Finite Group Databasebeta

← C59×#14095 #28426204

Subgroups — C59×#14095 #28426204

Order 15104.

2158 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#123×C59C211yesmaximal, characteristic
2C2×C59×#390C211yesmaximal, characteristic
3C2×C59×#387C211yesmaximal, characteristic, complemented
4C2×C4×C4⋊C4×C59C211yesmaximal, characteristic, complemented
5C2×C4×C22⋊C4×C59C211yesmaximal, characteristic, complemented
6C59×#1441C211yesmaximal, characteristic, complemented
7C59×#1439C211yesmaximal, characteristic, complemented
8C59×#1439C211yesmaximal, characteristic, complemented
9C59×#1438C211yesmaximal, characteristic
10C59×#1437C211yesmaximal, characteristic, complemented
11C59×#1437C211yesmaximal, characteristic, complemented
12C59×#1437C211yesmaximal, characteristic, complemented
13C59×#1437C211yesmaximal, characteristic, complemented
14C59×#1436C211yesmaximal, characteristic, complemented
15C59×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C59C2211yescharacteristic
17C24×C4×C59C2211yescharacteristic
18C2×#123×C59—24no—
19C2×#123×C59—24no—
20C2×#123×C59C418yescomplemented
21C22×C4⋊C4×C59C2211yescharacteristic
22C22×C4⋊C4×C59C2211yescharacteristic
23C22×C4⋊C4×C59C2211yescharacteristic
24C22×C4⋊C4×C59C2211yescharacteristic
25C22×C22⋊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×C42×C59C2211yescharacteristic
37C22×C42×C59C2211yescharacteristic
38C22×C42×C59C2211yescharacteristic
39C22×C42×C59C2211yescharacteristic
40C59×#390—24no—
41C59×#387—24no—
42C4×C4⋊C4×C59—24no—
43C4×C22⋊C4×C59—24no—
44C2×#95×C59C2211yescharacteristic
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
58C25×C59C2311yescharacteristic
59C25×C59C2311yescharacteristic
60C22×D4×C59—22no—
61C22×D4×C59—22no—
62C22×D4×C59—22no—
63C22×D4×C59—22no—
64C22×D4×C59—41no—
65C22×D4×C59—41no—
66C22×D4×C59C2×C414yes—
67C23×C4×C59—22no—
68C23×C4×C59—22no—
69C23×C4×C59—22no—
70C23×C4×C59—22no—
71C23×C4×C59—41no—
72C23×C4×C59—41no—
73C23×C4×C59C2×C414yes—
74C23×C4×C59C2311yescharacteristic
75C23×C4×C59C2311yescharacteristic
76C23×C4×C59C2311yescharacteristic
77C23×C4×C59C2311yescharacteristic
78C23×C4×C59C2311yescharacteristic
79C23×C4×C59C2311yescharacteristic
80C23×C4×C59C2311yescharacteristic
81C23×C4×C59C2311yescharacteristic
82C23×C4×C59C2311yescharacteristic
83C23×C4×C59C2311yescharacteristic
84C23×C4×C59C2311yescharacteristic
85C23×C4×C59C2311yescharacteristic
86C23×C4×C59C2311yescharacteristic
87#123×C59—232no—
88C2×C4⋊C4×C59—22no—
89C2×C4⋊C4×C59—22no—
90C2×C4⋊C4×C59—22no—
91C2×C4⋊C4×C59—22no—
92C2×C4⋊C4×C59—22no—
93C2×C4⋊C4×C59—22no—
94C2×C4⋊C4×C59—22no—
95C2×C4⋊C4×C59—41no—
96C2×C4⋊C4×C59C2×C414yes—
97C2×C4⋊C4×C59C2×C414yes—
98C2×C4⋊C4×C59D414yes—
99C2×C4⋊C4×C59D414yes—
100C2×C22⋊C4×C59—22no—
101C2×C22⋊C4×C59—22no—
102C2×C22⋊C4×C59—22no—
103C2×C22⋊C4×C59—22no—
104C2×C22⋊C4×C59—22no—
105C2×C22⋊C4×C59—22no—
106C2×C22⋊C4×C59—22no—
107C2×C22⋊C4×C59—22no—
108C2×C22⋊C4×C59—22no—
109C2×C22⋊C4×C59—22no—
110C2×C22⋊C4×C59—22no—
111C2×C22⋊C4×C59—22no—
112C2×C22⋊C4×C59—22no—
113C2×C22⋊C4×C59—22no—
114C2×C22⋊C4×C59—22no—
115C2×C22⋊C4×C59—22no—
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—41no—
124C2×C22⋊C4×C59—41no—
125C2×C22⋊C4×C59—41no—
126C2×C22⋊C4×C59—41no—
127C2×C22⋊C4×C59—41no—
128C2×C22⋊C4×C59—41no—
129C2×C22⋊C4×C59C2×C414yes—
130C2×C22⋊C4×C59C2×C414yes—
131C2×C22⋊C4×C59C2×C414yes—
132C2×C22⋊C4×C59D414yes—
133C2×C42×C59—22no—
134C2×C42×C59—22no—
135C2×C42×C59—22no—
136C2×C42×C59—22no—
137C2×C42×C59—22no—
138C2×C42×C59—22no—
139C2×C42×C59—22no—
140C2×C42×C59—22no—
141C2×C42×C59—22no—
142C2×C42×C59—41no—
143C2×C42×C59—41no—
144C2×C42×C59—41no—
145#95×C59—22no—
146#95×C59—22no—
147#95×C59—22no—
148#95×C59—22no—
149#95×C59—22no—
150#95×C59—22no—
151#95×C59—22no—
152#95×C59—22no—
153#95×C59—22no—
154#95×C59—22no—
155#95×C59—41no—
156#95×C59—41no—
157#95×C59—41no—
158#95×C59—41no—
159C24×C59—21no—
160C24×C59—21no—
161C24×C59—21no—
162C24×C59—21no—
163C24×C59—21no—
164C24×C59—21no—
165C24×C59—21no—
166C24×C59—21no—
167C24×C59—21no—
168C24×C59—21no—
169C24×C59—21no—
170C24×C59—21no—
171C24×C59—21no—
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×C59C22×C412yes—
186C24×C59C22×C412yes—
187C24×C59C2×D412yes—
188C24×C59#4112yes—
189C24×C59C2411yescharacteristic
190C2×D4×C59—28no—
191C2×D4×C59—28no—
192C2×D4×C59—44no—
193C2×D4×C59—44no—
194C2×D4×C59—44no—
195C2×D4×C59—44no—
196C2×D4×C59—44no—
197C22×C4×C59—21no—
198C22×C4×C59—21no—
199C22×C4×C59—21no—
200C22×C4×C59—21no—
201C22×C4×C59—21no—
202C22×C4×C59—21no—
203C22×C4×C59—21no—
204C22×C4×C59—21no—
205C22×C4×C59—21no—
206C22×C4×C59—21no—
207C22×C4×C59—21no—
208C22×C4×C59—21no—
209C22×C4×C59—21no—
210C22×C4×C59—21no—
211C22×C4×C59—21no—
212C22×C4×C59—21no—
213C22×C4×C59—28no—
214C22×C4×C59—21no—
215C22×C4×C59—21no—
216C22×C4×C59—21no—
217C22×C4×C59—21no—
218C22×C4×C59—21no—
219C22×C4×C59—21no—
220C22×C4×C59—21no—
221C22×C4×C59—21no—
222C22×C4×C59—21no—
223C22×C4×C59—21no—
224C22×C4×C59—21no—
225C22×C4×C59—21no—
226C22×C4×C59—21no—
227C22×C4×C59—21no—
228C22×C4×C59—21no—
229C22×C4×C59—21no—
230C22×C4×C59—21no—
231C22×C4×C59—21no—
232C22×C4×C59—21no—
233C22×C4×C59—21no—
234C22×C4×C59—21no—
235C22×C4×C59—21no—
236C22×C4×C59—21no—
237C22×C4×C59—21no—
238C22×C4×C59—21no—
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—21no—
248C22×C4×C59—21no—
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—28no—
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—44no—
272C22×C4×C59—44no—
273C22×C4×C59—44no—
274C22×C4×C59—44no—
275C22×C4×C59—44no—
276C22×C4×C59C22×C412yes—
277C22×C4×C59C22×C412yes—
278C22×C4×C59C22×C412yes—
279C22×C4×C59C22×C412yes—
280C22×C4×C59C22×C412yes—
281C22×C4×C59C2×D412yes—
282C22×C4×C59C2×D412yes—
283C22×C4×C59C2×D412yes—
284C22×C4×C59C2×D412yes—
285C22×C4×C59C2×D412yes—
286C22×C4×C59C2×D412yes—
287C22×C4×C59C2×D412yes—
288C22×C4×C59C2×D412yes—
289C22×C4×C59#4112yes—
290C22×C4×C59#4112yes—
291C22×C4×C59#4112yes—
292C22×C4×C59#4112yes—
293C22×C4×C59#4112yes—
294C22×C4×C59#4112yes—
295C4⋊C4×C59—28no—
296C4⋊C4×C59—28no—
297C4⋊C4×C59—44no—
298C4⋊C4×C59C22⋊C4116yescomplemented
299C22⋊C4×C59—28no—
300C22⋊C4×C59—28no—
301C22⋊C4×C59—28no—
302C22⋊C4×C59—28no—
303C22⋊C4×C59—28no—
304C22⋊C4×C59—44no—
305C22⋊C4×C59—44no—
306C22⋊C4×C59—44no—
307C22⋊C4×C59—44no—
308C22⋊C4×C59—44no—
309C22⋊C4×C59—44no—
310C42×C59—28no—
311C42×C59—44no—
312C42×C59—44no—
313C42×C59—44no—
314C23×C59—22no—
315C23×C59—22no—
316C23×C59—22no—
317C23×C59—22no—
318C23×C59—22no—
319C23×C59—22no—
320C23×C59—22no—
321C23×C59—22no—
322C23×C59—22no—
323C23×C59—22no—
324C23×C59—22no—
325C23×C59—22no—
326C23×C59—22no—
327C23×C59—22no—
328C23×C59—22no—
329C23×C59—22no—
330C23×C59—22no—
331C23×C59—22no—
332C23×C59—22no—
333C23×C59—22no—
334C23×C59—22no—
335C23×C59—22no—
336C23×C59—22no—
337C23×C59—22no—
338C23×C59—22no—
339C23×C59—41no—
340C23×C59—41no—
341C23×C59—41no—
342C23×C59—41no—
343C23×C59—41no—
344C23×C59—41no—
345C23×C59—41no—
346C23×C59—41no—
347C23×C59—41no—
348C23×C59—41no—
349C23×C59—41no—
350C23×C59—41no—
351C23×C59—41no—
352C23×C59—41no—
353C23×C59—41no—
354C23×C59—41no—
355C23×C59—41no—
356C23×C59—41no—
357C23×C59—41no—
358C23×C59—41no—
359C23×C59—41no—
360C23×C59—41no—
361C23×C59—41no—
362C23×C59—41no—
363C23×C59—41no—
364C23×C59—41no—
365C23×C59—41no—
366C23×C59—41no—
367C23×C59—41no—
368C23×C59—41no—
369C23×C59—41no—
370C23×C59—41no—
371C23×C59—41no—
372C23×C59—41no—
373C23×C59—41no—
374C23×C59—41no—
375C23×C59—41no—
376C23×C59—41no—
377C23×C59—41no—
378C23×C59—41no—
379C23×C59—41no—
380C23×C59—41no—
381C23×C59—41no—
382C23×C59—41no—
383C23×C59C4×D414yes—
384C23×C59C23×C411yescharacteristic
385C23×C59C22×D411yescharacteristic
386C23×C59C22×D411yescharacteristic
387C23×C59C22×D411yescharacteristic
388C23×C59C2×#4111yescharacteristic
389C23×C59C2×#4111yescharacteristic
390C23×C59C2×#4111yescharacteristic
391C23×C59C2×#4111yescharacteristic
392C23×C59C2×#4111yescharacteristic
393C23×C59C2×#4111yescharacteristic
394C23×C59C2×#4111yescharacteristic
395C23×C59H(5,𝔽2)11yescharacteristic
396C23×C59H(5,𝔽2)11yescharacteristic
397C23×C59H(5,𝔽2)11yescharacteristic
398C23×C592−1+411yescharacteristic
399D4×C59—416no—
400C2×C4×C59—22no—
401C2×C4×C59—22no—
402C2×C4×C59—22no—
403C2×C4×C59—22no—
404C2×C4×C59—22no—
405C2×C4×C59—22no—
406C2×C4×C59—22no—
407C2×C4×C59—22no—
408C2×C4×C59—22no—
409C2×C4×C59—22no—
410C2×C4×C59—22no—
411C2×C4×C59—22no—
412C2×C4×C59—22no—
413C2×C4×C59—22no—
414C2×C4×C59—22no—
415C2×C4×C59—22no—
416C2×C4×C59—22no—
417C2×C4×C59—22no—
418C2×C4×C59—22no—
419C2×C4×C59—22no—
420C2×C4×C59—22no—
421C2×C4×C59—22no—
422C2×C4×C59—22no—
423C2×C4×C59—22no—
424C2×C4×C59—22no—
425C2×C4×C59—22no—
426C2×C4×C59—22no—
427C2×C4×C59—22no—
428C2×C4×C59—22no—
429C2×C4×C59—22no—
430C2×C4×C59—22no—
431C2×C4×C59—22no—
432C2×C4×C59—22no—
433C2×C4×C59—22no—
434C2×C4×C59—22no—
435C2×C4×C59—22no—
436C2×C4×C59—22no—
437C2×C4×C59—22no—
438C2×C4×C59—22no—
439C2×C4×C59—22no—
440C2×C4×C59—22no—
441C2×C4×C59—22no—
442C2×C4×C59—22no—
443C2×C4×C59—22no—
444C2×C4×C59—22no—
445C2×C4×C59—416no—
446C2×C4×C59—41no—
447C2×C4×C59—41no—
448C2×C4×C59—41no—
449C2×C4×C59—41no—
450C2×C4×C59—41no—
451C2×C4×C59—41no—
452C2×C4×C59—41no—
453C2×C4×C59—41no—
454C2×C4×C59—41no—
455C2×C4×C59—41no—
456C2×C4×C59—41no—
457C2×C4×C59—41no—
458C2×C4×C59—41no—
459C2×C4×C59—41no—
460C2×C4×C59—41no—
461C2×C4×C59—41no—
462C2×C4×C59—41no—
463C2×C4×C59—41no—
464C2×C4×C59—41no—
465C2×C4×C59—41no—
466C2×C4×C59—41no—
467C2×C4×C59—41no—
468C2×C4×C59—41no—
469C2×C4×C59—41no—
470C2×C4×C59—41no—
471C2×C4×C59—41no—
472C2×C4×C59—41no—
473C2×C4×C59—41no—
474C2×C4×C59—41no—
475C2×C4×C59—41no—
476C2×C4×C59—41no—
477C2×C4×C59—41no—
478C2×C4×C59—41no—
479C2×C4×C59—41no—
480C2×C4×C59—41no—
481C2×C4×C59—41no—
482C2×C4×C59—41no—
483C2×C4×C59—41no—
484C2×C4×C59—41no—
485C2×C4×C59—41no—
486C2×C4×C59—41no—
487C2×C4×C59—41no—
488C2×C4×C59C2×C22⋊C414yes—
489C2×C4×C59C2×C22⋊C414yes—
490C2×C4×C59C2×C22⋊C414yes—
491C2×C4×C59#12314yescomplemented
492#14095C5911yesmaximal, characteristic, direct product factor, Sylow
493C22×C59—24no—
494C22×C59—24no—
495C22×C59—24no—
496C22×C59—42no—
497C22×C59—42no—
498C22×C59—42no—
499C22×C59—42no—
500C22×C59—42no—
501C22×C59—42no—
502C22×C59—42no—
503C22×C59—42no—
504C22×C59—42no—
505C22×C59—42no—
506C22×C59—42no—
507C22×C59—42no—
508C22×C59—42no—
509C22×C59—42no—
510C22×C59—42no—
511C22×C59—42no—
512C22×C59—42no—
513C22×C59—42no—
514C22×C59—42no—
515C22×C59—81no—
516C22×C59—81no—
517C22×C59—81no—
518C22×C59—81no—
519C22×C59—81no—
520C22×C59—81no—
521C22×C59—81no—
522C22×C59—81no—
523C22×C59C22×C22⋊C411yescharacteristic
524C22×C59C2×C4×D411yescharacteristic
525C22×C59C4×#4111yescharacteristic
526C22×C59C4×#4111yescharacteristic
527C22×C59C4×#4111yescharacteristic
528C22×C59#51811yescharacteristic
529C22×C59#52011yescharacteristic
530C22×C59C2×#12311yescharacteristic
531C22×C59#52511yescharacteristic
532C22×C59#52511yescharacteristic
533C22×C59#52511yescharacteristic
534C22×C59#52911yescharacteristic
535C22×C59#52911yescharacteristic
536C22×C59#53211yescharacteristic
537C22×C59#53211yescharacteristic
538C22×C59#53811yescharacteristic
539C22×C59#53911yescharacteristic
540C22×C59#54011yescharacteristic
541C22×C59#54211yescharacteristic
542C22×C59D4211yescharacteristic
543C22×C59D4211yescharacteristic
544C22×C59#54611yescharacteristic
545C22×C59#54611yescharacteristic
546C22×C59#54611yescharacteristic
547C22×C59#54711yescharacteristic
548C22×C59#54811yescharacteristic
549C22×C59#54811yescharacteristic
550C22×C59#55011yescharacteristic
551C22×C59#55011yescharacteristic
552C22×C59#55111yescharacteristic
553C22×C59#55111yescharacteristic
554C22×C59#55211yescharacteristic
555C22×C59#55311yescharacteristic
556C22×C59#55311yescharacteristic
557C22×C59#55911yescharacteristic
558C4×C59—24no—
559C4×C59—24no—
560C4×C59—24no—
561C4×C59—24no—
562C4×C59—42no—
563C4×C59—42no—
564C4×C59—42no—
565C4×C59—42no—
566C4×C59—42no—
567C4×C59—42no—
568C4×C59—42no—
569C4×C59—81no—
570C4×C59—81no—
571C22×#123C2×C5911yescharacteristic
572C2×#390C2×C5911yescharacteristic
573C2×#387C2×C5911yescharacteristic, complemented
574C2×C4×C4⋊C4C2×C5911yescharacteristic, complemented
575C2×C4×C22⋊C4C2×C5911yescharacteristic, complemented
576#1441C2×C5911yescharacteristic, complemented
577#1439C2×C5911yescharacteristic, complemented
578#1439C2×C5911yescharacteristic, complemented
579#1438C2×C5911yescharacteristic
580#1437C2×C5911yescharacteristic, complemented
581#1437C2×C5911yescharacteristic, complemented
582#1437C2×C5911yescharacteristic, complemented
583#1437C2×C5911yescharacteristic, complemented
584#1436C2×C5911yescharacteristic, complemented
585C22⋊#95C2×C5911yescharacteristic, complemented
586C2×C59—44no—
587C2×C59—82no—
588C2×C59#229711yescharacteristic
589C2×C59C4×#12311yescharacteristic
590C2×C59#233511yescharacteristic
591C2×C59D4×C22⋊C411yescharacteristic
592C2×C59#234111yescharacteristic
593C2×C59#235911yescharacteristic
594C2×C59#237411yescharacteristic
595C2×C59#244311yescharacteristic
596C2×C59#244511yescharacteristic
597C2×C59#245611yescharacteristic
598C2×C59#245811yescharacteristic
599C2×C59#246111yescharacteristic
600C2×C59#247111yescharacteristic
601C2×C59#255411yescharacteristic
602C2×C59#255811yescharacteristic
603C23×D4C22×C5911yescharacteristic
604C24×C4C22×C5911yescharacteristic
605C2×#123—24no—
606C2×#123—24no—
607C2×#123C4×C5918yescomplemented
608C22×C4⋊C4C22×C5911yescharacteristic
609C22×C4⋊C4C22×C5911yescharacteristic
610C22×C4⋊C4C22×C5911yescharacteristic
611C22×C4⋊C4C22×C5911yescharacteristic
612C22×C22⋊C4C22×C5911yescharacteristic
613C22×C22⋊C4C22×C5911yescharacteristic
614C22×C22⋊C4C22×C5911yescharacteristic
615C22×C22⋊C4C22×C5911yescharacteristic
616C22×C22⋊C4C22×C5911yescharacteristic
617C22×C22⋊C4C22×C5911yescharacteristic
618C22×C22⋊C4C22×C5911yescharacteristic
619C22×C22⋊C4C22×C5911yescharacteristic
620C22×C22⋊C4C22×C5911yescharacteristic
621C22×C22⋊C4C22×C5911yescharacteristic
622C22×C22⋊C4C22×C5911yescharacteristic
623C22×C42C22×C5911yescharacteristic
624C22×C42C22×C5911yescharacteristic
625C22×C42C22×C5911yescharacteristic
626C22×C42C22×C5911yescharacteristic
627#390—24no—
628#387—24no—
629C4×C4⋊C4—24no—
630C4×C22⋊C4—24no—
631C2×#95C22×C5911yescharacteristic
632C2×#95C22×C5911yescharacteristic
633C2×#95C22×C5911yescharacteristic
634C2×#95C22×C5911yescharacteristic
635C2×#95C22×C5911yescharacteristic
636C2×#95C22×C5911yescharacteristic
637C2×#95C22×C5911yescharacteristic
638C2×#95C22×C5911yescharacteristic
639C2×#95C22×C5911yescharacteristic
640C2×#95C22×C5911yescharacteristic
641C2×#95C22×C5911yescharacteristic
642C2×#95C22×C5911yescharacteristic
643C2×#95C22×C5911yescharacteristic
644C2×#95C22×C5911yescharacteristic
645C59#1409511yescharacteristic, direct product factor, Sylow
646C25C23×C5911yescharacteristic
647C25C23×C5911yescharacteristic
648C22×D4—22no—
649C22×D4—22no—
650C22×D4—22no—
651C22×D4—22no—
652C22×D4—41no—
653C22×D4—41no—
654C22×D4C2×C4×C5914yes—
655C23×C4—22no—
656C23×C4—22no—
657C23×C4—22no—
658C23×C4—22no—
659C23×C4—41no—
660C23×C4—41no—
661C23×C4C2×C4×C5914yes—
662C23×C4C23×C5911yescharacteristic
663C23×C4C23×C5911yescharacteristic
664C23×C4C23×C5911yescharacteristic
665C23×C4C23×C5911yescharacteristic
666C23×C4C23×C5911yescharacteristic
667C23×C4C23×C5911yescharacteristic
668C23×C4C23×C5911yescharacteristic
669C23×C4C23×C5911yescharacteristic
670C23×C4C23×C5911yescharacteristic
671C23×C4C23×C5911yescharacteristic
672C23×C4C23×C5911yescharacteristic
673C23×C4C23×C5911yescharacteristic
674C23×C4C23×C5911yescharacteristic
675#123—232no—
676C2×C4⋊C4—22no—
677C2×C4⋊C4—22no—
678C2×C4⋊C4—22no—
679C2×C4⋊C4—22no—
680C2×C4⋊C4—22no—
681C2×C4⋊C4—22no—
682C2×C4⋊C4—22no—
683C2×C4⋊C4—41no—
684C2×C4⋊C4C2×C4×C5914yes—
685C2×C4⋊C4C2×C4×C5914yes—
686C2×C4⋊C4D4×C5914yes—
687C2×C4⋊C4D4×C5914yes—
688C2×C22⋊C4—22no—
689C2×C22⋊C4—22no—
690C2×C22⋊C4—22no—
691C2×C22⋊C4—22no—
692C2×C22⋊C4—22no—
693C2×C22⋊C4—22no—
694C2×C22⋊C4—22no—
695C2×C22⋊C4—22no—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—22no—
701C2×C22⋊C4—22no—
702C2×C22⋊C4—22no—
703C2×C22⋊C4—22no—
704C2×C22⋊C4—22no—
705C2×C22⋊C4—22no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4—22no—
708C2×C22⋊C4—22no—
709C2×C22⋊C4—22no—
710C2×C22⋊C4—22no—
711C2×C22⋊C4—41no—
712C2×C22⋊C4—41no—
713C2×C22⋊C4—41no—
714C2×C22⋊C4—41no—
715C2×C22⋊C4—41no—
716C2×C22⋊C4—41no—
717C2×C22⋊C4C2×C4×C5914yes—
718C2×C22⋊C4C2×C4×C5914yes—
719C2×C22⋊C4C2×C4×C5914yes—
720C2×C22⋊C4D4×C5914yes—
721C2×C42—22no—
722C2×C42—22no—
723C2×C42—22no—
724C2×C42—22no—
725C2×C42—22no—
726C2×C42—22no—
727C2×C42—22no—
728C2×C42—22no—
729C2×C42—22no—
730C2×C42—41no—
731C2×C42—41no—
732C2×C42—41no—
733#95—22no—
734#95—22no—
735#95—22no—
736#95—22no—
737#95—22no—
738#95—22no—
739#95—22no—
740#95—22no—
741#95—22no—
742#95—22no—
743#95—41no—
744#95—41no—
745#95—41no—
746#95—41no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24C22×C4×C5912yes—
774C24C22×C4×C5912yes—
775C24C2×D4×C5912yes—
776C24#41×C5912yes—
777C24C24×C5911yescharacteristic
778C2×D4—28no—
779C2×D4—28no—
780C2×D4—44no—
781C2×D4—44no—
782C2×D4—44no—
783C2×D4—44no—
784C2×D4—44no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—28no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—28no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—44no—
860C22×C4—44no—
861C22×C4—44no—
862C22×C4—44no—
863C22×C4—44no—
864C22×C4C22×C4×C5912yes—
865C22×C4C22×C4×C5912yes—
866C22×C4C22×C4×C5912yes—
867C22×C4C22×C4×C5912yes—
868C22×C4C22×C4×C5912yes—
869C22×C4C2×D4×C5912yes—
870C22×C4C2×D4×C5912yes—
871C22×C4C2×D4×C5912yes—
872C22×C4C2×D4×C5912yes—
873C22×C4C2×D4×C5912yes—
874C22×C4C2×D4×C5912yes—
875C22×C4C2×D4×C5912yes—
876C22×C4C2×D4×C5912yes—
877C22×C4#41×C5912yes—
878C22×C4#41×C5912yes—
879C22×C4#41×C5912yes—
880C22×C4#41×C5912yes—
881C22×C4#41×C5912yes—
882C22×C4#41×C5912yes—
883C4⋊C4—28no—
884C4⋊C4—28no—
885C4⋊C4—44no—
886C4⋊C4C22⋊C4×C59116yescomplemented
887C22⋊C4—28no—
888C22⋊C4—28no—
889C22⋊C4—28no—
890C22⋊C4—28no—
891C22⋊C4—28no—
892C22⋊C4—44no—
893C22⋊C4—44no—
894C22⋊C4—44no—
895C22⋊C4—44no—
896C22⋊C4—44no—
897C22⋊C4—44no—
898C42—28no—
899C42—44no—
900C42—44no—
901C42—44no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23C4×D4×C5914yes—
972C23C23×C4×C5911yescharacteristic
973C23C22×D4×C5911yescharacteristic
974C23C22×D4×C5911yescharacteristic
975C23C22×D4×C5911yescharacteristic
976C23C2×#41×C5911yescharacteristic
977C23C2×#41×C5911yescharacteristic
978C23C2×#41×C5911yescharacteristic
979C23C2×#41×C5911yescharacteristic
980C23C2×#41×C5911yescharacteristic
981C23C2×#41×C5911yescharacteristic
982C23C2×#41×C5911yescharacteristic
983C23H(5,𝔽2)×C5911yescharacteristic
984C23H(5,𝔽2)×C5911yescharacteristic
985C23H(5,𝔽2)×C5911yescharacteristic
986C232−1+4×C5911yescharacteristic
987D4—416no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—416no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4C2×C22⋊C4×C5914yes—
1077C2×C4C2×C22⋊C4×C5914yes—
1078C2×C4C2×C22⋊C4×C5914yes—
1079C2×C4#123×C5914yescomplemented
1080C22—24no—
1081C22—24no—
1082C22—24no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—81no—
1103C22—81no—
1104C22—81no—
1105C22—81no—
1106C22—81no—
1107C22—81no—
1108C22—81no—
1109C22—81no—
1110C22C22×C22⋊C4×C5911yescharacteristic
1111C22C2×C4×D4×C5911yescharacteristic
1112C22C4×#41×C5911yescharacteristic
1113C22C4×#41×C5911yescharacteristic
1114C22C4×#41×C5911yescharacteristic
1115C22C59×#51811yescharacteristic
1116C22C59×#52011yescharacteristic
1117C22C2×#123×C5911yescharacteristic
1118C22C59×#52511yescharacteristic
1119C22C59×#52511yescharacteristic
1120C22C59×#52511yescharacteristic
1121C22C59×#52911yescharacteristic
1122C22C59×#52911yescharacteristic
1123C22C59×#53211yescharacteristic
1124C22C59×#53211yescharacteristic
1125C22C59×#53811yescharacteristic
1126C22C59×#53911yescharacteristic
1127C22C59×#54011yescharacteristic
1128C22C59×#54211yescharacteristic
1129C22D42×C5911yescharacteristic
1130C22D42×C5911yescharacteristic
1131C22C59×#54611yescharacteristic
1132C22C59×#54611yescharacteristic
1133C22C59×#54611yescharacteristic
1134C22C59×#54711yescharacteristic
1135C22C59×#54811yescharacteristic
1136C22C59×#54811yescharacteristic
1137C22C59×#55011yescharacteristic
1138C22C59×#55011yescharacteristic
1139C22C59×#55111yescharacteristic
1140C22C59×#55111yescharacteristic
1141C22C59×#55211yescharacteristic
1142C22C59×#55311yescharacteristic
1143C22C59×#55311yescharacteristic
1144C22C59×#55911yescharacteristic
1145C4—24no—
1146C4—24no—
1147C4—24no—
1148C4—24no—
1149C4—42no—
1150C4—42no—
1151C4—42no—
1152C4—42no—
1153C4—42no—
1154C4—42no—
1155C4—42no—
1156C4—81no—
1157C4—81no—
1158C2—44no—
1159C2—82no—
1160C2C59×#229711yescharacteristic
1161C2C4×#123×C5911yescharacteristic
1162C2C59×#233511yescharacteristic
1163C2D4×C22⋊C4×C5911yescharacteristic
1164C2C59×#234111yescharacteristic
1165C2C59×#235911yescharacteristic
1166C2C59×#237411yescharacteristic
1167C2C59×#244311yescharacteristic
1168C2C59×#244511yescharacteristic
1169C2C59×#245611yescharacteristic
1170C2C59×#245811yescharacteristic
1171C2C59×#246111yescharacteristic
1172C2C59×#247111yescharacteristic
1173C2C59×#255411yescharacteristic
1174C2C59×#255811yescharacteristic
subgroupG/H
center, socleC24×C59C24
commutatorC23C23×C4×C59
Frattini, cosocleC24C24×C59
prime radicalC23×D4×C59C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C59 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C59×#387C2semidirect
4. C2×C4×C4⋊C4×C59C2semidirect
5. C2×C4×C22⋊C4×C59C2semidirect
6. C59×#1441C2semidirect
7. C59×#1439C2semidirect
8. C59×#1439C2semidirect
10. C59×#1437C2semidirect
11. C59×#1437C2semidirect
12. C59×#1437C2semidirect
13. C59×#1437C2semidirect
14. C59×#1436C2semidirect
15. C59×C22⋊#95C2semidirect
20. C2×#123×C59C4semidirect
298. C4⋊C4×C59C22⋊C4semidirect
491. C2×C4×C59#123semidirect
492. #14095C59direct (N × H)
573. C2×#387C2×C59semidirect
574. C2×C4×C4⋊C4C2×C59semidirect
575. C2×C4×C22⋊C4C2×C59semidirect
576. #1441C2×C59semidirect
577. #1439C2×C59semidirect
578. #1439C2×C59semidirect
580. #1437C2×C59semidirect
581. #1437C2×C59semidirect
582. #1437C2×C59semidirect
583. #1437C2×C59semidirect
584. #1436C2×C59semidirect
585. C22⋊#95C2×C59semidirect
607. C2×#123C4×C59semidirect
645. C59#14095direct (N × H)
886. C4⋊C4C22⋊C4×C59semidirect
1079. C2×C4#123×C59semidirect

Maximal subgroups

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

subgroupindex
C22×#123×C592
C2×C59×#3902
C2×C59×#3872
C2×C4×C4⋊C4×C592
C2×C4×C22⋊C4×C592
C59×#14412
C59×#14392
C59×#14382
C59×#14372
C59×#14362
C59×C22⋊#952
#1409559