Finite Group Databasebeta

← C2×#21422356 #28510380

Subgroups — C2×#21422356 #28510380

Order 15104.

2638 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C59⋊#95C211yesmaximal, characteristic
2C22×C59⋊#95C211yesmaximal, characteristic
3C22×C59⋊#95C211yesmaximal, characteristic
4C22×C59⋊#95C211yesmaximal, characteristic
5C22×C59⋊#95C211yesmaximal, characteristic
6C22×C59⋊#95C211yesmaximal, characteristic
7#21422356C218yesmaximal, direct product factor
8C22×#95×C59C211yesmaximal, characteristic
9C24×Dic59C2211yescharacteristic
10C24×Dic59C2211yescharacteristic
11C24×Dic59C2211yescharacteristic
12C24×Dic59C2211yescharacteristic
13C2×C59⋊#95—24no—
14C2×C59⋊#95—24no—
15C2×C59⋊#95—24no—
16C2×C59⋊#95—24no—
17C2×C59⋊#95—24no—
18C2×C59⋊#95C418yescomplemented
19C2×C59⋊#95C2214yes—
20C2×C59⋊#95C2214yes—
21C2×C59⋊#95C2214yes—
22C2×C59⋊#95C2214yes—
23C2×C59⋊#95C2214yes—
24C2×C59⋊#95C2214yes—
25C24×C4×C59C2211yescharacteristic
26C24×C4×C59C2211yescharacteristic
27C24×C4×C59C2211yescharacteristic
28C2×#95×C59—24no—
29C2×#95×C59C2214yes—
30C23×Dic59—22no—
31C23×Dic59—22no—
32C23×Dic59—22no—
33C23×Dic59—22no—
34C23×Dic59—22no—
35C23×Dic59—22no—
36C23×Dic59—22no—
37C23×Dic59—22no—
38C23×Dic59—22no—
39C23×Dic59—22no—
40C23×Dic59—22no—
41C23×Dic59—22no—
42C23×Dic59—22no—
43C23×Dic59—22no—
44C23×Dic59—22no—
45C23×Dic59—22no—
46C23×Dic59—22no—
47C23×Dic59—22no—
48C23×Dic59—22no—
49C23×Dic59—22no—
50C23×Dic59—22no—
51C23×Dic59—22no—
52C23×Dic59—22no—
53C23×Dic59—22no—
54C23×Dic59C2×C414yes—
55C23×Dic59C2×C414yes—
56C23×Dic59D414yes—
57C23×Dic59Q814yes—
58C23×Dic59C2312yes—
59C23×Dic59C2312yes—
60C23×Dic59C2312yes—
61C23×Dic59C2312yes—
62C59⋊#95—28no—
63C59⋊#95—28no—
64C59⋊#95—28no—
65C59⋊#95—28no—
66C59⋊#95—28no—
67C59⋊#95C2×C4116yescomplemented
68C25×C59C2311yescharacteristic
69C23×C4×C59—22no—
70C23×C4×C59—22no—
71C23×C4×C59—22no—
72C23×C4×C59—22no—
73C23×C4×C59—22no—
74C23×C4×C59—22no—
75C23×C4×C59—22no—
76C23×C4×C59—22no—
77C23×C4×C59—22no—
78C23×C4×C59—22no—
79C23×C4×C59—22no—
80C23×C4×C59—22no—
81C23×C4×C59—22no—
82C23×C4×C59—22no—
83C23×C4×C59—22no—
84C23×C4×C59—22no—
85C23×C4×C59—22no—
86C23×C4×C59—22no—
87C23×C4×C59C2×C414yes—
88C23×C4×C59D414yes—
89C23×C4×C59D414yes—
90C23×C4×C59C2312yes—
91C23×C4×C59C2312yes—
92C23×C4×C59C2312yes—
93#95×C59—28no—
94C24×C59C22×C412yes—
95C24×C59C2×D412yes—
96C24×C59C2×D412yes—
97C24×C59C2×D412yes—
98C24×C59C2×Q812yes—
99C24×C59#4112yes—
100C24×C59#4112yes—
101C24×C59#4112yes—
102C24×C59#4112yes—
103C24×C59#4112yes—
104C24×C59#4112yes—
105C24×C59#4112yes—
106C24×C59#4112yes—
107C24×C59#4112yes—
108C24×C59#4112yes—
109C24×C59C2411yescharacteristic
110C22×C4×C59—28no—
111C22×C4×C59—28no—
112C22×C4×C59—28no—
113C22×C4×C59—28no—
114C22×C4×C59—28no—
115C22×C4×C59—28no—
116C22×C4×C59—28no—
117C22×C4×C59—28no—
118C22×C4×C59—28no—
119C22×C4×C59—22no—
120C22×C4×C59—22no—
121C22×C4×C59—22no—
122C22×C4×C59—22no—
123C22×C4×C59—22no—
124C22×C4×C59—22no—
125C22×C4×C59—22no—
126C22×C4×C59—22no—
127C22×C4×C59—22no—
128C22×C4×C59—22no—
129C22×C4×C59—22no—
130C22×C4×C59—22no—
131C22×C4×C59—22no—
132C22×C4×C59—22no—
133C22×C4×C59—22no—
134C22×C4×C59—22no—
135C22×C4×C59—22no—
136C22×C4×C59—22no—
137C22×C4×C59—44no—
138C22×C4×C59—44no—
139C22×C4×C59—44no—
140C22×C4×C59—44no—
141C22×C4×C59—44no—
142C22×C4×C59—44no—
143C22×C4×C59—44no—
144C22×C4×C59—44no—
145C22×C4×C59—44no—
146C22×C4×C59—44no—
147C22×C4×C59—44no—
148C22×C4×C59—44no—
149C22×C4×C59C22×C414yes—
150C22×C4×C59C2×D414yes—
151C22×C4×C59C2×D414yes—
152C22×Dic59—28no—
153C22×Dic59—28no—
154C22×Dic59—28no—
155C22×Dic59—28no—
156C22×Dic59—28no—
157C22×Dic59—28no—
158C22×Dic59—28no—
159C22×Dic59—28no—
160C22×Dic59—28no—
161C22×Dic59—28no—
162C22×Dic59—28no—
163C22×Dic59—28no—
164C22×Dic59—22no—
165C22×Dic59—22no—
166C22×Dic59—22no—
167C22×Dic59—22no—
168C22×Dic59—22no—
169C22×Dic59—22no—
170C22×Dic59—22no—
171C22×Dic59—22no—
172C22×Dic59—22no—
173C22×Dic59—22no—
174C22×Dic59—22no—
175C22×Dic59—22no—
176C22×Dic59—22no—
177C22×Dic59—22no—
178C22×Dic59—22no—
179C22×Dic59—22no—
180C22×Dic59—22no—
181C22×Dic59—22no—
182C22×Dic59—22no—
183C22×Dic59—22no—
184C22×Dic59—22no—
185C22×Dic59—22no—
186C22×Dic59—22no—
187C22×Dic59—22no—
188C22×Dic59—44no—
189C22×Dic59—44no—
190C22×Dic59—44no—
191C22×Dic59—44no—
192C22×Dic59—44no—
193C22×Dic59—44no—
194C22×Dic59—44no—
195C22×Dic59—44no—
196C22×Dic59—44no—
197C22×Dic59—44no—
198C22×Dic59—44no—
199C22×Dic59—44no—
200C22×Dic59—44no—
201C22×Dic59—44no—
202C22×Dic59—44no—
203C22×Dic59—44no—
204C22×Dic59C22×C414yes—
205C22×Dic59C22×C414yes—
206C22×Dic59C2×D414yes—
207C22×Dic59C2×Q814yes—
208C23×C59#11714yes—
209C23×C59#11714yes—
210C23×C59#11714yes—
211C23×C59C4×D414yes—
212C23×C59C4×D414yes—
213C23×C59C4×D414yes—
214C23×C59C4×Q814yes—
215C23×C59#12114yes—
216C23×C59#12114yes—
217C23×C59#12114yes—
218C23×C59C22⋊Q814yes—
219C23×C59C22⋊Q814yes—
220C23×C59C22⋊Q814yes—
221C23×C59#12314yes—
222C23×C59#12314yes—
223C23×C59#12314yes—
224C23×C59#12314yes—
225C23×C59#12314yes—
226C23×C59#12314yes—
227C23×C59#12414yes—
228C23×C59#12414yes—
229C23×C59#12414yes—
230C23×C59#12514yes—
231C23×C59#12514yes—
232C23×C59#12514yes—
233C23×C59#12614yes—
234C23×C59#12614yes—
235C23×C59#12614yes—
236C23×C59#12614yes—
237C23×C59#12614yes—
238C23×C59#12614yes—
239C23×C59#12614yes—
240C23×C59#12614yes—
241C23×C59#12614yes—
242C23×C59#12614yes—
243C23×C59C23×C411yescharacteristic
244C23×C59C22×D411yescharacteristic
245C23×C59C22×D411yescharacteristic
246C23×C59C22×D411yescharacteristic
247C23×C59C22×Q811yescharacteristic
248C23×C59C2×#4111yescharacteristic
249C23×C59C2×#4111yescharacteristic
250C23×C59C2×#4111yescharacteristic
251C23×C59C2×#4111yescharacteristic
252C23×C59C2×#4111yescharacteristic
253C23×C59C2×#4111yescharacteristic
254C23×C59C2×#4111yescharacteristic
255C23×C59C2×#4111yescharacteristic
256C23×C59C2×#4111yescharacteristic
257C23×C59C2×#4111yescharacteristic
258C2×C4×C59—24no—
259C2×C4×C59—24no—
260C2×C4×C59—24no—
261C2×C4×C59—24no—
262C2×C4×C59—24no—
263C2×C4×C59—24no—
264C2×C4×C59—24no—
265C2×C4×C59—24no—
266C2×C4×C59—24no—
267C2×C4×C59—42no—
268C2×C4×C59—42no—
269C2×C4×C59—42no—
270C2×C4×C59—42no—
271C2×C4×C59—42no—
272C2×C4×C59—42no—
273C2×C4×C59—42no—
274C2×C4×C59—42no—
275C2×C4×C59—42no—
276C2×C4×C59—42no—
277C2×C4×C59—42no—
278C2×C4×C59—42no—
279C2×C4×C59—416no—
280C2×C4×C59—416no—
281C2×C4×C59—416no—
282C2×Dic59—24no—
283C2×Dic59—24no—
284C2×Dic59—24no—
285C2×Dic59—24no—
286C2×Dic59—24no—
287C2×Dic59—24no—
288C2×Dic59—24no—
289C2×Dic59—24no—
290C2×Dic59—24no—
291C2×Dic59—24no—
292C2×Dic59—24no—
293C2×Dic59—24no—
294C2×Dic59—42no—
295C2×Dic59—42no—
296C2×Dic59—42no—
297C2×Dic59—42no—
298C2×Dic59—42no—
299C2×Dic59—42no—
300C2×Dic59—42no—
301C2×Dic59—42no—
302C2×Dic59—42no—
303C2×Dic59—42no—
304C2×Dic59—42no—
305C2×Dic59—42no—
306C2×Dic59—42no—
307C2×Dic59—42no—
308C2×Dic59—42no—
309C2×Dic59—42no—
310C2×Dic59—416no—
311C2×Dic59—416no—
312C2×Dic59—416no—
313C2×Dic59—416no—
314C2×#1443—591nomaximal, Sylow
315C22×C59#38318yes—
316C22×C59#38718yes—
317C22×C59#38718yes—
318C22×C59#38718yes—
319C22×C59#38818yes—
320C22×C59#38818yes—
321C22×C59#38818yes—
322C22×C59#39618yes—
323C22×C59#39718yes—
324C22×C59#39718yes—
325C22×C59#39718yes—
326C22×C59#40018yes—
327C22×C59#40018yes—
328C22×C59#40018yes—
329C22×C59#40118yes—
330C22×C59C2×#11711yescharacteristic
331C22×C59C2×#11711yescharacteristic
332C22×C59C2×#11711yescharacteristic
333C22×C59C2×C4×D411yescharacteristic
334C22×C59C2×C4×D411yescharacteristic
335C22×C59C2×C4×D411yescharacteristic
336C22×C59C2×C4×Q811yescharacteristic
337C22×C59C2×#12111yescharacteristic
338C22×C59C2×#12111yescharacteristic
339C22×C59C2×#12111yescharacteristic
340C22×C59C2×C22⋊Q811yescharacteristic
341C22×C59C2×C22⋊Q811yescharacteristic
342C22×C59C2×C22⋊Q811yescharacteristic
343C22×C59C2×#12311yescharacteristic
344C22×C59C2×#12311yescharacteristic
345C22×C59C2×#12311yescharacteristic
346C22×C59C2×#12311yescharacteristic
347C22×C59C2×#12311yescharacteristic
348C22×C59C2×#12311yescharacteristic
349C22×C59C2×#12411yescharacteristic
350C22×C59C2×#12411yescharacteristic
351C22×C59C2×#12411yescharacteristic
352C22×C59C2×#12511yescharacteristic
353C22×C59C2×#12511yescharacteristic
354C22×C59C2×#12511yescharacteristic
355C22×C59C2×#12611yescharacteristic
356C22×C59C2×#12611yescharacteristic
357C22×C59C2×#12611yescharacteristic
358C22×C59C2×#12611yescharacteristic
359C22×C59C2×#12611yescharacteristic
360C22×C59C2×#12611yescharacteristic
361C22×C59C2×#12611yescharacteristic
362C22×C59C2×#12611yescharacteristic
363C22×C59C2×#12611yescharacteristic
364C22×C59C2×#12611yescharacteristic
365C4×C59—44no—
366C4×C59—44no—
367C4×C59—44no—
368Dic59—44no—
369Dic59—44no—
370Dic59—44no—
371Dic59—44no—
372C22×#95—591no—
373C22×#95—591no—
374C22×#95—591no—
375C22×#95—591no—
376C22×#95—591no—
377C22×#95—591no—
378C22×#95D5911yescharacteristic
379#1443—598no—
380C2×C59#1443116yescomplemented
381C2×C59C2×#38311yescharacteristic
382C2×C59C2×#38711yescharacteristic
383C2×C59C2×#38711yescharacteristic
384C2×C59C2×#38711yescharacteristic
385C2×C59C2×#38811yescharacteristic
386C2×C59C2×#38811yescharacteristic
387C2×C59C2×#38811yescharacteristic
388C2×C59C2×#39611yescharacteristic
389C2×C59C2×#39711yescharacteristic
390C2×C59C2×#39711yescharacteristic
391C2×C59C2×#39711yescharacteristic
392C2×C59C2×#40011yescharacteristic
393C2×C59C2×#40011yescharacteristic
394C2×C59C2×#40011yescharacteristic
395C2×C59C2×#40111yescharacteristic
396C24×C4—591no—
397C24×C4—591no—
398C24×C4—591no—
399C24×C4—591no—
400C24×C4C2×D5911yescharacteristic
401C24×C4C2×D5911yescharacteristic
402C24×C4C2×D5911yescharacteristic
403C2×#95—24no—
404C2×#95—598no—
405C2×#95—594no—
406C2×#95—594no—
407C2×#95—594no—
408C2×#95—594no—
409C2×#95—594no—
410C2×#95—594no—
411C2×#95—1184no—
412C2×#95—1184no—
413C2×#95—1184no—
414C2×#95—1184no—
415C2×#95—1184no—
416C2×#95C2×D5914yes—
417C59C2×#144311yescharacteristic, complemented, Sylow
418C25C22×D5911yescharacteristic
419C23×C4—22no—
420C23×C4—22no—
421C23×C4—22no—
422C23×C4—22no—
423C23×C4—22no—
424C23×C4—22no—
425C23×C4—22no—
426C23×C4—22no—
427C23×C4—22no—
428C23×C4—22no—
429C23×C4—22no—
430C23×C4—22no—
431C23×C4—22no—
432C23×C4—22no—
433C23×C4—22no—
434C23×C4—22no—
435C23×C4—22no—
436C23×C4—22no—
437C23×C4—594no—
438C23×C4—594no—
439C23×C4—594no—
440C23×C4—594no—
441C23×C4—592no—
442C23×C4—592no—
443C23×C4—592no—
444C23×C4—592no—
445C23×C4—1182no—
446C23×C4—1182no—
447C23×C4—1182no—
448C23×C4—1182no—
449C23×C4—1182no—
450C23×C4—1182no—
451C23×C4—1182no—
452C23×C4—1182no—
453C23×C4—1182no—
454C23×C4—1182no—
455C23×C4—1182no—
456C23×C4—1182no—
457C23×C4—1182no—
458C23×C4—1182no—
459C23×C4—1182no—
460C23×C4—1182no—
461C23×C4—1182no—
462C23×C4—1182no—
463C23×C4—1182no—
464C23×C4—1182no—
465C23×C4—1182no—
466C23×C4—1182no—
467C23×C4—1182no—
468C23×C4—1182no—
469C23×C4C4×D5914yes—
470C23×C4D23614yes—
471C23×C4C22⋊D5914yes—
472C23×C4C22×D5912yes—
473C23×C4C22×D5912yes—
474C23×C4C22×D5912yes—
475#95—28no—
476#95—5916no—
477#95—1188no—
478#95—1188no—
479#95—1188no—
480#95—1188no—
481#95—1188no—
482C24C2×C4×D5912yes—
483C24C2×D23612yes—
484C24#1174568512yes—
485C24#1174568512yes—
486C24#1174568512yes—
487C24#1174568512yes—
488C24D4×D5912yes—
489C24#1174568712yes—
490C24#1174568712yes—
491C24#1174568712yes—
492C24#1174568712yes—
493C24#1174568712yes—
494C24Q8×D5912yes—
495C24#1174568912yes—
496C24C2×C22⋊D5912yes—
497C24C23×D5911yescharacteristic
498C22×C4—28no—
499C22×C4—28no—
500C22×C4—28no—
501C22×C4—28no—
502C22×C4—28no—
503C22×C4—28no—
504C22×C4—28no—
505C22×C4—28no—
506C22×C4—28no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—44no—
526C22×C4—44no—
527C22×C4—44no—
528C22×C4—44no—
529C22×C4—44no—
530C22×C4—44no—
531C22×C4—44no—
532C22×C4—44no—
533C22×C4—44no—
534C22×C4—44no—
535C22×C4—44no—
536C22×C4—44no—
537C22×C4—594no—
538C22×C4—594no—
539C22×C4—594no—
540C22×C4—594no—
541C22×C4—1188no—
542C22×C4—1188no—
543C22×C4—1188no—
544C22×C4—1188no—
545C22×C4—1188no—
546C22×C4—1188no—
547C22×C4—1188no—
548C22×C4—1188no—
549C22×C4—1188no—
550C22×C4—1188no—
551C22×C4—1188no—
552C22×C4—1188no—
553C22×C4—1182no—
554C22×C4—1182no—
555C22×C4—1182no—
556C22×C4—1182no—
557C22×C4—1182no—
558C22×C4—1182no—
559C22×C4—1182no—
560C22×C4—1182no—
561C22×C4—1182no—
562C22×C4—1182no—
563C22×C4—1182no—
564C22×C4—1182no—
565C22×C4—1182no—
566C22×C4—1182no—
567C22×C4—1182no—
568C22×C4—1182no—
569C22×C4—1182no—
570C22×C4—1182no—
571C22×C4—1182no—
572C22×C4—1182no—
573C22×C4—1182no—
574C22×C4—1182no—
575C22×C4—1182no—
576C22×C4—1182no—
577C22×C4—2364no—
578C22×C4—2364no—
579C22×C4—2364no—
580C22×C4—2364no—
581C22×C4—2364no—
582C22×C4—2364no—
583C22×C4—2364no—
584C22×C4—2364no—
585C22×C4—2364no—
586C22×C4—2364no—
587C22×C4—2364no—
588C22×C4—2364no—
589C22×C4—2364no—
590C22×C4—2364no—
591C22×C4—2364no—
592C22×C4—2364no—
593C22×C4C2×C4×D5914yes—
594C22×C4C2×D23614yes—
595C22×C4C2×C22⋊D5914yes—
596C23#1427368314yes—
597C23#1427368414yes—
598C23#1427368514yes—
599C23(C22⋊D59)⋊C414yes—
600C23C4×C22⋊D5914yes—
601C23C4×D23614yes—
602C23#1427369214yes—
603C23#1427369914yes—
604C23#1427370114yes—
605C23#1427370214yes—
606C23#1427370314yes—
607C23#1427370514yes—
608C23#1427370714yes—
609C23#1427370814yes—
610C23#1427370914yes—
611C23#1427370914yes—
612C23#1427371014yes—
613C23#1427371114yes—
614C23#1427371114yes—
615C23#1427371314yes—
616C23#1427371414yes—
617C23#1427371514yes—
618C23#1427371714yes—
619C23#1427371714yes—
620C23#1427371714yes—
621C23#1427372014yes—
622C23#1427372014yes—
623C23#1427372014yes—
624C23#1427372014yes—
625C23#1427372014yes—
626C23#1427372114yes—
627C23#1427372214yes—
628C23#1427372214yes—
629C23#1427372214yes—
630C23#1427372214yes—
631C23C22×C4×D5911yescharacteristic
632C23C2×D4×D5911yescharacteristic
633C23C22×C22⋊D5911yescharacteristic
634C23C22×D23611yescharacteristic
635C23C2×Q8×D5911yescharacteristic
636C23C2×#1174568711yescharacteristic
637C23C2×#1174568711yescharacteristic
638C23C2×#1174568711yescharacteristic
639C23C2×#1174568711yescharacteristic
640C23C2×#1174568711yescharacteristic
641C23C2×#1174568511yescharacteristic
642C23C2×#1174568511yescharacteristic
643C23C2×#1174568511yescharacteristic
644C23C2×#1174568511yescharacteristic
645C23C2×#1174568911yescharacteristic
646C2×C4—24no—
647C2×C4—24no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—24no—
653C2×C4—24no—
654C2×C4—24no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—416no—
668C2×C4—416no—
669C2×C4—416no—
670C2×C4—1184no—
671C2×C4—1184no—
672C2×C4—1184no—
673C2×C4—1184no—
674C2×C4—1184no—
675C2×C4—1184no—
676C2×C4—1184no—
677C2×C4—1184no—
678C2×C4—1184no—
679C2×C4—1184no—
680C2×C4—1184no—
681C2×C4—1184no—
682C2×C4—2362no—
683C2×C4—2362no—
684C2×C4—2362no—
685C2×C4—2362no—
686C2×C4—2362no—
687C2×C4—2362no—
688C2×C4—2362no—
689C2×C4—2362no—
690C2×C4—2362no—
691C2×C4—2362no—
692C2×C4—2362no—
693C2×C4—2362no—
694C2×C4—2362no—
695C2×C4—2362no—
696C2×C4—2362no—
697C2×C4—2362no—
698C2×C4—23616no—
699C2×C4—23616no—
700C2×C4—23616no—
701C2×C4—23616no—
702C22#1683726918yes—
703C22#1683728318yes—
704C22#1683728418yes—
705C22#1683728718yes—
706C22#1683729318yes—
707C22#1683729418yes—
708C22#1683729618yes—
709C22#1683732418yes—
710C22#1683732718yes—
711C22#1683732918yes—
712C22#1683733018yes—
713C22#1683734018yes—
714C22#1683734218yes—
715C22#1683734318yes—
716C22C59⋊#40118yes—
717C22C2×#1427368311yescharacteristic
718C22C2×#1427368411yescharacteristic
719C22C2×#1427368511yescharacteristic
720C22C2×(C22⋊D59)⋊C411yescharacteristic
721C22C2×C4×C22⋊D5911yescharacteristic
722C22C2×C4×D23611yescharacteristic
723C22C2×#1427369211yescharacteristic
724C22C2×#1427369911yescharacteristic
725C22C2×#1427370111yescharacteristic
726C22C2×#1427370211yescharacteristic
727C22C2×#1427370311yescharacteristic
728C22C2×#1427370511yescharacteristic
729C22C2×#1427370711yescharacteristic
730C22C2×#1427370811yescharacteristic
731C22C2×#1427370911yescharacteristic
732C22C2×#1427370911yescharacteristic
733C22C2×#1427371011yescharacteristic
734C22C2×#1427371111yescharacteristic
735C22C2×#1427371111yescharacteristic
736C22C2×#1427371311yescharacteristic
737C22C2×#1427371411yescharacteristic
738C22C2×#1427371511yescharacteristic
739C22C2×#1427371711yescharacteristic
740C22C2×#1427371711yescharacteristic
741C22C2×#1427371711yescharacteristic
742C22C2×#1427372011yescharacteristic
743C22C2×#1427372011yescharacteristic
744C22C2×#1427372011yescharacteristic
745C22C2×#1427372011yescharacteristic
746C22C2×#1427372011yescharacteristic
747C22C2×#1427372111yescharacteristic
748C22C2×#1427372211yescharacteristic
749C22C2×#1427372211yescharacteristic
750C22C2×#1427372211yescharacteristic
751C22C2×#1427372211yescharacteristic
752C4—44no—
753C4—44no—
754C4—44no—
755C4—2364no—
756C4—2364no—
757C4—2364no—
758C4—2364no—
759C2#21422356116yesdirect product factor
760C2C2×#1683726911yescharacteristic
761C2C2×#1683728311yescharacteristic
762C2C2×#1683728411yescharacteristic
763C2C2×#1683728711yescharacteristic
764C2C2×#1683729311yescharacteristic
765C2C2×#1683729411yescharacteristic
766C2C2×#1683729611yescharacteristic
767C2C2×#1683732411yescharacteristic
768C2C2×#1683732711yescharacteristic
769C2C2×#1683732911yescharacteristic
770C2C2×#1683733011yescharacteristic
771C2C2×#1683734011yescharacteristic
772C2C2×#1683734211yescharacteristic
773C2C2×#1683734311yescharacteristic
774C2C2×C59⋊#40111yescharacteristic
subgroupG/H
centerC25C22×D59
commutatorC23×C59C23×C4
FrattiniC24C23×D59
FittingC22×#95×C59C2
socle, prime radicalC25×C59C23
cosocleC24×C59C24
hypercenterC22×#95D59
hypocenterC59C2×#1443
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C25 ◁ C22×#95

Complements

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

NH ≅ G/Ntype
7. #21422356C2direct (N × H)
18. C2×C59⋊#95C4semidirect
67. C59⋊#95C2×C4semidirect
380. C2×C59#1443semidirect
417. C59C2×#1443semidirect
759. C2#21422356direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C59⋊#952
#214223562
C22×#95×C592
C2×#144359