Finite Group Databasebeta

← C101×#23005 #38805156

Subgroups — C101×#23005 #38805156

Order 25856.

1022 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#463×C101C211yesmaximal, characteristic
2C2×#442×C101C211yesmaximal, characteristic
3C2×#440×C101C211yesmaximal, characteristic, complemented
4C101×#2367C211yesmaximal, characteristic, complemented
5C101×#2349C211yesmaximal, characteristic, complemented
6C101×#1958C211yesmaximal, characteristic, complemented
7C101×#1949C211yesmaximal, characteristic, complemented
8C101×#1936C211yesmaximal, characteristic, complemented
9C101×#1935C211yesmaximal, characteristic, complemented
10C101×#1879C211yesmaximal, characteristic
11C101×#1877C211yesmaximal, characteristic, complemented
12C101×#1865C211yesmaximal, characteristic, complemented
13C101×#1862C211yesmaximal, characteristic, complemented
14C101×#1770C211yesmaximal, characteristic, complemented
15C4×#102×C101C211yesmaximal, characteristic, complemented
16C22×SD16×C101C2211yescharacteristic
17C22×D8×C101C2211yescharacteristic
18C2×#124×C101C2211yescharacteristic
19C2×C4×Q8×C101C2211yescharacteristic
20C2×C4×D4×C101C2211yescharacteristic
21C2×C4×D4×C101C2211yescharacteristic
22C2×C4×D4×C101C2211yescharacteristic
23C2×C4×D4×C101C2211yescharacteristic
24#463×C101C418yescomplemented
25#442×C101—24no—
26#440×C101—24no—
27C2×#107×C101C2211yescharacteristic
28C2×#106×C101C2211yescharacteristic
29C2×C4⋊C8×C101C2211yescharacteristic
30C2×#103×C101C2211yescharacteristic
31C2×#103×C101C2211yescharacteristic
32C2×#103×C101C2211yescharacteristic
33C2×#102×C101C2211yescharacteristic
34C2×#102×C101C2211yescharacteristic
35C2×#102×C101C2211yescharacteristic
36C2×#102×C101C2211yescharacteristic
37C2×#102×C101C2211yescharacteristic
38C2×#97×C101C2211yescharacteristic
39C2×#97×C101C2211yescharacteristic
40C2×C4×C8×C101C2211yescharacteristic
41#391×C101C2211yescharacteristic
42#390×C101C2211yescharacteristic
43#389×C101C2211yescharacteristic
44#389×C101C2211yescharacteristic
45#388×C101—21no—
46#388×C101—21no—
47#385×C101—21no—
48#385×C101—21no—
49#385×C101—21no—
50#382×C101C2211yescharacteristic
51#380×C101—21no—
52C4×C4⋊C4×C101C2211yescharacteristic
53C4×C4⋊C4×C101C2211yescharacteristic
54C4×C22⋊C4×C101—21no—
55C2×#95×C101—21no—
56#340×C101C2211yescharacteristic
57#340×C101C2211yescharacteristic
58#340×C101C2211yescharacteristic
59#340×C101C2211yescharacteristic
60#336×C101C2211yescharacteristic
61#336×C101C2211yescharacteristic
62C22×Q8×C101C2311yescharacteristic
63C22×D4×C101C2311yescharacteristic
64C22×D4×C101C2311yescharacteristic
65C23×C4×C101—21no—
66C23×C4×C101—21no—
67C23×C4×C101—21no—
68C23×C4×C101—21no—
69C2×SD16×C101—22no—
70C2×SD16×C101—22no—
71C2×SD16×C101C2×C414yescomplemented
72C2×D8×C101—22no—
73C2×D8×C101—22no—
74C2×D8×C101C2×C414yes—
75C22×C8×C101C2311yescharacteristic
76C22×C8×C101C2311yescharacteristic
77C22×C8×C101C2311yescharacteristic
78C22×C8×C101C2311yescharacteristic
79#124×C101—22no—
80#124×C101C2×C414yescomplemented
81C4×Q8×C101—22no—
82C4×Q8×C101—41no—
83C4×D4×C101—22no—
84C4×D4×C101—22no—
85C4×D4×C101—22no—
86C4×D4×C101—22no—
87C4×D4×C101—41no—
88C4×D4×C101—41no—
89C4×D4×C101—41no—
90C4×D4×C101C2×C414yescomplemented
91C2×C4⋊C4×C101—21no—
92C2×C4⋊C4×C101—21no—
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×C42×C101—21no—
110C2×C42×C101—21no—
111C2×C42×C101C2311yescharacteristic
112C2×C42×C101C2311yescharacteristic
113C2×C42×C101C2311yescharacteristic
114#107×C101—22no—
115#106×C101—22no—
116C4⋊C8×C101C2×C414yescomplemented
117#103×C101—22no—
118#103×C101—41no—
119#103×C101C2×C414yescomplemented
120#102×C101—22no—
121#102×C101—22no—
122#102×C101—41no—
123#102×C101C2×C414yescomplemented
124#102×C101D414yes—
125#97×C101—22no—
126#97×C101—22no—
127C4×C8×C101—22no—
128#95×C101—21no—
129#95×C101—21no—
130#95×C101—21no—
131#95×C101—21no—
132#95×C101—21no—
133#95×C101—21no—
134#95×C101—21no—
135#95×C101D411yescharacteristic
136#95×C101D411yescharacteristic
137C24×C101—21no—
138C24×C101—21no—
139C2×Q8×C101—21no—
140C2×Q8×C101—21no—
141C2×Q8×C101—21no—
142C2×Q8×C101—21no—
143C2×Q8×C101—21no—
144C2×Q8×C101C22×C412yes—
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×C101C22×C412yes—
154C2×D4×C101C22×C412yes—
155C2×D4×C101C2×D412yes—
156C2×D4×C101#4112yes—
157C22×C4×C101—21no—
158C22×C4×C101—21no—
159C22×C4×C101—21no—
160C22×C4×C101—24no—
161C22×C4×C101—21no—
162C22×C4×C101—21no—
163C22×C4×C101—21no—
164C22×C4×C101—42no—
165C22×C4×C101—42no—
166C22×C4×C101—42no—
167C22×C4×C101—42no—
168C22×C4×C101—42no—
169C22×C4×C101—42no—
170C22×C4×C101—81no—
171C22×C4×C101—81no—
172C22×C4×C101—81no—
173C22×C4×C101—81no—
174C22×C4×C101—81no—
175C22×C4×C101C2×D411yescharacteristic
176C22×C4×C101C2×D411yescharacteristic
177C22×C4×C101C2×D411yescharacteristic
178C22×C4×C101C2×D411yescharacteristic
179C22×C4×C101C2×D411yescharacteristic
180C22×C4×C101C2×D411yescharacteristic
181C22×C4×C101C2411yescharacteristic
182SD16×C101—28no—
183D8×C101—28no—
184C2×C8×C101—21no—
185C2×C8×C101—21no—
186C2×C8×C101—21no—
187C2×C8×C101—21no—
188C2×C8×C101—21no—
189C2×C8×C101—21no—
190C2×C8×C101—21no—
191C2×C8×C101—21no—
192C2×C8×C101—21no—
193C2×C8×C101C22×C412yes—
194C2×C8×C101C22×C412yes—
195C2×C8×C101C2×D412yes—
196C4⋊C4×C101—21no—
197C4⋊C4×C101—21no—
198C4⋊C4×C101—21no—
199C4⋊C4×C101—21no—
200C4⋊C4×C101—21no—
201C4⋊C4×C101—21no—
202C4⋊C4×C101—21no—
203C4⋊C4×C101—21no—
204C4⋊C4×C101—41no—
205C4⋊C4×C101—41no—
206C4⋊C4×C101—42no—
207C4⋊C4×C101—81no—
208C4⋊C4×C101—81no—
209C4⋊C4×C101C22×C412yes—
210C4⋊C4×C101C2×D412yes—
211C22⋊C4×C101—24no—
212C22⋊C4×C101—24no—
213C22⋊C4×C101—24no—
214C22⋊C4×C101—42no—
215C22⋊C4×C101—42no—
216C22⋊C4×C101—42no—
217C22⋊C4×C101—42no—
218C22⋊C4×C101—81no—
219C42×C101—21no—
220C42×C101—21no—
221C42×C101—21no—
222C42×C101—21no—
223C42×C101—42no—
224C42×C101—81no—
225C42×C101C22×C412yes—
226C42×C101#4112yes—
227C23×C101—22no—
228C23×C101—22no—
229C23×C101—22no—
230C23×C101—22no—
231C23×C101—41no—
232C23×C101—41no—
233C23×C101—41no—
234C23×C101—41no—
235C23×C101—41no—
236C23×C101—41no—
237C23×C101—41no—
238C23×C101—41no—
239C23×C101—41no—
240C23×C101—41no—
241C23×C101C22×D411yescharacteristic
242Q8×C101—22no—
243Q8×C101—22no—
244Q8×C101—41no—
245Q8×C101—41no—
246D4×C101—22no—
247D4×C101—22no—
248D4×C101—22no—
249D4×C101—22no—
250D4×C101—22no—
251D4×C101—41no—
252D4×C101—41no—
253D4×C101C4×D414yes—
254C2×C4×C101—21no—
255C2×C4×C101—21no—
256C2×C4×C101—21no—
257C2×C4×C101—21no—
258C2×C4×C101—22no—
259C2×C4×C101—22no—
260C2×C4×C101—21no—
261C2×C4×C101—21no—
262C2×C4×C101—21no—
263C2×C4×C101—21no—
264C2×C4×C101—22no—
265C2×C4×C101—21no—
266C2×C4×C101—21no—
267C2×C4×C101—21no—
268C2×C4×C101—21no—
269C2×C4×C101—21no—
270C2×C4×C101—21no—
271C2×C4×C101—21no—
272C2×C4×C101—21no—
273C2×C4×C101—41no—
274C2×C4×C101—41no—
275C2×C4×C101—41no—
276C2×C4×C101—41no—
277C2×C4×C101—41no—
278C2×C4×C101—41no—
279C2×C4×C101—41no—
280C2×C4×C101—41no—
281C2×C4×C101—41no—
282C2×C4×C101—41no—
283C2×C4×C101—41no—
284C2×C4×C101—41no—
285C2×C4×C101—41no—
286C2×C4×C101—41no—
287C2×C4×C101—41no—
288C2×C4×C101—84no—
289C2×C4×C101—84no—
290C2×C4×C101—84no—
291C2×C4×C101—84no—
292C2×C4×C101C4×D412yes—
293C2×C4×C101C4×D412yes—
294C2×C4×C101C23×C411yescharacteristic
295C2×C4×C101C22×D411yescharacteristic
296C2×C4×C101C2×#4111yescharacteristic
297C2×C4×C101C2×#4111yescharacteristic
298C2×C4×C101H(5,𝔽2)11yescharacteristic
299C2×C4×C1012−1+411yescharacteristic
300C8×C101—22no—
301C8×C101—22no—
302C8×C101—22no—
303C8×C101—41no—
304C22×C101—24no—
305C22×C101—42no—
306C22×C101—42no—
307C22×C101—42no—
308C22×C101—42no—
309C22×C101—42no—
310C22×C101—42no—
311C22×C101—42no—
312C22×C101—42no—
313C22×C101—42no—
314C22×C101—81no—
315C22×C101—81no—
316C22×C101—81no—
317C22×C101—81no—
318C22×C101C2×C4×D411yescharacteristic
319C22×C101D4211yescharacteristic
320C22×C101#54811yescharacteristic
321C22×C101#57511yescharacteristic
322C22×C101#57511yescharacteristic
323C22×C101#57611yescharacteristic
324C22×C101#57711yescharacteristic
325C4×C101—22no—
326C4×C101—22no—
327C4×C101—42no—
328C4×C101—42no—
329C4×C101—41no—
330C4×C101—41no—
331C4×C101—42no—
332C4×C101—41no—
333C4×C101—41no—
334C4×C101—81no—
335C4×C101—81no—
336C4×C101—81no—
337C4×C101C2×C4×D411yescharacteristic
338C4×C101#52011yescharacteristic
339C4×C101#54711yescharacteristic
340C4×C101#55311yescharacteristic
341#23005C10111yesmaximal, characteristic, direct product factor, Sylow
342C2×C101—44no—
343C2×C101—82no—
344C2×C101#236111yescharacteristic
345C2×C101#294311yescharacteristic
346C2×C101#294611yescharacteristic
347C2×C101#327311yescharacteristic
348C2×C101#327511yescharacteristic
349C2×C101#337011yescharacteristic
350C2×C101#337611yescharacteristic
351C2×#463C2×C10111yescharacteristic
352C2×#442C2×C10111yescharacteristic
353C2×#440C2×C10111yescharacteristic, complemented
354#2367C2×C10111yescharacteristic, complemented
355#2349C2×C10111yescharacteristic, complemented
356#1958C2×C10111yescharacteristic, complemented
357#1949C2×C10111yescharacteristic, complemented
358#1936C2×C10111yescharacteristic, complemented
359#1935C2×C10111yescharacteristic, complemented
360#1879C2×C10111yescharacteristic
361#1877C2×C10111yescharacteristic, complemented
362#1865C2×C10111yescharacteristic, complemented
363#1862C2×C10111yescharacteristic, complemented
364#1770C2×C10111yescharacteristic, complemented
365C4×#102C2×C10111yescharacteristic, complemented
366C101#2300511yescharacteristic, direct product factor, Sylow
367C22×SD16C22×C10111yescharacteristic
368C22×D8C22×C10111yescharacteristic
369C2×#124C22×C10111yescharacteristic
370C2×C4×Q8C22×C10111yescharacteristic
371C2×C4×D4C22×C10111yescharacteristic
372C2×C4×D4C22×C10111yescharacteristic
373C2×C4×D4C22×C10111yescharacteristic
374C2×C4×D4C22×C10111yescharacteristic
375#463C4×C10118yescomplemented
376#442—24no—
377#440—24no—
378C2×#107C22×C10111yescharacteristic
379C2×#106C22×C10111yescharacteristic
380C2×C4⋊C8C22×C10111yescharacteristic
381C2×#103C22×C10111yescharacteristic
382C2×#103C22×C10111yescharacteristic
383C2×#103C22×C10111yescharacteristic
384C2×#102C22×C10111yescharacteristic
385C2×#102C22×C10111yescharacteristic
386C2×#102C22×C10111yescharacteristic
387C2×#102C22×C10111yescharacteristic
388C2×#102C22×C10111yescharacteristic
389C2×#97C22×C10111yescharacteristic
390C2×#97C22×C10111yescharacteristic
391C2×C4×C8C22×C10111yescharacteristic
392#391C22×C10111yescharacteristic
393#390C22×C10111yescharacteristic
394#389C22×C10111yescharacteristic
395#389C22×C10111yescharacteristic
396#388—21no—
397#388—21no—
398#385—21no—
399#385—21no—
400#385—21no—
401#382C22×C10111yescharacteristic
402#380—21no—
403C4×C4⋊C4C22×C10111yescharacteristic
404C4×C4⋊C4C22×C10111yescharacteristic
405C4×C22⋊C4—21no—
406C2×#95—21no—
407#340C22×C10111yescharacteristic
408#340C22×C10111yescharacteristic
409#340C22×C10111yescharacteristic
410#340C22×C10111yescharacteristic
411#336C22×C10111yescharacteristic
412#336C22×C10111yescharacteristic
413C22×Q8C23×C10111yescharacteristic
414C22×D4C23×C10111yescharacteristic
415C22×D4C23×C10111yescharacteristic
416C23×C4—21no—
417C23×C4—21no—
418C23×C4—21no—
419C23×C4—21no—
420C2×SD16—22no—
421C2×SD16—22no—
422C2×SD16C2×C4×C10114yescomplemented
423C2×D8—22no—
424C2×D8—22no—
425C2×D8C2×C4×C10114yes—
426C22×C8C23×C10111yescharacteristic
427C22×C8C23×C10111yescharacteristic
428C22×C8C23×C10111yescharacteristic
429C22×C8C23×C10111yescharacteristic
430#124—22no—
431#124C2×C4×C10114yescomplemented
432C4×Q8—22no—
433C4×Q8—41no—
434C4×D4—22no—
435C4×D4—22no—
436C4×D4—22no—
437C4×D4—22no—
438C4×D4—41no—
439C4×D4—41no—
440C4×D4—41no—
441C4×D4C2×C4×C10114yescomplemented
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4D4×C10111yescharacteristic
446C2×C4⋊C4D4×C10111yescharacteristic
447C2×C4⋊C4C23×C10111yescharacteristic
448C2×C4⋊C4C23×C10111yescharacteristic
449C2×C4⋊C4C23×C10111yescharacteristic
450C2×C4⋊C4C23×C10111yescharacteristic
451C2×C4⋊C4C23×C10111yescharacteristic
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C42—21no—
461C2×C42—21no—
462C2×C42C23×C10111yescharacteristic
463C2×C42C23×C10111yescharacteristic
464C2×C42C23×C10111yescharacteristic
465#107—22no—
466#106—22no—
467C4⋊C8C2×C4×C10114yescomplemented
468#103—22no—
469#103—41no—
470#103C2×C4×C10114yescomplemented
471#102—22no—
472#102—22no—
473#102—41no—
474#102C2×C4×C10114yescomplemented
475#102D4×C10114yes—
476#97—22no—
477#97—22no—
478C4×C8—22no—
479#95—21no—
480#95—21no—
481#95—21no—
482#95—21no—
483#95—21no—
484#95—21no—
485#95—21no—
486#95D4×C10111yescharacteristic
487#95D4×C10111yescharacteristic
488C24—21no—
489C24—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8C22×C4×C10112yes—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4C22×C4×C10112yes—
505C2×D4C22×C4×C10112yes—
506C2×D4C2×D4×C10112yes—
507C2×D4#41×C10112yes—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—24no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—42no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—81no—
522C22×C4—81no—
523C22×C4—81no—
524C22×C4—81no—
525C22×C4—81no—
526C22×C4C2×D4×C10111yescharacteristic
527C22×C4C2×D4×C10111yescharacteristic
528C22×C4C2×D4×C10111yescharacteristic
529C22×C4C2×D4×C10111yescharacteristic
530C22×C4C2×D4×C10111yescharacteristic
531C22×C4C2×D4×C10111yescharacteristic
532C22×C4C24×C10111yescharacteristic
533SD16—28no—
534D8—28no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8C22×C4×C10112yes—
545C2×C8C22×C4×C10112yes—
546C2×C8C2×D4×C10112yes—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—41no—
556C4⋊C4—41no—
557C4⋊C4—42no—
558C4⋊C4—81no—
559C4⋊C4—81no—
560C4⋊C4C22×C4×C10112yes—
561C4⋊C4C2×D4×C10112yes—
562C22⋊C4—24no—
563C22⋊C4—24no—
564C22⋊C4—24no—
565C22⋊C4—42no—
566C22⋊C4—42no—
567C22⋊C4—42no—
568C22⋊C4—42no—
569C22⋊C4—81no—
570C42—21no—
571C42—21no—
572C42—21no—
573C42—21no—
574C42—42no—
575C42—81no—
576C42C22×C4×C10112yes—
577C42#41×C10112yes—
578C23—22no—
579C23—22no—
580C23—22no—
581C23—22no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23C22×D4×C10111yescharacteristic
593Q8—22no—
594Q8—22no—
595Q8—41no—
596Q8—41no—
597D4—22no—
598D4—22no—
599D4—22no—
600D4—22no—
601D4—22no—
602D4—41no—
603D4—41no—
604D4C4×D4×C10114yes—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—22no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—84no—
640C2×C4—84no—
641C2×C4—84no—
642C2×C4—84no—
643C2×C4C4×D4×C10112yes—
644C2×C4C4×D4×C10112yes—
645C2×C4C23×C4×C10111yescharacteristic
646C2×C4C22×D4×C10111yescharacteristic
647C2×C4C2×#41×C10111yescharacteristic
648C2×C4C2×#41×C10111yescharacteristic
649C2×C4H(5,𝔽2)×C10111yescharacteristic
650C2×C42−1+4×C10111yescharacteristic
651C8—22no—
652C8—22no—
653C8—22no—
654C8—41no—
655C22—24no—
656C22—42no—
657C22—42no—
658C22—42no—
659C22—42no—
660C22—42no—
661C22—42no—
662C22—42no—
663C22—42no—
664C22—42no—
665C22—81no—
666C22—81no—
667C22—81no—
668C22—81no—
669C22C2×C4×D4×C10111yescharacteristic
670C22D42×C10111yescharacteristic
671C22#548×C10111yescharacteristic
672C22#575×C10111yescharacteristic
673C22#575×C10111yescharacteristic
674C22#576×C10111yescharacteristic
675C22#577×C10111yescharacteristic
676C4—22no—
677C4—22no—
678C4—42no—
679C4—41no—
680C4—41no—
681C4—42no—
682C4—41no—
683C4—41no—
684C4—42no—
685C4—81no—
686C4—81no—
687C4—81no—
688C4C2×C4×D4×C10111yescharacteristic
689C4#520×C10111yescharacteristic
690C4#547×C10111yescharacteristic
691C4#553×C10111yescharacteristic
692C2—44no—
693C2—82no—
694C2C101×#236111yescharacteristic
695C2C101×#294311yescharacteristic
696C2C101×#294611yescharacteristic
697C2C101×#327311yescharacteristic
698C2C101×#327511yescharacteristic
699C2C101×#337011yescharacteristic
700C2C101×#337611yescharacteristic
subgroupG/H
center, socleC23×C101C22×D4
commutatorC2×C4C23×C4×C101
Frattini, cosocleC22×C4C24×C101
prime radicalC22×D8×C101C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C101 ◁ C4×C4⋊C4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×#440×C101C2semidirect
4. C101×#2367C2semidirect
5. C101×#2349C2semidirect
6. C101×#1958C2semidirect
7. C101×#1949C2semidirect
8. C101×#1936C2semidirect
9. C101×#1935C2semidirect
11. C101×#1877C2semidirect
12. C101×#1865C2semidirect
13. C101×#1862C2semidirect
14. C101×#1770C2semidirect
15. C4×#102×C101C2semidirect
24. #463×C101C4semidirect
71. C2×SD16×C101C2×C4semidirect
80. #124×C101C2×C4semidirect
90. C4×D4×C101C2×C4semidirect
116. C4⋊C8×C101C2×C4semidirect
119. #103×C101C2×C4semidirect
123. #102×C101C2×C4semidirect
341. #23005C101direct (N × H)
353. C2×#440C2×C101semidirect
354. #2367C2×C101semidirect
355. #2349C2×C101semidirect
356. #1958C2×C101semidirect
357. #1949C2×C101semidirect
358. #1936C2×C101semidirect
359. #1935C2×C101semidirect
361. #1877C2×C101semidirect
362. #1865C2×C101semidirect
363. #1862C2×C101semidirect
364. #1770C2×C101semidirect
365. C4×#102C2×C101semidirect
366. C101#23005direct (N × H)
375. #463C4×C101semidirect
422. C2×SD16C2×C4×C101semidirect
431. #124C2×C4×C101semidirect
441. C4×D4C2×C4×C101semidirect
467. C4⋊C8C2×C4×C101semidirect
470. #103C2×C4×C101semidirect
474. #102C2×C4×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#463×C1012
C2×#442×C1012
C2×#440×C1012
C101×#23672
C101×#23492
C101×#19582
C101×#19492
C101×#19362
C101×#19352
C101×#18792
C101×#18772
C101×#18652
C101×#18622
C101×#17702
C4×#102×C1012
#23005101