Finite Group Databasebeta

← C59×#14730 #28426839

Subgroups — C59×#14730 #28426839

Order 15104.

2578 conjugacy classes of subgroups.

The subgroup lattice has 1346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D4×C59C211yesmaximal, characteristic, complemented
2C2×C59×#394C211yesmaximal, characteristic, complemented
3C2×C59×#392C211yesmaximal, characteristic
4C2×C59×#386C211yesmaximal, characteristic, complemented
5C2×C59×#386C211yesmaximal, characteristic, complemented
6C2×C59×#381C211yesmaximal, characteristic, complemented
7C59×#1442C211yesmaximal, characteristic, complemented
8C59×#1440C211yesmaximal, characteristic, complemented
9C59×#1439C211yesmaximal, characteristic, complemented
10C59×#1439C211yesmaximal, characteristic, complemented
11C59×#1438C211yesmaximal, characteristic, complemented
12C59×#1438C211yesmaximal, characteristic, complemented
13C59×#1437C211yesmaximal, characteristic, complemented
14C59×#1436C211yesmaximal, characteristic, complemented
15C59×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C59C2211yescharacteristic
17C23×D4×C59C2211yescharacteristic
18C23×D4×C59C2211yescharacteristic
19C24×C4×C59C2211yescharacteristic
20C24×C4×C59C2211yescharacteristic
21C2×C4×D4×C59—24no—
22C2×C4×D4×C59—24no—
23C2×C4×D4×C59—24no—
24C22×C4⋊C4×C59C2211yescharacteristic
25C22×C4⋊C4×C59C2211yescharacteristic
26C22×C22⋊C4×C59C2211yescharacteristic
27C22×C22⋊C4×C59C2211yescharacteristic
28C22×C22⋊C4×C59C2211yescharacteristic
29C22×C22⋊C4×C59C2211yescharacteristic
30C22×C22⋊C4×C59C2211yescharacteristic
31C22×C22⋊C4×C59C2211yescharacteristic
32C22×C22⋊C4×C59C2211yescharacteristic
33C22×C22⋊C4×C59C2211yescharacteristic
34C22×C22⋊C4×C59C2211yescharacteristic
35C22×C22⋊C4×C59C2211yescharacteristic
36C22×C22⋊C4×C59C2211yescharacteristic
37C22×C22⋊C4×C59C2211yescharacteristic
38C22×C22⋊C4×C59C2211yescharacteristic
39C22×C42×C59C2211yescharacteristic
40C59×#394—24no—
41C59×#392—24no—
42C59×#386—24no—
43C59×#386—24no—
44C59×#381—24no—
45C2×#95×C59C2211yescharacteristic
46C2×#95×C59C2211yescharacteristic
47C2×#95×C59C2211yescharacteristic
48C2×#95×C59C2211yescharacteristic
49C2×#95×C59C2211yescharacteristic
50C2×#95×C59C2211yescharacteristic
51C2×#95×C59C2211yescharacteristic
52C2×#95×C59C2211yescharacteristic
53C2×#95×C59C2211yescharacteristic
54C2×#95×C59C2211yescharacteristic
55C2×#95×C59C2211yescharacteristic
56C2×#95×C59C2211yescharacteristic
57C2×#95×C59C2211yescharacteristic
58C2×#95×C59C2211yescharacteristic
59C25×C59C2311yescharacteristic
60C25×C59C2311yescharacteristic
61C25×C59C2311yescharacteristic
62C22×D4×C59—22no—
63C22×D4×C59—22no—
64C22×D4×C59—22no—
65C22×D4×C59—22no—
66C22×D4×C59—22no—
67C22×D4×C59—22no—
68C22×D4×C59—22no—
69C22×D4×C59—22no—
70C22×D4×C59—22no—
71C22×D4×C59—22no—
72C22×D4×C59—22no—
73C22×D4×C59—22no—
74C22×D4×C59—22no—
75C22×D4×C59—22no—
76C22×D4×C59—22no—
77C22×D4×C59—22no—
78C22×D4×C59—41no—
79C22×D4×C59—41no—
80C22×D4×C59—41no—
81C22×D4×C59—41no—
82C22×D4×C59D414yes—
83C23×C4×C59—22no—
84C23×C4×C59—22no—
85C23×C4×C59—22no—
86C23×C4×C59—22no—
87C23×C4×C59—22no—
88C23×C4×C59—22no—
89C23×C4×C59—22no—
90C23×C4×C59—22no—
91C23×C4×C59—22no—
92C23×C4×C59—41no—
93C23×C4×C59—41no—
94C23×C4×C59—41no—
95C23×C4×C59—41no—
96C23×C4×C59D414yescomplemented
97C23×C4×C59C2311yescharacteristic
98C23×C4×C59C2311yescharacteristic
99C23×C4×C59C2311yescharacteristic
100C23×C4×C59C2311yescharacteristic
101C23×C4×C59C2311yescharacteristic
102C23×C4×C59C2311yescharacteristic
103C23×C4×C59C2311yescharacteristic
104C23×C4×C59C2311yescharacteristic
105C23×C4×C59C2311yescharacteristic
106C23×C4×C59C2311yescharacteristic
107C23×C4×C59C2311yescharacteristic
108C23×C4×C59C2311yescharacteristic
109C4×D4×C59—232no—
110C2×C4⋊C4×C59—22no—
111C2×C4⋊C4×C59—22no—
112C2×C4⋊C4×C59—22no—
113C2×C4⋊C4×C59—22no—
114C2×C4⋊C4×C59—22no—
115C2×C4⋊C4×C59—41no—
116C2×C22⋊C4×C59—22no—
117C2×C22⋊C4×C59—22no—
118C2×C22⋊C4×C59—22no—
119C2×C22⋊C4×C59—22no—
120C2×C22⋊C4×C59—22no—
121C2×C22⋊C4×C59—22no—
122C2×C22⋊C4×C59—22no—
123C2×C22⋊C4×C59—22no—
124C2×C22⋊C4×C59—22no—
125C2×C22⋊C4×C59—22no—
126C2×C22⋊C4×C59—22no—
127C2×C22⋊C4×C59—22no—
128C2×C22⋊C4×C59—22no—
129C2×C22⋊C4×C59—22no—
130C2×C22⋊C4×C59—22no—
131C2×C22⋊C4×C59—22no—
132C2×C22⋊C4×C59—22no—
133C2×C22⋊C4×C59—22no—
134C2×C22⋊C4×C59—22no—
135C2×C22⋊C4×C59—22no—
136C2×C22⋊C4×C59—22no—
137C2×C22⋊C4×C59—22no—
138C2×C22⋊C4×C59—22no—
139C2×C22⋊C4×C59—22no—
140C2×C22⋊C4×C59—22no—
141C2×C22⋊C4×C59—22no—
142C2×C22⋊C4×C59—41no—
143C2×C22⋊C4×C59—41no—
144C2×C22⋊C4×C59—41no—
145C2×C22⋊C4×C59—41no—
146C2×C22⋊C4×C59—41no—
147C2×C22⋊C4×C59—41no—
148C2×C22⋊C4×C59—41no—
149C2×C22⋊C4×C59—41no—
150C2×C22⋊C4×C59—41no—
151C2×C22⋊C4×C59—41no—
152C2×C22⋊C4×C59—41no—
153C2×C22⋊C4×C59—41no—
154C2×C22⋊C4×C59D414yescomplemented
155C2×C42×C59—22no—
156C2×C42×C59—22no—
157C2×C42×C59—22no—
158#95×C59—22no—
159#95×C59—22no—
160#95×C59—22no—
161#95×C59—22no—
162#95×C59—22no—
163#95×C59—22no—
164#95×C59—22no—
165#95×C59—22no—
166#95×C59—22no—
167#95×C59—22no—
168#95×C59—41no—
169#95×C59—41no—
170#95×C59—41no—
171#95×C59D414yescomplemented
172C24×C59—21no—
173C24×C59—21no—
174C24×C59—21no—
175C24×C59—21no—
176C24×C59—21no—
177C24×C59—21no—
178C24×C59—21no—
179C24×C59—21no—
180C24×C59—21no—
181C24×C59—21no—
182C24×C59—21no—
183C24×C59—21no—
184C24×C59—21no—
185C24×C59—21no—
186C24×C59—21no—
187C24×C59—21no—
188C24×C59—21no—
189C24×C59—21no—
190C24×C59—21no—
191C24×C59—21no—
192C24×C59—21no—
193C24×C59—21no—
194C24×C59—21no—
195C24×C59—21no—
196C24×C59—21no—
197C24×C59—21no—
198C24×C59—21no—
199C24×C59—21no—
200C24×C59—21no—
201C24×C59—21no—
202C24×C59—21no—
203C24×C59—21no—
204C24×C59—21no—
205C24×C59—21no—
206C24×C59—21no—
207C24×C59—21no—
208C24×C59—21no—
209C24×C59—21no—
210C24×C59C2×D412yes—
211C24×C59C2×D412yes—
212C24×C59C2×D412yes—
213C24×C59C2×D412yes—
214C24×C59#4112yes—
215C24×C59#4112yes—
216C24×C59#4112yes—
217C24×C59C2411yescharacteristic
218C2×D4×C59—28no—
219C2×D4×C59—28no—
220C2×D4×C59—28no—
221C2×D4×C59—28no—
222C2×D4×C59—28no—
223C2×D4×C59—28no—
224C2×D4×C59—28no—
225C2×D4×C59—28no—
226C2×D4×C59—28no—
227C2×D4×C59—44no—
228C2×D4×C59—44no—
229C2×D4×C59—44no—
230C2×D4×C59—44no—
231C2×D4×C59—44no—
232C2×D4×C59—44no—
233C2×D4×C59—44no—
234C2×D4×C59—44no—
235C2×D4×C59—44no—
236C2×D4×C59—44no—
237C2×D4×C59—44no—
238C2×D4×C59—44no—
239C22×C4×C59—21no—
240C22×C4×C59—21no—
241C22×C4×C59—21no—
242C22×C4×C59—21no—
243C22×C4×C59—21no—
244C22×C4×C59—21no—
245C22×C4×C59—21no—
246C22×C4×C59—21no—
247C22×C4×C59—28no—
248C22×C4×C59—28no—
249C22×C4×C59—21no—
250C22×C4×C59—21no—
251C22×C4×C59—21no—
252C22×C4×C59—21no—
253C22×C4×C59—21no—
254C22×C4×C59—21no—
255C22×C4×C59—21no—
256C22×C4×C59—21no—
257C22×C4×C59—21no—
258C22×C4×C59—21no—
259C22×C4×C59—21no—
260C22×C4×C59—21no—
261C22×C4×C59—21no—
262C22×C4×C59—21no—
263C22×C4×C59—21no—
264C22×C4×C59—21no—
265C22×C4×C59—21no—
266C22×C4×C59—21no—
267C22×C4×C59—21no—
268C22×C4×C59—21no—
269C22×C4×C59—21no—
270C22×C4×C59—21no—
271C22×C4×C59—21no—
272C22×C4×C59—21no—
273C22×C4×C59—21no—
274C22×C4×C59—21no—
275C22×C4×C59—21no—
276C22×C4×C59—21no—
277C22×C4×C59—21no—
278C22×C4×C59—21no—
279C22×C4×C59—21no—
280C22×C4×C59—21no—
281C22×C4×C59—21no—
282C22×C4×C59—21no—
283C22×C4×C59—21no—
284C22×C4×C59—21no—
285C22×C4×C59—28no—
286C22×C4×C59—21no—
287C22×C4×C59—21no—
288C22×C4×C59—21no—
289C22×C4×C59—21no—
290C22×C4×C59—21no—
291C22×C4×C59—21no—
292C22×C4×C59—21no—
293C22×C4×C59—21no—
294C22×C4×C59—21no—
295C22×C4×C59—21no—
296C22×C4×C59—21no—
297C22×C4×C59—21no—
298C22×C4×C59—21no—
299C22×C4×C59—21no—
300C22×C4×C59—21no—
301C22×C4×C59—21no—
302C22×C4×C59—21no—
303C22×C4×C59—21no—
304C22×C4×C59—21no—
305C22×C4×C59—21no—
306C22×C4×C59—21no—
307C22×C4×C59—21no—
308C22×C4×C59—21no—
309C22×C4×C59—21no—
310C22×C4×C59—21no—
311C22×C4×C59—21no—
312C22×C4×C59—21no—
313C22×C4×C59—21no—
314C22×C4×C59—44no—
315C22×C4×C59—44no—
316C22×C4×C59—44no—
317C22×C4×C59—44no—
318C22×C4×C59—44no—
319C22×C4×C59—44no—
320C22×C4×C59—44no—
321C22×C4×C59—44no—
322C22×C4×C59—44no—
323C22×C4×C59—44no—
324C22×C4×C59—44no—
325C22×C4×C59C2×D412yes—
326C22×C4×C59C2×D412yes—
327C22×C4×C59C2×D412yes—
328C22×C4×C59C2×D412yes—
329C22×C4×C59C2×D412yes—
330C22×C4×C59C2×D412yes—
331C22×C4×C59C2×D412yes—
332C22×C4×C59C2×D412yes—
333C22×C4×C59#4112yes—
334C22×C4×C59#4112yes—
335C22×C4×C59#4112yes—
336C22×C4×C59#4112yes—
337C4⋊C4×C59—28no—
338C4⋊C4×C59—44no—
339C22⋊C4×C59—28no—
340C22⋊C4×C59—28no—
341C22⋊C4×C59—44no—
342C22⋊C4×C59—44no—
343C22⋊C4×C59—44no—
344C22⋊C4×C59—44no—
345C22⋊C4×C59—44no—
346C22⋊C4×C59—44no—
347C22⋊C4×C59—44no—
348C22⋊C4×C59—44no—
349C22⋊C4×C59—44no—
350C22⋊C4×C59—44no—
351C22⋊C4×C59—44no—
352C42×C59—28no—
353C23×C59—22no—
354C23×C59—22no—
355C23×C59—22no—
356C23×C59—22no—
357C23×C59—22no—
358C23×C59—22no—
359C23×C59—22no—
360C23×C59—22no—
361C23×C59—22no—
362C23×C59—22no—
363C23×C59—22no—
364C23×C59—22no—
365C23×C59—22no—
366C23×C59—22no—
367C23×C59—22no—
368C23×C59—22no—
369C23×C59—22no—
370C23×C59—22no—
371C23×C59—22no—
372C23×C59—22no—
373C23×C59—22no—
374C23×C59—22no—
375C23×C59—22no—
376C23×C59—22no—
377C23×C59—22no—
378C23×C59—22no—
379C23×C59—22no—
380C23×C59—22no—
381C23×C59—22no—
382C23×C59—22no—
383C23×C59—22no—
384C23×C59—22no—
385C23×C59—22no—
386C23×C59—22no—
387C23×C59—22no—
388C23×C59—22no—
389C23×C59—22no—
390C23×C59—22no—
391C23×C59—22no—
392C23×C59—22no—
393C23×C59—22no—
394C23×C59—22no—
395C23×C59—22no—
396C23×C59—41no—
397C23×C59—41no—
398C23×C59—41no—
399C23×C59—41no—
400C23×C59—41no—
401C23×C59—41no—
402C23×C59—41no—
403C23×C59—41no—
404C23×C59—41no—
405C23×C59—41no—
406C23×C59—41no—
407C23×C59—41no—
408C23×C59—41no—
409C23×C59—41no—
410C23×C59—41no—
411C23×C59—41no—
412C23×C59—41no—
413C23×C59—41no—
414C23×C59—41no—
415C23×C59—41no—
416C23×C59—41no—
417C23×C59—41no—
418C23×C59—41no—
419C23×C59—41no—
420C23×C59—41no—
421C23×C59—41no—
422C23×C59—41no—
423C23×C59—41no—
424C23×C59—41no—
425C23×C59—41no—
426C23×C59—41no—
427C23×C59—41no—
428C23×C59—41no—
429C23×C59—41no—
430C23×C59—41no—
431C23×C59—41no—
432C23×C59—41no—
433C23×C59—41no—
434C23×C59—41no—
435C23×C59—41no—
436C23×C59—41no—
437C23×C59—41no—
438C23×C59—41no—
439C23×C59—41no—
440C23×C59—41no—
441C23×C59—41no—
442C23×C59—41no—
443C23×C59—41no—
444C23×C59—41no—
445C23×C59—41no—
446C23×C59—41no—
447C23×C59—41no—
448C23×C59—41no—
449C23×C59—41no—
450C23×C59—41no—
451C23×C59—41no—
452C23×C59—41no—
453C23×C59—41no—
454C23×C59—41no—
455C23×C59—41no—
456C23×C59#12014yes—
457C23×C59#12314yes—
458C23×C59C22×D411yescharacteristic
459C23×C59C22×D411yescharacteristic
460C23×C59C22×D411yescharacteristic
461C23×C59C22×D411yescharacteristic
462C23×C59C2×#4111yescharacteristic
463C23×C59C2×#4111yescharacteristic
464C23×C59C2×#4111yescharacteristic
465C23×C59C2×#4111yescharacteristic
466C23×C59C2×#4111yescharacteristic
467C23×C59C2×#4111yescharacteristic
468C23×C59C2×#4111yescharacteristic
469C23×C59H(5,𝔽2)11yescharacteristic
470C23×C59H(5,𝔽2)11yescharacteristic
471C23×C59H(5,𝔽2)11yescharacteristic
472C23×C59H(5,𝔽2)11yescharacteristic
473D4×C59—232no—
474D4×C59—416no—
475D4×C59—416no—
476C2×C4×C59—22no—
477C2×C4×C59—22no—
478C2×C4×C59—22no—
479C2×C4×C59—22no—
480C2×C4×C59—22no—
481C2×C4×C59—22no—
482C2×C4×C59—22no—
483C2×C4×C59—22no—
484C2×C4×C59—22no—
485C2×C4×C59—22no—
486C2×C4×C59—22no—
487C2×C4×C59—22no—
488C2×C4×C59—22no—
489C2×C4×C59—22no—
490C2×C4×C59—22no—
491C2×C4×C59—22no—
492C2×C4×C59—22no—
493C2×C4×C59—22no—
494C2×C4×C59—22no—
495C2×C4×C59—22no—
496C2×C4×C59—22no—
497C2×C4×C59—22no—
498C2×C4×C59—22no—
499C2×C4×C59—22no—
500C2×C4×C59—22no—
501C2×C4×C59—22no—
502C2×C4×C59—22no—
503C2×C4×C59—22no—
504C2×C4×C59—22no—
505C2×C4×C59—22no—
506C2×C4×C59—416no—
507C2×C4×C59—416no—
508C2×C4×C59—41no—
509C2×C4×C59—41no—
510C2×C4×C59—41no—
511C2×C4×C59—41no—
512C2×C4×C59—41no—
513C2×C4×C59—41no—
514C2×C4×C59—41no—
515C2×C4×C59—41no—
516C2×C4×C59—41no—
517C2×C4×C59—41no—
518C2×C4×C59—41no—
519C2×C4×C59—41no—
520C2×C4×C59—41no—
521C2×C4×C59—41no—
522C2×C4×C59—41no—
523C2×C4×C59—41no—
524C2×C4×C59—41no—
525C2×C4×C59—41no—
526C2×C4×C59—41no—
527C2×C4×C59—41no—
528C2×C4×C59—41no—
529C2×C4×C59—41no—
530C2×C4×C59—41no—
531C2×C4×C59—41no—
532C2×C4×C59—41no—
533C2×C4×C59—41no—
534C2×C4×C59—41no—
535C2×C4×C59—41no—
536C2×C4×C59—41no—
537C2×C4×C59—41no—
538C2×C4×C59—41no—
539C2×C4×C59—41no—
540C2×C4×C59—41no—
541C2×C4×C59—41no—
542C2×C4×C59—41no—
543C2×C4×C59—41no—
544C2×C4×C59—41no—
545C2×C4×C59—41no—
546C2×C4×C59—41no—
547C2×C4×C59—41no—
548C2×C4×C59—41no—
549C2×C4×C59—41no—
550C2×C4×C59—41no—
551C2×C4×C59—41no—
552C2×C4×C59—41no—
553C2×C4×C59—41no—
554C2×C4×C59—41no—
555C2×C4×C59—41no—
556C2×C4×C59—41no—
557C2×C4×C59—41no—
558C2×C4×C59—41no—
559C2×C4×C59—41no—
560C2×C4×C59#12114yes—
561C2×C4×C59#12314yes—
562#14730C5911yesmaximal, characteristic, direct product factor, Sylow
563C22×C59—24no—
564C22×C59—24no—
565C22×C59—24no—
566C22×C59—24no—
567C22×C59—24no—
568C22×C59—24no—
569C22×C59—42no—
570C22×C59—42no—
571C22×C59—42no—
572C22×C59—42no—
573C22×C59—42no—
574C22×C59—42no—
575C22×C59—42no—
576C22×C59—42no—
577C22×C59—42no—
578C22×C59—42no—
579C22×C59—42no—
580C22×C59—42no—
581C22×C59—42no—
582C22×C59—42no—
583C22×C59—42no—
584C22×C59—42no—
585C22×C59—42no—
586C22×C59—42no—
587C22×C59—42no—
588C22×C59—42no—
589C22×C59—42no—
590C22×C59—42no—
591C22×C59—42no—
592C22×C59—42no—
593C22×C59—42no—
594C22×C59—42no—
595C22×C59—42no—
596C22×C59—42no—
597C22×C59—42no—
598C22×C59—42no—
599C22×C59—42no—
600C22×C59—81no—
601C22×C59—81no—
602C22×C59—81no—
603C22×C59—81no—
604C22×C59—81no—
605C22×C59—81no—
606C22×C59—81no—
607C22×C59—81no—
608C22×C59C2×#12011yescharacteristic
609C22×C59C2×#12111yescharacteristic
610C22×C59C2×#12311yescharacteristic
611C22×C59C2×#12311yescharacteristic
612C22×C59#52511yescharacteristic
613C22×C59#52511yescharacteristic
614C22×C59#52511yescharacteristic
615C22×C59#52511yescharacteristic
616C22×C59#52511yescharacteristic
617C22×C59#52511yescharacteristic
618C22×C59#52911yescharacteristic
619C22×C59#52911yescharacteristic
620C22×C59#53211yescharacteristic
621C22×C59#53411yescharacteristic
622C22×C59#53511yescharacteristic
623C22×C59#53811yescharacteristic
624C22×C59#53811yescharacteristic
625C22×C59#54011yescharacteristic
626C22×C59#54011yescharacteristic
627C22×C59D4211yescharacteristic
628C22×C59D4211yescharacteristic
629C22×C59#54611yescharacteristic
630C22×C59#54611yescharacteristic
631C22×C59#54611yescharacteristic
632C22×C59#54611yescharacteristic
633C22×C59#54611yescharacteristic
634C22×C59#54611yescharacteristic
635C22×C59#54611yescharacteristic
636C22×C59#55011yescharacteristic
637C22×C59#55111yescharacteristic
638C22×C59#55311yescharacteristic
639C22×C59#55311yescharacteristic
640C22×C59#55311yescharacteristic
641C22×C59#55511yescharacteristic
642C22×C59#55911yescharacteristic
643C4×C59—24no—
644C4×C59—24no—
645C4×C59—42no—
646C4×C59—42no—
647C4×C59—42no—
648C4×C59—42no—
649C4×C59—42no—
650C4×C59—42no—
651C4×C59—81no—
652C4×C59—81no—
653C4×C59—81no—
654C4×C59—81no—
655C22×C4×D4C2×C5911yescharacteristic, complemented
656C2×#394C2×C5911yescharacteristic, complemented
657C2×#392C2×C5911yescharacteristic
658C2×#386C2×C5911yescharacteristic, complemented
659C2×#386C2×C5911yescharacteristic, complemented
660C2×#381C2×C5911yescharacteristic, complemented
661#1442C2×C5911yescharacteristic, complemented
662#1440C2×C5911yescharacteristic, complemented
663#1439C2×C5911yescharacteristic, complemented
664#1439C2×C5911yescharacteristic, complemented
665#1438C2×C5911yescharacteristic, complemented
666#1438C2×C5911yescharacteristic, complemented
667#1437C2×C5911yescharacteristic, complemented
668#1436C2×C5911yescharacteristic, complemented
669C22⋊#95C2×C5911yescharacteristic, complemented
670C2×C59—44no—
671C2×C59—44no—
672C2×C59—82no—
673C2×C59#239211yescharacteristic
674C2×C59#240411yescharacteristic
675C2×C59#241011yescharacteristic
676C2×C59#241411yescharacteristic
677C2×C59#241811yescharacteristic
678C2×C59#242011yescharacteristic
679C2×C59#244411yescharacteristic
680C2×C59#244511yescharacteristic
681C2×C59#245611yescharacteristic
682C2×C59#245711yescharacteristic
683C2×C59#245911yescharacteristic
684C2×C59#246411yescharacteristic
685C2×C59#260011yescharacteristic
686C2×C59#263511yescharacteristic
687C2×C59#284911yescharacteristic
688C23×D4C22×C5911yescharacteristic
689C23×D4C22×C5911yescharacteristic
690C23×D4C22×C5911yescharacteristic
691C24×C4C22×C5911yescharacteristic
692C24×C4C22×C5911yescharacteristic
693C2×C4×D4—24no—
694C2×C4×D4—24no—
695C2×C4×D4—24no—
696C22×C4⋊C4C22×C5911yescharacteristic
697C22×C4⋊C4C22×C5911yescharacteristic
698C22×C22⋊C4C22×C5911yescharacteristic
699C22×C22⋊C4C22×C5911yescharacteristic
700C22×C22⋊C4C22×C5911yescharacteristic
701C22×C22⋊C4C22×C5911yescharacteristic
702C22×C22⋊C4C22×C5911yescharacteristic
703C22×C22⋊C4C22×C5911yescharacteristic
704C22×C22⋊C4C22×C5911yescharacteristic
705C22×C22⋊C4C22×C5911yescharacteristic
706C22×C22⋊C4C22×C5911yescharacteristic
707C22×C22⋊C4C22×C5911yescharacteristic
708C22×C22⋊C4C22×C5911yescharacteristic
709C22×C22⋊C4C22×C5911yescharacteristic
710C22×C22⋊C4C22×C5911yescharacteristic
711C22×C42C22×C5911yescharacteristic
712#394—24no—
713#392—24no—
714#386—24no—
715#386—24no—
716#381—24no—
717C2×#95C22×C5911yescharacteristic
718C2×#95C22×C5911yescharacteristic
719C2×#95C22×C5911yescharacteristic
720C2×#95C22×C5911yescharacteristic
721C2×#95C22×C5911yescharacteristic
722C2×#95C22×C5911yescharacteristic
723C2×#95C22×C5911yescharacteristic
724C2×#95C22×C5911yescharacteristic
725C2×#95C22×C5911yescharacteristic
726C2×#95C22×C5911yescharacteristic
727C2×#95C22×C5911yescharacteristic
728C2×#95C22×C5911yescharacteristic
729C2×#95C22×C5911yescharacteristic
730C2×#95C22×C5911yescharacteristic
731C59#1473011yescharacteristic, direct product factor, Sylow
732C25C23×C5911yescharacteristic
733C25C23×C5911yescharacteristic
734C25C23×C5911yescharacteristic
735C22×D4—22no—
736C22×D4—22no—
737C22×D4—22no—
738C22×D4—22no—
739C22×D4—22no—
740C22×D4—22no—
741C22×D4—22no—
742C22×D4—22no—
743C22×D4—22no—
744C22×D4—22no—
745C22×D4—22no—
746C22×D4—22no—
747C22×D4—22no—
748C22×D4—22no—
749C22×D4—22no—
750C22×D4—22no—
751C22×D4—41no—
752C22×D4—41no—
753C22×D4—41no—
754C22×D4—41no—
755C22×D4D4×C5914yes—
756C23×C4—22no—
757C23×C4—22no—
758C23×C4—22no—
759C23×C4—22no—
760C23×C4—22no—
761C23×C4—22no—
762C23×C4—22no—
763C23×C4—22no—
764C23×C4—22no—
765C23×C4—41no—
766C23×C4—41no—
767C23×C4—41no—
768C23×C4—41no—
769C23×C4D4×C5914yescomplemented
770C23×C4C23×C5911yescharacteristic
771C23×C4C23×C5911yescharacteristic
772C23×C4C23×C5911yescharacteristic
773C23×C4C23×C5911yescharacteristic
774C23×C4C23×C5911yescharacteristic
775C23×C4C23×C5911yescharacteristic
776C23×C4C23×C5911yescharacteristic
777C23×C4C23×C5911yescharacteristic
778C23×C4C23×C5911yescharacteristic
779C23×C4C23×C5911yescharacteristic
780C23×C4C23×C5911yescharacteristic
781C23×C4C23×C5911yescharacteristic
782C4×D4—232no—
783C2×C4⋊C4—22no—
784C2×C4⋊C4—22no—
785C2×C4⋊C4—22no—
786C2×C4⋊C4—22no—
787C2×C4⋊C4—22no—
788C2×C4⋊C4—41no—
789C2×C22⋊C4—22no—
790C2×C22⋊C4—22no—
791C2×C22⋊C4—22no—
792C2×C22⋊C4—22no—
793C2×C22⋊C4—22no—
794C2×C22⋊C4—22no—
795C2×C22⋊C4—22no—
796C2×C22⋊C4—22no—
797C2×C22⋊C4—22no—
798C2×C22⋊C4—22no—
799C2×C22⋊C4—22no—
800C2×C22⋊C4—22no—
801C2×C22⋊C4—22no—
802C2×C22⋊C4—22no—
803C2×C22⋊C4—22no—
804C2×C22⋊C4—22no—
805C2×C22⋊C4—22no—
806C2×C22⋊C4—22no—
807C2×C22⋊C4—22no—
808C2×C22⋊C4—22no—
809C2×C22⋊C4—22no—
810C2×C22⋊C4—22no—
811C2×C22⋊C4—22no—
812C2×C22⋊C4—22no—
813C2×C22⋊C4—22no—
814C2×C22⋊C4—22no—
815C2×C22⋊C4—41no—
816C2×C22⋊C4—41no—
817C2×C22⋊C4—41no—
818C2×C22⋊C4—41no—
819C2×C22⋊C4—41no—
820C2×C22⋊C4—41no—
821C2×C22⋊C4—41no—
822C2×C22⋊C4—41no—
823C2×C22⋊C4—41no—
824C2×C22⋊C4—41no—
825C2×C22⋊C4—41no—
826C2×C22⋊C4—41no—
827C2×C22⋊C4D4×C5914yescomplemented
828C2×C42—22no—
829C2×C42—22no—
830C2×C42—22no—
831#95—22no—
832#95—22no—
833#95—22no—
834#95—22no—
835#95—22no—
836#95—22no—
837#95—22no—
838#95—22no—
839#95—22no—
840#95—22no—
841#95—41no—
842#95—41no—
843#95—41no—
844#95D4×C5914yescomplemented
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
854C24—21no—
855C24—21no—
856C24—21no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24—21no—
862C24—21no—
863C24—21no—
864C24—21no—
865C24—21no—
866C24—21no—
867C24—21no—
868C24—21no—
869C24—21no—
870C24—21no—
871C24—21no—
872C24—21no—
873C24—21no—
874C24—21no—
875C24—21no—
876C24—21no—
877C24—21no—
878C24—21no—
879C24—21no—
880C24—21no—
881C24—21no—
882C24—21no—
883C24C2×D4×C5912yes—
884C24C2×D4×C5912yes—
885C24C2×D4×C5912yes—
886C24C2×D4×C5912yes—
887C24#41×C5912yes—
888C24#41×C5912yes—
889C24#41×C5912yes—
890C24C24×C5911yescharacteristic
891C2×D4—28no—
892C2×D4—28no—
893C2×D4—28no—
894C2×D4—28no—
895C2×D4—28no—
896C2×D4—28no—
897C2×D4—28no—
898C2×D4—28no—
899C2×D4—28no—
900C2×D4—44no—
901C2×D4—44no—
902C2×D4—44no—
903C2×D4—44no—
904C2×D4—44no—
905C2×D4—44no—
906C2×D4—44no—
907C2×D4—44no—
908C2×D4—44no—
909C2×D4—44no—
910C2×D4—44no—
911C2×D4—44no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—28no—
921C22×C4—28no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—28no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—21no—
977C22×C4—21no—
978C22×C4—21no—
979C22×C4—21no—
980C22×C4—21no—
981C22×C4—21no—
982C22×C4—21no—
983C22×C4—21no—
984C22×C4—21no—
985C22×C4—21no—
986C22×C4—21no—
987C22×C4—44no—
988C22×C4—44no—
989C22×C4—44no—
990C22×C4—44no—
991C22×C4—44no—
992C22×C4—44no—
993C22×C4—44no—
994C22×C4—44no—
995C22×C4—44no—
996C22×C4—44no—
997C22×C4—44no—
998C22×C4C2×D4×C5912yes—
999C22×C4C2×D4×C5912yes—
1000C22×C4C2×D4×C5912yes—
1001C22×C4C2×D4×C5912yes—
1002C22×C4C2×D4×C5912yes—
1003C22×C4C2×D4×C5912yes—
1004C22×C4C2×D4×C5912yes—
1005C22×C4C2×D4×C5912yes—
1006C22×C4#41×C5912yes—
1007C22×C4#41×C5912yes—
1008C22×C4#41×C5912yes—
1009C22×C4#41×C5912yes—
1010C4⋊C4—28no—
1011C4⋊C4—44no—
1012C22⋊C4—28no—
1013C22⋊C4—28no—
1014C22⋊C4—44no—
1015C22⋊C4—44no—
1016C22⋊C4—44no—
1017C22⋊C4—44no—
1018C22⋊C4—44no—
1019C22⋊C4—44no—
1020C22⋊C4—44no—
1021C22⋊C4—44no—
1022C22⋊C4—44no—
1023C22⋊C4—44no—
1024C22⋊C4—44no—
1025C42—28no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—22no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—22no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—22no—
1065C23—22no—
1066C23—22no—
1067C23—22no—
1068C23—22no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23#120×C5914yes—
1130C23#123×C5914yes—
1131C23C22×D4×C5911yescharacteristic
1132C23C22×D4×C5911yescharacteristic
1133C23C22×D4×C5911yescharacteristic
1134C23C22×D4×C5911yescharacteristic
1135C23C2×#41×C5911yescharacteristic
1136C23C2×#41×C5911yescharacteristic
1137C23C2×#41×C5911yescharacteristic
1138C23C2×#41×C5911yescharacteristic
1139C23C2×#41×C5911yescharacteristic
1140C23C2×#41×C5911yescharacteristic
1141C23C2×#41×C5911yescharacteristic
1142C23H(5,𝔽2)×C5911yescharacteristic
1143C23H(5,𝔽2)×C5911yescharacteristic
1144C23H(5,𝔽2)×C5911yescharacteristic
1145C23H(5,𝔽2)×C5911yescharacteristic
1146D4—232no—
1147D4—416no—
1148D4—416no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—416no—
1180C2×C4—416no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4#121×C5914yes—
1234C2×C4#123×C5914yes—
1235C22—24no—
1236C22—24no—
1237C22—24no—
1238C22—24no—
1239C22—24no—
1240C22—24no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—42no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
1250C22—42no—
1251C22—42no—
1252C22—42no—
1253C22—42no—
1254C22—42no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—42no—
1271C22—42no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22C2×#120×C5911yescharacteristic
1281C22C2×#121×C5911yescharacteristic
1282C22C2×#123×C5911yescharacteristic
1283C22C2×#123×C5911yescharacteristic
1284C22C59×#52511yescharacteristic
1285C22C59×#52511yescharacteristic
1286C22C59×#52511yescharacteristic
1287C22C59×#52511yescharacteristic
1288C22C59×#52511yescharacteristic
1289C22C59×#52511yescharacteristic
1290C22C59×#52911yescharacteristic
1291C22C59×#52911yescharacteristic
1292C22C59×#53211yescharacteristic
1293C22C59×#53411yescharacteristic
1294C22C59×#53511yescharacteristic
1295C22C59×#53811yescharacteristic
1296C22C59×#53811yescharacteristic
1297C22C59×#54011yescharacteristic
1298C22C59×#54011yescharacteristic
1299C22D42×C5911yescharacteristic
1300C22D42×C5911yescharacteristic
1301C22C59×#54611yescharacteristic
1302C22C59×#54611yescharacteristic
1303C22C59×#54611yescharacteristic
1304C22C59×#54611yescharacteristic
1305C22C59×#54611yescharacteristic
1306C22C59×#54611yescharacteristic
1307C22C59×#54611yescharacteristic
1308C22C59×#55011yescharacteristic
1309C22C59×#55111yescharacteristic
1310C22C59×#55311yescharacteristic
1311C22C59×#55311yescharacteristic
1312C22C59×#55311yescharacteristic
1313C22C59×#55511yescharacteristic
1314C22C59×#55911yescharacteristic
1315C4—24no—
1316C4—24no—
1317C4—42no—
1318C4—42no—
1319C4—42no—
1320C4—42no—
1321C4—42no—
1322C4—42no—
1323C4—81no—
1324C4—81no—
1325C4—81no—
1326C4—81no—
1327C2—44no—
1328C2—44no—
1329C2—82no—
1330C2C59×#239211yescharacteristic
1331C2C59×#240411yescharacteristic
1332C2C59×#241011yescharacteristic
1333C2C59×#241411yescharacteristic
1334C2C59×#241811yescharacteristic
1335C2C59×#242011yescharacteristic
1336C2C59×#244411yescharacteristic
1337C2C59×#244511yescharacteristic
1338C2C59×#245611yescharacteristic
1339C2C59×#245711yescharacteristic
1340C2C59×#245911yescharacteristic
1341C2C59×#246411yescharacteristic
1342C2C59×#260011yescharacteristic
1343C2C59×#263511yescharacteristic
1344C2C59×#284911yescharacteristic
subgroupG/H
center, socleC24×C59C24
commutator, Frattini, cosocleC24C24×C59
prime radicalC2×C59×#392C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C59 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C4×D4×C59C2semidirect
2. C2×C59×#394C2semidirect
4. C2×C59×#386C2semidirect
5. C2×C59×#386C2semidirect
6. C2×C59×#381C2semidirect
7. C59×#1442C2semidirect
8. C59×#1440C2semidirect
9. C59×#1439C2semidirect
10. C59×#1439C2semidirect
11. C59×#1438C2semidirect
12. C59×#1438C2semidirect
13. C59×#1437C2semidirect
14. C59×#1436C2semidirect
15. C59×C22⋊#95C2semidirect
96. C23×C4×C59D4semidirect
154. C2×C22⋊C4×C59D4semidirect
171. #95×C59D4semidirect
562. #14730C59direct (N × H)
655. C22×C4×D4C2×C59semidirect
656. C2×#394C2×C59semidirect
658. C2×#386C2×C59semidirect
659. C2×#386C2×C59semidirect
660. C2×#381C2×C59semidirect
661. #1442C2×C59semidirect
662. #1440C2×C59semidirect
663. #1439C2×C59semidirect
664. #1439C2×C59semidirect
665. #1438C2×C59semidirect
666. #1438C2×C59semidirect
667. #1437C2×C59semidirect
668. #1436C2×C59semidirect
669. C22⋊#95C2×C59semidirect
731. C59#14730direct (N × H)
769. C23×C4D4×C59semidirect
827. C2×C22⋊C4D4×C59semidirect
844. #95D4×C59semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D4×C592
C2×C59×#3942
C2×C59×#3922
C2×C59×#3862
C2×C59×#3812
C59×#14422
C59×#14402
C59×#14392
C59×#14382
C59×#14372
C59×#14362
C59×C22⋊#952
#1473059