Finite Group Databasebeta

← C4×#16837276 #28509857

Subgroups — C4×#16837276 #28509857

Order 15104.

2782 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C42×D59C211yesmaximal, characteristic
2C2×#16837276C212yesmaximal
3C2×C4×Dic59⋊C4C211yesmaximal, characteristic, complemented
4C2×C4×C4⋊Dic59C211yesmaximal, characteristic, complemented
5C2×C4×(C2×D59)⋊C4C211yesmaximal, characteristic
6C2×C4×(C2×D59)⋊C4C211yesmaximal, characteristic
7#21422331C212yesmaximal, complemented
8#21422330C212yesmaximal, complemented
9(C2×D59)⋊#95C212yesmaximal
10C4×C59⋊#95C211yesmaximal, characteristic, complemented
11C4×#95×C59C211yesmaximal, characteristic, complemented
12C23×C4×D59C2212yes—
13C23×C4×D59C2211yescharacteristic
14C22×C4⋊Dic59C2212yes—
15C22×Dic59⋊C4C2212yes—
16C22×(C2×D59)⋊C4C2212yes—
17C22×(C2×D59)⋊C4C2211yescharacteristic
18C22×(C2×D59)⋊C4C2211yescharacteristic
19C22×C4×Dic59C2211yescharacteristic
20C22×C4×Dic59C2212yes—
21C22×C4×Dic59C2211yescharacteristic
22C22×C4×Dic59C2211yescharacteristic
23C2×C42×D59—24no—
24C2×C42×D59—24no—
25C2×C42×D59—24no—
26#16837276C4116yesdirect product factor
27C4×Dic59⋊C4—24no—
28C4×C4⋊Dic59—24no—
29C4×(C2×D59)⋊C4—24no—
30C4×(C2×D59)⋊C4C418yescomplemented
31C2×C59⋊#95C2212yes—
32C2×C59⋊#95C2212yes—
33C2×C59⋊#95C2212yes—
34C2×C59⋊#95C2212yes—
35C2×C59⋊#95C2212yes—
36C2×C59⋊#95C2211yescharacteristic
37C2×C59⋊#95C2211yescharacteristic
38C22×C42×C59C2211yescharacteristic
39C22×C42×C59C2211yescharacteristic
40C22×C42×C59C2211yescharacteristic
41C2×#95×C59C2212yes—
42C2×#95×C59C2212yes—
43C24×D59C2311yescharacteristic
44C23×Dic59C2311yescharacteristic
45C23×Dic59C2312yes—
46C23×Dic59C2311yescharacteristic
47C23×Dic59C2311yescharacteristic
48C23×Dic59C2312yes—
49C22×C4×D59—24no—
50C22×C4×D59—24no—
51C22×C4×D59—24no—
52C22×C4×D59—22no—
53C22×C4×D59—22no—
54C22×C4×D59—24no—
55C22×C4×D59—22no—
56C22×C4×D59—22no—
57C22×C4×D59—24no—
58C22×C4×D59—24no—
59C22×C4×D59C2×C418yes—
60C22×C4×D59C2×C414yes—
61C22×C4×D59D414yes—
62C22×C4×D59Q814yes—
63C2×C4⋊Dic59—24no—
64C2×C4⋊Dic59—24no—
65C2×C4⋊Dic59C2×C418yescomplemented
66C2×Dic59⋊C4—24no—
67C2×Dic59⋊C4—24no—
68C2×Dic59⋊C4C2×C418yescomplemented
69C2×(C2×D59)⋊C4—24no—
70C2×(C2×D59)⋊C4—24no—
71C2×(C2×D59)⋊C4—24no—
72C2×(C2×D59)⋊C4C2×C414yes—
73C2×(C2×D59)⋊C4C2×C418yes—
74C2×(C2×D59)⋊C4C2×C414yes—
75C2×(C2×D59)⋊C4C2×C418yes—
76C2×C4×Dic59—22no—
77C2×C4×Dic59—24no—
78C2×C4×Dic59—22no—
79C2×C4×Dic59—22no—
80C2×C4×Dic59—22no—
81C2×C4×Dic59—24no—
82C2×C4×Dic59—24no—
83C2×C4×Dic59—22no—
84C2×C4×Dic59—22no—
85C2×C4×Dic59—22no—
86C2×C4×Dic59C2×C414yescomplemented
87C2×C4×Dic59D414yes—
88C42×D59—232no—
89C59⋊#95—24no—
90C59⋊#95—24no—
91C59⋊#95—24no—
92C59⋊#95—24no—
93C59⋊#95C2×C414yescomplemented
94C59⋊#95C2×C414yescomplemented
95C59⋊#95C2×C418yescomplemented
96C23×C4×C59C2311yescharacteristic
97C23×C4×C59C2312yes—
98C23×C4×C59C2311yescharacteristic
99C23×C4×C59C2312yes—
100C23×C4×C59C2311yescharacteristic
101C2×C42×C59—22no—
102C2×C42×C59—22no—
103C2×C42×C59—22no—
104C2×C42×C59—22no—
105C2×C42×C59—22no—
106C2×C42×C59—22no—
107C2×C42×C59—22no—
108C2×C42×C59C2×C414yescomplemented
109C2×C42×C59D414yes—
110#95×C59—24no—
111#95×C59C2×C418yescomplemented
112C24×C59C2411yescharacteristic
113C23×D59—21no—
114C23×D59—21no—
115C23×D59—21no—
116C23×D59—21no—
117C23×D59—22no—
118C23×D59—22no—
119C23×D59C22×C412yes—
120C23×D59C22×C414yes—
121C23×D59C2×D412yes—
122C23×D59C2×Q812yes—
123C23×D59#4114yes—
124C22×C4×C59—22no—
125C22×C4×C59—22no—
126C22×C4×C59—21no—
127C22×C4×C59—21no—
128C22×C4×C59—22no—
129C22×C4×C59—22no—
130C22×C4×C59—22no—
131C22×C4×C59—21no—
132C22×C4×C59—22no—
133C22×C4×C59—22no—
134C22×C4×C59—22no—
135C22×C4×C59—21no—
136C22×C4×C59—22no—
137C22×C4×C59—22no—
138C22×C4×C59—22no—
139C22×C4×C59—22no—
140C22×C4×C59—22no—
141C22×C4×C59C22×C414yes—
142C22×C4×C59C22×C412yes—
143C22×C4×C59C22×C414yes—
144C22×C4×C59C22×C412yes—
145C22×C4×C59C22×C414yes—
146C22×C4×C59C22×C412yes—
147C22×C4×C59C2×D414yes—
148C22×C4×C59C2×D412yes—
149C22×C4×C59C2×D412yes—
150C22×C4×C59C2×D412yes—
151C22×C4×C59C2×Q812yes—
152C22×C4×C59#4114yes—
153C22×C4×C59#4112yes—
154C22×C4×C59#4112yes—
155C22×Dic59—21no—
156C22×Dic59—21no—
157C22×Dic59—22no—
158C22×Dic59—22no—
159C22×Dic59—21no—
160C22×Dic59—21no—
161C22×Dic59—22no—
162C22×Dic59—21no—
163C22×Dic59—21no—
164C22×Dic59—22no—
165C22×Dic59—22no—
166C22×Dic59—21no—
167C22×Dic59—22no—
168C22×Dic59—22no—
169C22×Dic59—22no—
170C22×Dic59—22no—
171C22×Dic59—21no—
172C22×Dic59—22no—
173C22×Dic59—22no—
174C22×Dic59—22no—
175C22×Dic59—22no—
176C22×Dic59C22×C412yes—
177C22×Dic59C22×C414yes—
178C22×Dic59C22×C412yes—
179C22×Dic59C22×C414yes—
180C22×Dic59C22×C412yes—
181C22×Dic59C22×C414yes—
182C22×Dic59C2×D412yes—
183C22×Dic59C2×D414yes—
184C22×Dic59C2×Q812yes—
185C22×Dic59#4114yes—
186C2×C4×D59—216no—
187C2×C4×D59—216no—
188C2×C4×D59—216no—
189C2×C4×D59—216no—
190C2×C4×D59—216no—
191C2×C4×D59—216no—
192C2×C4×D59—28no—
193C2×C4×D59—28no—
194C2×C4×D59—28no—
195C2×C4×D59—28no—
196C2×C4×D59—28no—
197C2×C4×D59—28no—
198C2×C4×D59—216no—
199C2×C4×D59C4⋊C4116yescomplemented
200C42×C59—28no—
201C42×C59—28no—
202C42×C59—44no—
203(C2×D59)⋊C4—28no—
204(C2×D59)⋊C4—216no—
205(C2×D59)⋊C4C42116yescomplemented
206C4⋊Dic59—216no—
207Dic59⋊C4—216no—
208C4×Dic59—216no—
209C4×Dic59—28no—
210C4×Dic59—28no—
211C4×Dic59—44no—
212C23×C59C23×C411yescharacteristic
213C23×C59C23×C412yes—
214C23×C59C22×D411yescharacteristic
215C23×C59C22×D411yescharacteristic
216C23×C59C22×D411yescharacteristic
217C23×C59C22×Q811yescharacteristic
218C23×C59C2×#4112yes—
219C23×C59C2×#4112yes—
220C23×C59C2×#4111yescharacteristic
221C23×C59C2×#4111yescharacteristic
222C23×C59C2×#4112yes—
223C22×D59—24no—
224C22×D59—22no—
225C22×D59—22no—
226C22×D59—24no—
227C22×D59—24no—
228C22×D59—22no—
229C22×D59—22no—
230C22×D59—24no—
231C22×D59—22no—
232C22×D59—22no—
233C22×D59—22no—
234C22×D59—22no—
235C22×D59—24no—
236C22×D59—24no—
237C22×D59—24no—
238C22×D59—24no—
239C22×D59—24no—
240C22×D59—24no—
241C22×D59C2×C4214yes—
242C22×D59C2×C4⋊C414yes—
243C22×D59#11714yes—
244C22×D59C4×D418yes—
245C22×D59C4×Q818yes—
246C2×C4×C59—24no—
247C2×C4×C59—22no—
248C2×C4×C59—24no—
249C2×C4×C59—24no—
250C2×C4×C59—24no—
251C2×C4×C59—22no—
252C2×C4×C59—24no—
253C2×C4×C59—24no—
254C2×C4×C59—24no—
255C2×C4×C59—24no—
256C2×C4×C59—22no—
257C2×C4×C59—24no—
258C2×C4×C59—22no—
259C2×C4×C59—24no—
260C2×C4×C59—22no—
261C2×C4×C59—24no—
262C2×C4×C59—42no—
263C2×C4×C59—42no—
264C2×C4×C59—42no—
265C2×C4×C59—42no—
266C2×C4×C59—42no—
267C2×C4×C59—42no—
268C2×C4×C59C2×C4214yescomplemented
269C2×C4×C59C2×C4⋊C414yes—
270C2×C4×C59C4×D414yes—
271C2×C4×C59C4×D418yes—
272C2×C4×C59C4×D414yes—
273C2×C4×C59#12014yes—
274C2×C4×C59C22⋊Q814yes—
275C2×C4×C59C22⋊Q814yes—
276C2×C4×C59#12314yes—
277C2×Dic59—22no—
278C2×Dic59—24no—
279C2×Dic59—24no—
280C2×Dic59—22no—
281C2×Dic59—22no—
282C2×Dic59—24no—
283C2×Dic59—22no—
284C2×Dic59—24no—
285C2×Dic59—22no—
286C2×Dic59—24no—
287C2×Dic59—22no—
288C2×Dic59—22no—
289C2×Dic59—22no—
290C2×Dic59—24no—
291C2×Dic59—24no—
292C2×Dic59—24no—
293C2×Dic59—22no—
294C2×Dic59—22no—
295C2×Dic59—24no—
296C2×Dic59—24no—
297C2×Dic59—24no—
298C2×Dic59—22no—
299C2×Dic59—42no—
300C2×Dic59—42no—
301C2×Dic59—42no—
302C2×Dic59—42no—
303C2×Dic59—42no—
304C2×Dic59—42no—
305C2×Dic59C2×C4214yescomplemented
306C2×Dic59C2×C4⋊C414yes—
307C2×Dic59C4×D418yes—
308C4×D59—264no—
309C4×D59—232no—
310C4×#385—591nomaximal, Sylow
311C22×C59C22×C4211yescharacteristic
312C22×C59C22×C4⋊C411yescharacteristic
313C22×C59C2×#11711yescharacteristic
314C22×C59C2×C4×D412yes—
315C22×C59C2×C4×D412yes—
316C22×C59C2×C4×D411yescharacteristic
317C22×C59C2×C4×D411yescharacteristic
318C22×C59C2×C4×D412yes—
319C22×C59C2×C4×Q812yes—
320C22×C59C4×#4112yes—
321C22×C59C4×#4111yescharacteristic
322C22×C59C4×#4111yescharacteristic
323C22×C59C4×#4112yes—
324C22×C59C2×#12011yescharacteristic
325C22×C59C2×C22⋊Q811yescharacteristic
326C22×C59C2×C22⋊Q811yescharacteristic
327C22×C59C2×#12311yescharacteristic
328C22×C59#52512yes—
329C22×C59#52512yes—
330C22×C59#52512yes—
331C22×C59#52912yes—
332C22×C59#52912yes—
333C22×C59#53312yes—
334C2×D59—24no—
335C2×D59—24no—
336C2×D59—24no—
337C2×D59—24no—
338C2×D59—24no—
339C2×D59—24no—
340C2×D59—28no—
341C2×D59—28no—
342C2×D59—28no—
343C2×D59—28no—
344C2×D59C4×C4⋊C418yescomplemented
345C4×C59—24no—
346C4×C59—28no—
347C4×C59—42no—
348C4×C59—44no—
349C4×C59#38518yescomplemented
350Dic59—24no—
351Dic59—24no—
352Dic59—28no—
353Dic59—42no—
354Dic59—44no—
355C23×C42—591no—
356C2×#385—592no—
357C2×C4×C4⋊C4—591no—
358C2×C4×C4⋊C4—591no—
359C2×C4×C22⋊C4—591no—
360C2×C4×C22⋊C4—591no—
361#1436—592no—
362#1436—592no—
363C22⋊#95—592no—
364C4×#95—591no—
365C4×#95D5911yescharacteristic, complemented
366C2×C59C2×C4×C4⋊C411yescharacteristic
367C2×C59C42×D411yescharacteristic
368C2×C59C42×D411yescharacteristic
369C2×C59C2×#38511yescharacteristic
370C2×C59#229011yescharacteristic
371C2×C59#229011yescharacteristic
372C2×C59#229611yescharacteristic
373C2×C59C4×#12012yes—
374C2×C59C4×#12312yes—
375C2×C59C4×C22⋊Q812yes—
376C2×C59C4×C22⋊Q812yes—
377D59—28no—
378C24×C4—591no—
379C24×C4—592no—
380C22×C4⋊C4—592no—
381C22×C4⋊C4—592no—
382C22×C22⋊C4—591no—
383C22×C22⋊C4—591no—
384C22×C22⋊C4—592no—
385C22×C42—591no—
386C22×C42—591no—
387C22×C42—592no—
388C22×C42—591no—
389C22×C42—1184no—
390C22×C42—1184no—
391C22×C42—1184no—
392C22×C42C2×D5911yescharacteristic
393C22×C42C2×D5911yescharacteristic
394C22×C42C2×D5911yescharacteristic
395#385—5916no—
396C4×C4⋊C4—1184no—
397C4×C4⋊C4—1184no—
398C4×C22⋊C4—598no—
399C4×C22⋊C4—1184no—
400C2×#95—592no—
401C2×#95—591no—
402C2×#95—591no—
403C2×#95—592no—
404C2×#95—592no—
405C2×#95—592no—
406C2×#95—592no—
407C2×#95C2×D5912yes—
408C2×#95C2×D5912yes—
409C59C4×#38511yescharacteristic, complemented, Sylow
410C25—591no—
411C23×C4—591no—
412C23×C4—592no—
413C23×C4—591no—
414C23×C4—594no—
415C23×C4—594no—
416C23×C4—594no—
417C23×C4—592no—
418C23×C4—591no—
419C23×C4—598no—
420C23×C4—1184no—
421C23×C4—1184no—
422C23×C4—1184no—
423C23×C4—1184no—
424C23×C4—1184no—
425C23×C4—1182no—
426C23×C4—1184no—
427C23×C4—1182no—
428C23×C4—1182no—
429C23×C4—1182no—
430C23×C4C22×D5911yescharacteristic
431C23×C4C22×D5912yes—
432C23×C4C22×D5911yescharacteristic
433C23×C4C22×D5912yes—
434C23×C4C22×D5911yescharacteristic
435C2×C4⋊C4—598no—
436C2×C4⋊C4—598no—
437C2×C4⋊C4—1184no—
438C2×C4⋊C4—1184no—
439C2×C4⋊C4—1184no—
440C2×C4⋊C4—1184no—
441C2×C22⋊C4—594no—
442C2×C22⋊C4—598no—
443C2×C22⋊C4—594no—
444C2×C22⋊C4—598no—
445C2×C22⋊C4—1184no—
446C2×C22⋊C4—1184no—
447C2×C22⋊C4—1184no—
448C2×C42—22no—
449C2×C42—22no—
450C2×C42—22no—
451C2×C42—22no—
452C2×C42—22no—
453C2×C42—22no—
454C2×C42—22no—
455C2×C42—594no—
456C2×C42—594no—
457C2×C42—11832no—
458C2×C42—1184no—
459C2×C42—1184no—
460C2×C42—1182no—
461C2×C42—1184no—
462C2×C42—1182no—
463C2×C42—1182no—
464C2×C42—1182no—
465C2×C42—1182no—
466C2×C42—1182no—
467C2×C42—1182no—
468C2×C42C4×D5914yescomplemented
469C2×C42D23614yes—
470#95—24no—
471#95—594no—
472#95—594no—
473#95—598no—
474#95—1184no—
475#95—1184no—
476#95—1184no—
477#95—1184no—
478#95C4×D5918yescomplemented
479C24—592no—
480C24—594no—
481C24—592no—
482C24—592no—
483C24—594no—
484C24—1181no—
485C24—1181no—
486C24—1182no—
487C24—1181no—
488C24—1181no—
489C24—1182no—
490C24C23×D5911yescharacteristic
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—21no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—592no—
509C22×C4—592no—
510C22×C4—594no—
511C22×C4—594no—
512C22×C4—592no—
513C22×C4—594no—
514C22×C4—592no—
515C22×C4—594no—
516C22×C4—5916no—
517C22×C4—592no—
518C22×C4—594no—
519C22×C4—11816no—
520C22×C4—11816no—
521C22×C4—11816no—
522C22×C4—11816no—
523C22×C4—11816no—
524C22×C4—11816no—
525C22×C4—1181no—
526C22×C4—1182no—
527C22×C4—1181no—
528C22×C4—1182no—
529C22×C4—1181no—
530C22×C4—1182no—
531C22×C4—1181no—
532C22×C4—1181no—
533C22×C4—1182no—
534C22×C4—1181no—
535C22×C4—1182no—
536C22×C4—1188no—
537C22×C4—11816no—
538C22×C4—1188no—
539C22×C4—1188no—
540C22×C4—1188no—
541C22×C4—1188no—
542C22×C4—1188no—
543C22×C4—1182no—
544C22×C4—1182no—
545C22×C4—1181no—
546C22×C4—1182no—
547C22×C4—1182no—
548C22×C4—1182no—
549C22×C4—1182no—
550C22×C4—1182no—
551C22×C4—1181no—
552C22×C4—1182no—
553C22×C4C2×C4×D5914yes—
554C22×C4C2×C4×D5912yes—
555C22×C4C2×C4×D5912yes—
556C22×C4C2×C4×D5914yes—
557C22×C4C2×C4×D5914yes—
558C22×C4C2×C4×D5912yes—
559C22×C4C2×D23614yes—
560C22×C4C2×D23612yes—
561C22×C4#1174568514yes—
562C22×C4#1174568512yes—
563C22×C4D4×D5912yes—
564C22×C4D4×D5912yes—
565C22×C4#1174568712yes—
566C22×C4Q8×D5912yes—
567C4⋊C4—11816no—
568C4⋊C4—11816no—
569C22⋊C4—5916no—
570C22⋊C4—1188no—
571C22⋊C4—11816no—
572C42—28no—
573C42—28no—
574C42—44no—
575C42—11816no—
576C42—1188no—
577C42—1188no—
578C42—2364no—
579C23—594no—
580C23—594no—
581C23—594no—
582C23—598no—
583C23—598no—
584C23—1182no—
585C23—1182no—
586C23—1182no—
587C23—1182no—
588C23—1184no—
589C23—1184no—
590C23—1184no—
591C23—1184no—
592C23—1184no—
593C23—1184no—
594C23—1184no—
595C23—1182no—
596C23—1182no—
597C23—1184no—
598C23—1184no—
599C23—1182no—
600C23—1182no—
601C23—1184no—
602C23C22×C4×D5911yescharacteristic
603C23C22×C4×D5912yes—
604C23C2×D4×D5911yescharacteristic
605C23C2×D4×D5911yescharacteristic
606C23C22×D23611yescharacteristic
607C23C2×Q8×D5911yescharacteristic
608C23#41×D5912yes—
609C23#41×D5912yes—
610C23C2×#1174568711yescharacteristic
611C23C2×#1174568511yescharacteristic
612C23C2×#1174568512yes—
613C2×C4—24no—
614C2×C4—24no—
615C2×C4—24no—
616C2×C4—24no—
617C2×C4—24no—
618C2×C4—24no—
619C2×C4—24no—
620C2×C4—22no—
621C2×C4—24no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—24no—
625C2×C4—22no—
626C2×C4—24no—
627C2×C4—22no—
628C2×C4—24no—
629C2×C4—42no—
630C2×C4—42no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—594no—
636C2×C4—594no—
637C2×C4—598no—
638C2×C4—11864no—
639C2×C4—1182no—
640C2×C4—1184no—
641C2×C4—1182no—
642C2×C4—1182no—
643C2×C4—1182no—
644C2×C4—1184no—
645C2×C4—1184no—
646C2×C4—1184no—
647C2×C4—1184no—
648C2×C4—1182no—
649C2×C4—1182no—
650C2×C4—1184no—
651C2×C4—1182no—
652C2×C4—1184no—
653C2×C4—1182no—
654C2×C4—1184no—
655C2×C4—11832no—
656C2×C4—1182no—
657C2×C4—1184no—
658C2×C4—1184no—
659C2×C4—1182no—
660C2×C4—1184no—
661C2×C4—1182no—
662C2×C4—2362no—
663C2×C4—2362no—
664C2×C4—2362no—
665C2×C4—2362no—
666C2×C4—2362no—
667C2×C4—2362no—
668C2×C4C42×D5914yescomplemented
669C2×C4C4⋊C4×D5914yes—
670C2×C4(C22⋊D59)⋊C414yes—
671C2×C4C4×D23618yes—
672C2×C4C4×D23614yes—
673C2×C4#1427369714yes—
674C2×C4#1427370514yes—
675C2×C4#1427370714yes—
676C2×C4#1427370914yes—
677C22—598no—
678C22—1184no—
679C22—1184no—
680C22—1184no—
681C22—1184no—
682C22—1184no—
683C22—1184no—
684C22—1188no—
685C22—1188no—
686C22—1188no—
687C22—1188no—
688C22C2×C42×D5911yescharacteristic
689C22C2×C4⋊C4×D5911yescharacteristic
690C22#117×D5911yescharacteristic
691C22C4×D4×D5912yes—
692C22C4×D4×D5912yes—
693C22C2×(C22⋊D59)⋊C411yescharacteristic
694C22C2×C4×D23611yescharacteristic
695C22C2×C4×D23612yes—
696C22C4×Q8×D5912yes—
697C22C4×#1174568712yes—
698C22#1683787011yescharacteristic
699C22C4×#1174568511yescharacteristic
700C22C4×#1174568512yes—
701C22C2×#1427369711yescharacteristic
702C22C2×#1427370511yescharacteristic
703C22C2×#1427370711yescharacteristic
704C22C2×#1427370911yescharacteristic
705C22#1683791112yes—
706C22#1683791112yes—
707C22#1683791412yes—
708C22#1683793012yes—
709C22#1683793412yes—
710C22#1683795612yes—
711C4—24no—
712C4—28no—
713C4—42no—
714C4—44no—
715C4—1184no—
716C4—1184no—
717C4—1188no—
718C4—2362no—
719C4—2364no—
720C4#1683727618yesdirect product factor
721C2—1188no—
722C2C4×C4⋊C4×D5911yescharacteristic
723C2C4×(C22⋊D59)⋊C411yescharacteristic
724C2C42×D23611yescharacteristic
725C2C2×#1683727611yescharacteristic
726C2#2142654011yescharacteristic
727C2#2142654211yescharacteristic
728C2#2142657611yescharacteristic
729C2C4×#1427369712yes—
730C2C4×#1427370912yes—
731C2C4×#1427370512yes—
732C2C4×#1427370712yes—
subgroupG/H
centerC23×C4C22×D59
commutatorC22×C59C22×C42
FrattiniC24C23×D59
FittingC4×#95×C59C2
socle, cosocleC24×C59C24
prime radicalC24×D59C23
hypercenterC4×#95D59
hypocenterC59C4×#385
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C23×C4 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
3. C2×C4×Dic59⋊C4C2semidirect
4. C2×C4×C4⋊Dic59C2semidirect
7. #21422331C2semidirect
8. #21422330C2semidirect
10. C4×C59⋊#95C2semidirect
11. C4×#95×C59C2semidirect
26. #16837276C4direct (N × H)
30. C4×(C2×D59)⋊C4C4semidirect
65. C2×C4⋊Dic59C2×C4semidirect
68. C2×Dic59⋊C4C2×C4semidirect
86. C2×C4×Dic59C2×C4semidirect
93. C59⋊#95C2×C4semidirect
94. C59⋊#95C2×C4semidirect
95. C59⋊#95C2×C4semidirect
108. C2×C42×C59C2×C4semidirect
111. #95×C59C2×C4semidirect
199. C2×C4×D59C4⋊C4semidirect
205. (C2×D59)⋊C4C42semidirect
268. C2×C4×C59C2×C42semidirect
305. C2×Dic59C2×C42semidirect
344. C2×D59C4×C4⋊C4semidirect
349. C4×C59#385semidirect
365. C4×#95D59semidirect
409. C59C4×#385semidirect
468. C2×C42C4×D59semidirect
478. #95C4×D59semidirect
668. C2×C4C42×D59semidirect
720. C4#16837276direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C42×D592
C2×#168372762
C2×C4×Dic59⋊C42
C2×C4×C4⋊Dic592
C2×C4×(C2×D59)⋊C42
#214223312
#214223302
(C2×D59)⋊#952
C4×C59⋊#952
C4×#95×C592
C4×#38559