Finite Group Databasebeta

← C101×#26926 #38809077

Subgroups — C101×#26926 #38809077

Order 25856.

1082 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#480×C101C211yesmaximal, characteristic, complemented
2C2×#459×C101C211yesmaximal, characteristic, complemented
3C101×#2428C211yesmaximal, characteristic, complemented
4C101×#2361C211yesmaximal, characteristic, complemented
5C101×#2086C211yesmaximal, characteristic, complemented
6C101×#2041C211yesmaximal, characteristic, complemented
7C101×#1999C211yesmaximal, characteristic, complemented
8C101×#1999C211yesmaximal, characteristic, complemented
9C101×#1970C211yesmaximal, characteristic, complemented
10C101×#1925C211yesmaximal, characteristic, complemented
11C101×#1923C211yesmaximal, characteristic, complemented
12C101×#1879C211yesmaximal, characteristic, complemented
13C101×#1874C211yesmaximal, characteristic, complemented
14C101×#1862C211yesmaximal, 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×C101—21no—
24C2×C4×D4×C101C2211yescharacteristic
25C2×C4×D4×C101C2211yescharacteristic
26C22×C4⋊C4×C101C2211yescharacteristic
27#480×C101—24no—
28#459×C101—24no—
29C2×#107×C101C2211yescharacteristic
30C2×#107×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×C4×C8×C101C2211yescharacteristic
43#394×C101—21no—
44#392×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—
52#385×C101—21no—
53C4×C4⋊C4×C101C2211yescharacteristic
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×C101—21no—
72C23×C4×C101C2311yescharacteristic
73C2×D8×C101—22no—
74C2×D8×C101—22no—
75C2×D8×C101—22no—
76C2×D8×C101—22no—
77C2×D8×C101—41no—
78C2×D8×C101—41no—
79C22×C8×C101C2311yescharacteristic
80C22×C8×C101C2311yescharacteristic
81C22×C8×C101C2311yescharacteristic
82C22×C8×C101C2311yescharacteristic
83#127×C101—22no—
84#127×C101—41no—
85#121×C101—22no—
86#121×C101—22no—
87#121×C101—22no—
88#121×C101—22no—
89#121×C101—41no—
90#121×C101—41no—
91#121×C101—44no—
92C4×D4×C101—22no—
93C4×D4×C101—22no—
94C4×D4×C101—41no—
95C4×D4×C101—41no—
96C4×D4×C101—44no—
97C2×C4⋊C4×C101—22no—
98C2×C4⋊C4×C101—21no—
99C2×C4⋊C4×C101—21no—
100C2×C4⋊C4×C101—21no—
101C2×C4⋊C4×C101—41no—
102C2×C4⋊C4×C101C2311yescharacteristic
103C2×C4⋊C4×C101C2311yescharacteristic
104C2×C4⋊C4×C101C2311yescharacteristic
105C2×C4⋊C4×C101C2311yescharacteristic
106C2×C4⋊C4×C101C2311yescharacteristic
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×C101—21no—
115C2×C22⋊C4×C101—21no—
116C2×C22⋊C4×C101D411yescharacteristic
117C2×C22⋊C4×C101D411yescharacteristic
118C2×C42×C101—21no—
119C2×C42×C101C2311yescharacteristic
120C2×C42×C101C2311yescharacteristic
121#107×C101—22no—
122#107×C101—22no—
123C4⋊C8×C101—22no—
124#102×C101—22no—
125#102×C101—22no—
126#102×C101—22no—
127#102×C101—22no—
128#102×C101—22no—
129#102×C101—41no—
130#102×C101—41no—
131#102×C101D414yescomplemented
132C22⋊C8×C101—22no—
133C22⋊C8×C101—41no—
134C4×C8×C101—41no—
135#95×C101—21no—
136#95×C101—21no—
137#95×C101—21no—
138#95×C101D411yescharacteristic
139#95×C101D411yescharacteristic
140C24×C101—21no—
141C24×C101—21no—
142C24×C101—21no—
143C24×C101C2×D411yescharacteristic
144C2×D4×C101—24no—
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—21no—
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—42no—
171C2×D4×C101—81no—
172C2×D4×C101—81no—
173C2×D4×C101—81no—
174C2×D4×C101—81no—
175C2×D4×C101C2×D412yes—
176C2×D4×C101#4112yes—
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—42no—
189C22×C4×C101—42no—
190C22×C4×C101—42no—
191C22×C4×C101—42no—
192C22×C4×C101—42no—
193C22×C4×C101—42no—
194C22×C4×C101—81no—
195C22×C4×C101—81no—
196C22×C4×C101—81no—
197C22×C4×C101C2×D411yescharacteristic
198C22×C4×C101C2×D411yescharacteristic
199C22×C4×C101C2×D411yescharacteristic
200C22×C4×C101C2×D411yescharacteristic
201C22×C4×C101C2×D411yescharacteristic
202C22×C4×C101C2411yescharacteristic
203D8×C101—44no—
204D8×C101—44no—
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×C101—21no—
214C2×C8×C101—21no—
215C2×C8×C101—21no—
216C2×C8×C101C2×D412yes—
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×C101—42no—
226C4⋊C4×C101—42no—
227C4⋊C4×C101C2×D412yes—
228C4⋊C4×C101#4112yes—
229C4⋊C4×C101#4112yes—
230C22⋊C4×C101—24no—
231C22⋊C4×C101—41no—
232C22⋊C4×C101—42no—
233C22⋊C4×C101—42no—
234C22⋊C4×C101—42no—
235C22⋊C4×C101—42no—
236C22⋊C4×C101—42no—
237C22⋊C4×C101—42no—
238C22⋊C4×C101—81no—
239C22⋊C4×C101—81no—
240C22⋊C4×C101D814yescomplemented
241C42×C101—21no—
242C42×C101—21no—
243C42×C101—21no—
244C42×C101—21no—
245C42×C101—42no—
246C23×C101—21no—
247C23×C101—21no—
248C23×C101—21no—
249C23×C101—21no—
250C23×C101—21no—
251C23×C101—21no—
252C23×C101—22no—
253C23×C101—22no—
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×C101—41no—
272C23×C101—41no—
273C23×C101C2×D812yes—
274C23×C101C22×D411yescharacteristic
275D4×C101—22no—
276D4×C101—22no—
277D4×C101—22no—
278D4×C101—22no—
279D4×C101—48no—
280D4×C101—41no—
281D4×C101—41no—
282D4×C101—41no—
283D4×C101—41no—
284D4×C101—41no—
285D4×C101—41no—
286D4×C101—41no—
287D4×C101—41no—
288D4×C101—84no—
289D4×C101—84no—
290D4×C101—84no—
291D4×C101—84no—
292C2×C4×C101—21no—
293C2×C4×C101—21no—
294C2×C4×C101—21no—
295C2×C4×C101—21no—
296C2×C4×C101—21no—
297C2×C4×C101—22no—
298C2×C4×C101—21no—
299C2×C4×C101—21no—
300C2×C4×C101—22no—
301C2×C4×C101—21no—
302C2×C4×C101—22no—
303C2×C4×C101—21no—
304C2×C4×C101—21no—
305C2×C4×C101—21no—
306C2×C4×C101—21no—
307C2×C4×C101—21no—
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—41no—
323C2×C4×C101—41no—
324C2×C4×C101—84no—
325C2×C4×C101—84no—
326C2×C4×C101—84no—
327C2×C4×C101C2×D812yes—
328C2×C4×C101C2×D812yes—
329C2×C4×C101C22×D411yescharacteristic
330C2×C4×C101C2×#4111yescharacteristic
331C2×C4×C101C2×#4111yescharacteristic
332C2×C4×C101C2×#4111yescharacteristic
333C2×C4×C101H(5,𝔽2)11yescharacteristic
334C2×C4×C101H(5,𝔽2)11yescharacteristic
335C8×C101—22no—
336C8×C101—41no—
337C8×C101—41no—
338C8×C101—41no—
339C22×C101—22no—
340C22×C101—22no—
341C22×C101—22no—
342C22×C101—41no—
343C22×C101—41no—
344C22×C101—41no—
345C22×C101—41no—
346C22×C101—42no—
347C22×C101—42no—
348C22×C101—42no—
349C22×C101—42no—
350C22×C101—42no—
351C22×C101—42no—
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—81no—
364C22×C101—81no—
365C22×C101—81no—
366C22×C101—81no—
367C22×C101#52511yescharacteristic
368C22×C101D4211yescharacteristic
369C22×C101#54611yescharacteristic
370C22×C101C22×D811yescharacteristic
371C22×C101#57511yescharacteristic
372C22×C101#57611yescharacteristic
373C22×C101#57711yescharacteristic
374C4×C101—22no—
375C4×C101—22no—
376C4×C101—42no—
377C4×C101—41no—
378C4×C101—41no—
379C4×C101—42no—
380C4×C101—42no—
381C4×C101—41no—
382C4×C101—81no—
383C4×C101—81no—
384C4×C101#53211yescharacteristic
385C4×C101#54011yescharacteristic
386C4×C101#54611yescharacteristic
387C4×C101#55311yescharacteristic
388#26926C10111yesmaximal, characteristic, direct product factor, Sylow
389C2×C101—42no—
390C2×C101—82no—
391C2×C101—82no—
392C2×C101—161no—
393C2×C101#246411yescharacteristic
394C2×C101#310011yescharacteristic
395C2×C101#311911yescharacteristic
396C2×C101#327511yescharacteristic
397C2×C101D4×D811yescharacteristic
398C2×C101#329411yescharacteristic
399C2×C101#330911yescharacteristic
400C2×#480C2×C10111yescharacteristic, complemented
401C2×#459C2×C10111yescharacteristic, complemented
402#2428C2×C10111yescharacteristic, complemented
403#2361C2×C10111yescharacteristic, complemented
404#2086C2×C10111yescharacteristic, complemented
405#2041C2×C10111yescharacteristic, complemented
406#1999C2×C10111yescharacteristic, complemented
407#1999C2×C10111yescharacteristic, complemented
408#1970C2×C10111yescharacteristic, complemented
409#1925C2×C10111yescharacteristic, complemented
410#1923C2×C10111yescharacteristic, complemented
411#1879C2×C10111yescharacteristic, complemented
412#1874C2×C10111yescharacteristic, complemented
413#1862C2×C10111yescharacteristic, complemented
414C4×#102C2×C10111yescharacteristic, complemented
415C101#2692611yescharacteristic, direct product factor, Sylow
416C22×D8C22×C10111yescharacteristic
417C22×D8C22×C10111yescharacteristic
418C2×#127C22×C10111yescharacteristic
419C2×#121—21no—
420C2×#121C22×C10111yescharacteristic
421C2×#121C22×C10111yescharacteristic
422C2×#121C22×C10111yescharacteristic
423C2×C4×D4—21no—
424C2×C4×D4C22×C10111yescharacteristic
425C2×C4×D4C22×C10111yescharacteristic
426C22×C4⋊C4C22×C10111yescharacteristic
427#480—24no—
428#459—24no—
429C2×#107C22×C10111yescharacteristic
430C2×#107C22×C10111yescharacteristic
431C2×C4⋊C8C22×C10111yescharacteristic
432C2×#102C22×C10111yescharacteristic
433C2×#102C22×C10111yescharacteristic
434C2×#102C22×C10111yescharacteristic
435C2×#102C22×C10111yescharacteristic
436C2×#102C22×C10111yescharacteristic
437C2×#102C22×C10111yescharacteristic
438C2×#102C22×C10111yescharacteristic
439C2×#102C22×C10111yescharacteristic
440C2×C22⋊C8C22×C10111yescharacteristic
441C2×C22⋊C8C22×C10111yescharacteristic
442C2×C4×C8C22×C10111yescharacteristic
443#394—21no—
444#392—21no—
445#390C22×C10111yescharacteristic
446#390C22×C10111yescharacteristic
447#389C22×C10111yescharacteristic
448#389C22×C10111yescharacteristic
449#388—21no—
450#386—21no—
451#386—21no—
452#385—21no—
453C4×C4⋊C4C22×C10111yescharacteristic
454C4×C22⋊C4C22×C10111yescharacteristic
455#340C22×C10111yescharacteristic
456#340C22×C10111yescharacteristic
457#340C22×C10111yescharacteristic
458#340C22×C10111yescharacteristic
459#336C22×C10111yescharacteristic
460#336C22×C10111yescharacteristic
461C22×D4—21no—
462C22×D4—21no—
463C22×D4—21no—
464C22×D4—21no—
465C22×D4—21no—
466C22×D4C23×C10111yescharacteristic
467C22×D4C23×C10111yescharacteristic
468C22×D4C23×C10111yescharacteristic
469C23×C4—21no—
470C23×C4—21no—
471C23×C4—21no—
472C23×C4C23×C10111yescharacteristic
473C2×D8—22no—
474C2×D8—22no—
475C2×D8—22no—
476C2×D8—22no—
477C2×D8—41no—
478C2×D8—41no—
479C22×C8C23×C10111yescharacteristic
480C22×C8C23×C10111yescharacteristic
481C22×C8C23×C10111yescharacteristic
482C22×C8C23×C10111yescharacteristic
483#127—22no—
484#127—41no—
485#121—22no—
486#121—22no—
487#121—22no—
488#121—22no—
489#121—41no—
490#121—41no—
491#121—44no—
492C4×D4—22no—
493C4×D4—22no—
494C4×D4—41no—
495C4×D4—41no—
496C4×D4—44no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—41no—
502C2×C4⋊C4C23×C10111yescharacteristic
503C2×C4⋊C4C23×C10111yescharacteristic
504C2×C4⋊C4C23×C10111yescharacteristic
505C2×C4⋊C4C23×C10111yescharacteristic
506C2×C4⋊C4C23×C10111yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4D4×C10111yescharacteristic
517C2×C22⋊C4D4×C10111yescharacteristic
518C2×C42—21no—
519C2×C42C23×C10111yescharacteristic
520C2×C42C23×C10111yescharacteristic
521#107—22no—
522#107—22no—
523C4⋊C8—22no—
524#102—22no—
525#102—22no—
526#102—22no—
527#102—22no—
528#102—22no—
529#102—41no—
530#102—41no—
531#102D4×C10114yescomplemented
532C22⋊C8—22no—
533C22⋊C8—41no—
534C4×C8—41no—
535#95—21no—
536#95—21no—
537#95—21no—
538#95D4×C10111yescharacteristic
539#95D4×C10111yescharacteristic
540C24—21no—
541C24—21no—
542C24—21no—
543C24C2×D4×C10111yescharacteristic
544C2×D4—24no—
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—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—42no—
567C2×D4—42no—
568C2×D4—42no—
569C2×D4—42no—
570C2×D4—42no—
571C2×D4—81no—
572C2×D4—81no—
573C2×D4—81no—
574C2×D4—81no—
575C2×D4C2×D4×C10112yes—
576C2×D4#41×C10112yes—
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—42no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—81no—
595C22×C4—81no—
596C22×C4—81no—
597C22×C4C2×D4×C10111yescharacteristic
598C22×C4C2×D4×C10111yescharacteristic
599C22×C4C2×D4×C10111yescharacteristic
600C22×C4C2×D4×C10111yescharacteristic
601C22×C4C2×D4×C10111yescharacteristic
602C22×C4C24×C10111yescharacteristic
603D8—44no—
604D8—44no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8C2×D4×C10112yes—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—42no—
625C4⋊C4—42no—
626C4⋊C4—42no—
627C4⋊C4C2×D4×C10112yes—
628C4⋊C4#41×C10112yes—
629C4⋊C4#41×C10112yes—
630C22⋊C4—24no—
631C22⋊C4—41no—
632C22⋊C4—42no—
633C22⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—81no—
639C22⋊C4—81no—
640C22⋊C4D8×C10114yescomplemented
641C42—21no—
642C42—21no—
643C42—21no—
644C42—21no—
645C42—42no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—22no—
653C23—22no—
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—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23C2×D8×C10112yes—
674C23C22×D4×C10111yescharacteristic
675D4—22no—
676D4—22no—
677D4—22no—
678D4—22no—
679D4—48no—
680D4—41no—
681D4—41no—
682D4—41no—
683D4—41no—
684D4—41no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—84no—
689D4—84no—
690D4—84no—
691D4—84no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—22no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—22no—
701C2×C4—21no—
702C2×C4—22no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
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—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—84no—
725C2×C4—84no—
726C2×C4—84no—
727C2×C4C2×D8×C10112yes—
728C2×C4C2×D8×C10112yes—
729C2×C4C22×D4×C10111yescharacteristic
730C2×C4C2×#41×C10111yescharacteristic
731C2×C4C2×#41×C10111yescharacteristic
732C2×C4C2×#41×C10111yescharacteristic
733C2×C4H(5,𝔽2)×C10111yescharacteristic
734C2×C4H(5,𝔽2)×C10111yescharacteristic
735C8—22no—
736C8—41no—
737C8—41no—
738C8—41no—
739C22—22no—
740C22—22no—
741C22—22no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22#525×C10111yescharacteristic
768C22D42×C10111yescharacteristic
769C22#546×C10111yescharacteristic
770C22C22×D8×C10111yescharacteristic
771C22#575×C10111yescharacteristic
772C22#576×C10111yescharacteristic
773C22#577×C10111yescharacteristic
774C4—22no—
775C4—22no—
776C4—41no—
777C4—41no—
778C4—42no—
779C4—42no—
780C4—41no—
781C4—42no—
782C4—81no—
783C4—81no—
784C4#532×C10111yescharacteristic
785C4#540×C10111yescharacteristic
786C4#546×C10111yescharacteristic
787C4#553×C10111yescharacteristic
788C2—42no—
789C2—82no—
790C2—82no—
791C2—161no—
792C2C101×#246411yescharacteristic
793C2C101×#310011yescharacteristic
794C2C101×#311911yescharacteristic
795C2C101×#327511yescharacteristic
796C2D4×D8×C10111yescharacteristic
797C2C101×#329411yescharacteristic
798C2C101×#330911yescharacteristic
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×#480×C101C2semidirect
2. C2×#459×C101C2semidirect
3. C101×#2428C2semidirect
4. C101×#2361C2semidirect
5. C101×#2086C2semidirect
6. C101×#2041C2semidirect
7. C101×#1999C2semidirect
8. C101×#1999C2semidirect
9. C101×#1970C2semidirect
10. C101×#1925C2semidirect
11. C101×#1923C2semidirect
12. C101×#1879C2semidirect
13. C101×#1874C2semidirect
14. C101×#1862C2semidirect
15. C4×#102×C101C2semidirect
131. #102×C101D4semidirect
240. C22⋊C4×C101D8semidirect
388. #26926C101direct (N × H)
400. C2×#480C2×C101semidirect
401. C2×#459C2×C101semidirect
402. #2428C2×C101semidirect
403. #2361C2×C101semidirect
404. #2086C2×C101semidirect
405. #2041C2×C101semidirect
406. #1999C2×C101semidirect
407. #1999C2×C101semidirect
408. #1970C2×C101semidirect
409. #1925C2×C101semidirect
410. #1923C2×C101semidirect
411. #1879C2×C101semidirect
412. #1874C2×C101semidirect
413. #1862C2×C101semidirect
414. C4×#102C2×C101semidirect
415. C101#26926direct (N × H)
531. #102D4×C101semidirect
640. C22⋊C4D8×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#480×C1012
C2×#459×C1012
C101×#24282
C101×#23612
C101×#20862
C101×#20412
C101×#19992
C101×#19702
C101×#19252
C101×#19232
C101×#18792
C101×#18742
C101×#18622
C4×#102×C1012
#26926101