacteristic
392C2×C101#327411yescharacteristic
393C2×C101#328011yescharacteristic
394C2×C101#330511yescharacteristic
395C2×C101#331811yescharacteristic
396C2×#482C2×C10111yescharacteristic, complemented
397C2×#459C2×C10111yescharacteristic, complemented
398#2428C2×C10111yescharacteristic, complemented
399#2363C2×C10111yescharacteristic, complemented
400#2087C2×C10111yescharacteristic, complemented
401#2041C2×C10111yescharacteristic, complemented
402#1999C2×C10111yescharacteristic, complemented
403#1999C2×C10111yescharacteristic, complemented
404#1970C2×C10111yescharacteristic, complemented
405#1926C2×C10111yescharacteristic, complemented
406#1923C2×C10111yescharacteristic, complemented
407#1879C2×C10111yescharacteristic, complemented
408#1875C2×C10111yescharacteristic, complemented
409#1864C2×C10111yescharacteristic, complemented
410C4×#102C2×C10111yescharacteristic, complemented
411C101#2693911yescharacteristic, direct product factor, Sylow
412C22×D8C22×C10111yescharacteristic
413C22×D8C22×C10111yescharacteristic
414C2×#127C22×C10111yescharacteristic
415C2×#121—21no—
416C2×#121C22×C10111yescharacteristic
417C2×#121C22×C10111yescharacteristic
418C2×#121C22×C10111yescharacteristic
419C2×C4×D4C22×C10111yescharacteristic
420C2×C4×D4C22×C10111yescharacteristic
421C2×#117C22×C10111yescharacteristic
422#482—24no—
423#459—24no—
424C2×#107C22×C10111yescharacteristic
425C2×#106C22×C10111yescharacteristic
426C2×C4⋊C8C22×C10111yescharacteristic
427C2×#102C22×C10111yescharacteristic
428C2×#102C22×C10111yescharacteristic
429C2×#102C22×C10111yescharacteristic
430C2×#102C22×C10111yescharacteristic
431C2×#102C22×C10111yescharacteristic
432C2×#102C22×C10111yescharacteristic
433C2×#102C22×C10111yescharacteristic
434C2×#102C22×C10111yescharacteristic
435C2×C22⋊C8C22×C10111yescharacteristic
436C2×C22⋊C8C22×C10111yescharacteristic
437C2×C4×C8C22×C10111yescharacteristic
438#394—21no—
439#392—21no—
440#390—21no—
441#390C22×C10111yescharacteristic
442#390C22×C10111yescharacteristic
443#389C22×C10111yescharacteristic
444#389C22×C10111yescharacteristic
445#388—21no—
446#386—21no—
447#386—21no—
448C4×C4⋊C4C22×C10111yescharacteristic
449C4×C22⋊C4—21no—
450C4×C22⋊C4C22×C10111yescharacteristic
451#340C22×C10111yescharacteristic
452#340C22×C10111yescharacteristic
453#340C22×C10111yescharacteristic
454#340C22×C10111yescharacteristic
455#336C22×C10111yescharacteristic
456#336C22×C10111yescharacteristic
457C22×D4—21no—
458C22×D4—21no—
459C22×D4—21no—
460C22×D4—21no—
461C22×D4—21no—
462C22×D4C23×C10111yescharacteristic
463C22×D4C23×C10111yescharacteristic
464C22×D4C23×C10111yescharacteristic
465C23×C4—21no—
466C23×C4—21no—
467C23×C4C23×C10111yescharacteristic
468C2×D8—22no—
469C2×D8—22no—
470C2×D8—22no—
471C2×D8—22no—
472C2×D8—41no—
473C2×D8—41no—
474C22×C8C23×C10111yescharacteristic
475C22×C8C23×C10111yescharacteristic
476C22×C8C23×C10111yescharacteristic
477C22×C8C23×C10111yescharacteristic
478#127—22no—
479#127—41no—
480#121—22no—
481#121—22no—
482#121—22no—
483#121—22no—
484#121—44no—
485#121—41no—
486#121—41no—
487C4×D4—22no—
488C4×D4—22no—
489C4×D4—41no—
490C4×D4—41no—
491#117—22no—
492#117—41no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4C23×C10111yescharacteristic
496C2×C4⋊C4C23×C10111yescharacteristic
497C2×C4⋊C4C23×C10111yescharacteristic
498C2×C4⋊C4C23×C10111yescharacteristic
499C2×C4⋊C4C23×C10111yescharacteristic
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4D4×C10111yescharacteristic
511C2×C22⋊C4D4×C10111yescharacteristic
512C2×C42—21no—
513C2×C42—21no—
514C2×C42C23×C10111yescharacteristic
515C2×C42C23×C10111yescharacteristic
516#107—22no—
517#106—22no—
518C4⋊C8—22no—
519#102—22no—
520#102—22no—
521#102—22no—
522#102—22no—
523#102—22no—
524#102—41no—
525#102—41no—
526#102D4×C10114yescomplemented
527C22⋊C8—22no—
528C22⋊C8—41no—
529C4×C8—41no—
530#95—21no—
531#95—21no—
532#95—21no—
533#95D4×C10111yescharacteristic
534#95D4×C10111yescharacteristic
535C24—21no—
536C24—21no—
537C24—21no—
538C24C2×D4×C10111yescharacteristic
539C2×D4—24no—
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—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
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—81no—
565C2×D4—81no—
566C2×D4—81no—
567C2×D4—81no—
568C2×D4—81no—
569C2×D4—81no—
570C2×D4C2×D4×C10112yes—
571C2×D4#41×C10112yes—
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—42no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—81no—
588C22×C4—81no—
589C22×C4C2×D4×C10111yescharacteristic
590C22×C4C2×D4×C10111yescharacteristic
591C22×C4C2×D4×C10111yescharacteristic
592C22×C4C2×D4×C10111yescharacteristic
593C22×C4C2×D4×C10111yescharacteristic
594C22×C4C24×C10111yescharacteristic
595D8—44no—
596D8—44no—
597C2×C8—21no—
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×C8C2×D4×C10112yes—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—42no—
617C4⋊C4—81no—
618C4⋊C4C2×D4×C10112yes—
619C4⋊C4#41×C10112yes—
620C4⋊C4#41×C10112yes—
621C22⋊C4—24no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—42no—
625C22⋊C4—42no—
626C22⋊C4—42no—
627C22⋊C4—42no—
628C22⋊C4—42no—
629C22⋊C4—42no—
630C22⋊C4—42no—
631C22⋊C4—81no—
632C22⋊C4—81no—
633C42—21no—
634C42—21no—
635C42—21no—
636C42—21no—
637C42—42no—
638C42—81no—
639C23—22no—
640C23—21no—
641C23—21no—
642C23—22no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—41no—
649C23—41no—
650C23—41no—
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—
665C23—41no—
666C23—41no—
667C23C22×D4×C10111yescharacteristic
668D4—22no—
669D4—22no—
670D4—22no—
671D4—22no—
672D4—41no—
673D4—41no—
674D4—41no—
675D4—41no—
676D4—41no—
677D4—41no—
678D4—41no—
679D4—41no—
680D4—84no—
681D4—84no—
682D4—84no—
683D4—84no—
684D4—84no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—22no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—22no—
694C2×C4—21no—
695C2×C4—22no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
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—84no—
718C2×C4—84no—
719C2×C4#135×C10112yes—
720C2×C4AGL(1,ℤ/8)×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—41no—
732C22—42no—
733C22—42no—
734C22—41no—
735C22—42no—
736C22—42no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—42no—
742C22—41no—
743C22—42no—
744C22—81no—
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—
759C22#525×C10111yescharacteristic
760C22D42×C10111yescharacteristic
761C22#546×C10111yescharacteristic
762C22C2×#135×C10111yescharacteristic
763C22C2×AGL(1,ℤ/8)×C10111yescharacteristic
764C22#576×C10111yescharacteristic
765C22#576×C10111yescharacteristic
766C4—22no—
767C4—22no—
768C4—41no—
769C4—41no—
770C4—42no—
771C4—41no—
772C4—42no—
773C4—42no—
774C4—81no—
775C4—81no—
776C4#532×C10111yescharacteristic
777C4#540×C10111yescharacteristic
778C4#546×C10111yescharacteristic
779C4#553×C10111yescharacteristic
780C2—81no—
781C2—82no—
782C2—82no—
783C2—161no—
784C2C101×#246411yescharacteristic
785C2C101×#310611yescharacteristic
786C2C101×#312211yescharacteristic
787C2C101×#327411yescharacteristic
788C2C101×#328011yescharacteristic
789C2C101×#330511yescharacteristic
790C2C101×#331811yescharacteristic
subgroupG/H
center, socleC23×C101C22×D4
commutator, Frattini, cosocleC22×C4C24×C101
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C101 ◁ C4×C22⋊C4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#482×C101C2semidirect
2. C2×#459×C101C2semidirect
3. C101×#2428C2semidirect
4. C101×#2363C2semidirect
5. C101×#2087C2semidirect
6. C101×#2041C2semidirect
7. C101×#1999C2semidirect
8. C101×#1999C2semidirect
9. C101×#1970C2semidirect
10. C101×#1926C2semidirect
11. C101×#1923C2semidirect
12. C101×#1879C2semidirect
13. C101×#1875C2semidirect
14. C101×#1864C2semidirect
15. C4×#102×C101C2semidirect
130. #102×C101D4semidirect
384. #26939C101direct (N × H)
396. C2×#482C2×C101semidirect
397. C2×#459C2×C101semidirect
398. #2428C2×C101semidirect
399. #2363C2×C101semidirect
400. #2087C2×C101semidirect
401. #2041C2×C101semidirect
402. #1999C2×C101semidirect
403. #1999C2×C101semidirect
404. #1970C2×C101semidirect
405. #1926C2×C101semidirect
406. #1923C2×C101semidirect
407. #1879C2×C101semidirect
408. #1875C2×C101semidirect
409. #1864C2×C101semidirect
410. C4×#102C2×C101semidirect
411. C101#26939direct (N × H)
526. #102D4×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#482×C1012
C2×#459×C1012
C101×#24282
C101×#23632
C101×#20872
C101×#20412
C101×#19992
C101×#19702
C101×#19262
C101×#19232
C101×#18792
C101×#18752
C101×#18642
C4×#102×C1012
#26939101