Finite Group Databasebeta

← C59×#14421 #28426530

Subgroups — C59×#14421 #28426530

Order 15104.

2126 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#124×C59C211yesmaximal, characteristic
2C2×C59×#391C211yesmaximal, characteristic, complemented
3C2×C59×#388C211yesmaximal, characteristic, complemented
4C2×C59×#386C211yesmaximal, characteristic
5C2×C59×#385C211yesmaximal, characteristic, complemented
6C59×#1446C211yesmaximal, characteristic, complemented
7C59×#1440C211yesmaximal, characteristic, complemented
8C59×#1439C211yesmaximal, characteristic, complemented
9C59×#1439C211yesmaximal, characteristic, complemented
10C59×#1439C211yesmaximal, characteristic, complemented
11C59×#1438C211yesmaximal, characteristic
12C59×#1437C211yesmaximal, characteristic, complemented
13C59×C4⋊#95C211yesmaximal, characteristic, complemented
14C59×#1434C211yesmaximal, characteristic, complemented
15C59×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×Q8×C59C2211yescharacteristic
17C23×D4×C59C2211yescharacteristic
18C24×C4×C59C2211yescharacteristic
19C2×#124×C59—24no—
20C2×#124×C59—24no—
21C2×#124×C59C418yescomplemented
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
38C59×#391—24no—
39C59×#388—24no—
40C59×#386—24no—
41C59×#385—24no—
42C2×#95×C59C2211yescharacteristic
43C2×#95×C59C2211yescharacteristic
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×Q8×C59—22no—
61C22×Q8×C59—22no—
62C22×Q8×C59—22no—
63C22×Q8×C59—22no—
64C22×Q8×C59—41no—
65C22×Q8×C59—41no—
66C22×Q8×C59C2×C414yescomplemented
67C22×D4×C59—22no—
68C22×D4×C59—22no—
69C22×D4×C59—22no—
70C22×D4×C59—22no—
71C22×D4×C59—41no—
72C22×D4×C59—41no—
73C22×D4×C59C2×C414yes—
74C23×C4×C59—22no—
75C23×C4×C59—22no—
76C23×C4×C59—22no—
77C23×C4×C59—41no—
78C23×C4×C59—41no—
79C23×C4×C59—41no—
80C23×C4×C59—41no—
81C23×C4×C59C2311yescharacteristic
82C23×C4×C59C2311yescharacteristic
83C23×C4×C59C2311yescharacteristic
84C23×C4×C59C2311yescharacteristic
85C23×C4×C59C2311yescharacteristic
86C23×C4×C59C2311yescharacteristic
87C23×C4×C59C2311yescharacteristic
88C23×C4×C59C2311yescharacteristic
89C23×C4×C59C2311yescharacteristic
90C23×C4×C59C2311yescharacteristic
91C23×C4×C59C2311yescharacteristic
92C23×C4×C59C2311yescharacteristic
93C23×C4×C59C2311yescharacteristic
94#124×C59—232no—
95C2×C4⋊C4×C59—22no—
96C2×C4⋊C4×C59—22no—
97C2×C4⋊C4×C59—22no—
98C2×C4⋊C4×C59—22no—
99C2×C4⋊C4×C59—22no—
100C2×C4⋊C4×C59—22no—
101C2×C4⋊C4×C59—41no—
102C2×C4⋊C4×C59—41no—
103C2×C4⋊C4×C59—41no—
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—41no—
120C2×C22⋊C4×C59—41no—
121C2×C22⋊C4×C59—41no—
122C2×C22⋊C4×C59—41no—
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×C59—41no—
130C2×C22⋊C4×C59—41no—
131C2×C22⋊C4×C59C2×C414yes—
132C2×C22⋊C4×C59C2×C414yes—
133C2×C22⋊C4×C59C2×C414yescomplemented
134C2×C22⋊C4×C59C2×C414yescomplemented
135C2×C22⋊C4×C59D414yes—
136C2×C22⋊C4×C59D414yes—
137C2×C42×C59—22no—
138C2×C42×C59—22no—
139C2×C42×C59—22no—
140C2×C42×C59—22no—
141C2×C42×C59—41no—
142C2×C42×C59C2×C414yescomplemented
143#95×C59—22no—
144#95×C59—22no—
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—41no—
153#95×C59—41no—
154#95×C59—41no—
155#95×C59—41no—
156#95×C59—41no—
157#95×C59—41no—
158#95×C59D414yes—
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×C59C2×D412yes—
189C24×C59C2411yescharacteristic
190C2×Q8×C59—28no—
191C2×Q8×C59—28no—
192C2×Q8×C59—44no—
193C2×Q8×C59—44no—
194C2×Q8×C59—44no—
195C2×Q8×C59—44no—
196C2×Q8×C59—44no—
197C2×D4×C59—28no—
198C2×D4×C59—28no—
199C2×D4×C59—44no—
200C2×D4×C59—44no—
201C2×D4×C59—44no—
202C2×D4×C59—44no—
203C2×D4×C59—44no—
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—21no—
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—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—44no—
281C22×C4×C59—44no—
282C22×C4×C59—44no—
283C22×C4×C59—44no—
284C22×C4×C59—44no—
285C22×C4×C59—44no—
286C22×C4×C59—44no—
287C22×C4×C59C22×C412yes—
288C22×C4×C59C22×C412yes—
289C22×C4×C59C22×C412yes—
290C22×C4×C59C22×C412yes—
291C22×C4×C59C22×C412yes—
292C22×C4×C59C2×D412yes—
293C22×C4×C59C2×D412yes—
294C22×C4×C59C2×D412yes—
295C22×C4×C59C2×D412yes—
296C22×C4×C59C2×D412yes—
297C22×C4×C59C2×D412yes—
298C22×C4×C59C2×D412yes—
299C22×C4×C59#4112yes—
300C22×C4×C59#4112yes—
301C22×C4×C59#4112yes—
302C4⋊C4×C59—44no—
303C4⋊C4×C59—44no—
304C4⋊C4×C59—44no—
305C22⋊C4×C59—28no—
306C22⋊C4×C59—28no—
307C22⋊C4×C59—28no—
308C22⋊C4×C59—44no—
309C22⋊C4×C59—44no—
310C22⋊C4×C59—44no—
311C22⋊C4×C59—44no—
312C22⋊C4×C59—44no—
313C22⋊C4×C59—44no—
314C22⋊C4×C59—44no—
315C22⋊C4×C59C22⋊C4116yescomplemented
316C42×C59—28no—
317C42×C59—44no—
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—22no—
340C23×C59—22no—
341C23×C59—22no—
342C23×C59—22no—
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×C59—41no—
384C23×C59—41no—
385C23×C59—41no—
386C23×C59—41no—
387C23×C59C2×C22⋊C414yes—
388C23×C59C23×C411yescharacteristic
389C23×C59C22×D411yescharacteristic
390C23×C59C22×D411yescharacteristic
391C23×C59C22×D411yescharacteristic
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×C59H(5,𝔽2)11yescharacteristic
399C23×C59H(5,𝔽2)11yescharacteristic
400C23×C592−1+411yescharacteristic
401C23×C592−1+411yescharacteristic
402C23×C592−1+411yescharacteristic
403Q8×C59—416no—
404D4×C59—416no—
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—416no—
442C2×C4×C59—41no—
443C2×C4×C59—41no—
444C2×C4×C59—41no—
445C2×C4×C59—41no—
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×C59—41no—
489C2×C4×C59—41no—
490C2×C4×C59—41no—
491C2×C4×C59—41no—
492C2×C4×C59—41no—
493C2×C4×C59—41no—
494C2×C4×C59C2×C22⋊C414yes—
495C2×C4×C59C2×C22⋊C414yes—
496C2×C4×C59C4×D414yes—
497#14421C5911yesmaximal, characteristic, direct product factor, Sylow
498C22×C59—24no—
499C22×C59—24no—
500C22×C59—24no—
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—42no—
516C22×C59—42no—
517C22×C59—42no—
518C22×C59—42no—
519C22×C59—42no—
520C22×C59—81no—
521C22×C59—81no—
522C22×C59—81no—
523C22×C59—81no—
524C22×C59—81no—
525C22×C59—81no—
526C22×C59—81no—
527C22×C59—81no—
528C22×C59C22×C22⋊C411yescharacteristic
529C22×C59C2×C4×D411yescharacteristic
530C22×C59C4×#4111yescharacteristic
531C22×C59#51811yescharacteristic
532C22×C59#52011yescharacteristic
533C22×C59#52011yescharacteristic
534C22×C59#52011yescharacteristic
535C22×C59#53511yescharacteristic
536C22×C59#53511yescharacteristic
537C22×C59#53611yescharacteristic
538C22×C59#53611yescharacteristic
539C22×C59#53711yescharacteristic
540C22×C59#53711yescharacteristic
541C22×C59#53811yescharacteristic
542C22×C59#53811yescharacteristic
543C22×C59#54211yescharacteristic
544C22×C59#54211yescharacteristic
545C22×C59#54211yescharacteristic
546C22×C59#54211yescharacteristic
547C22×C59D4211yescharacteristic
548C22×C59D4211yescharacteristic
549C22×C59#54611yescharacteristic
550C22×C59#54611yescharacteristic
551C22×C59#54611yescharacteristic
552C22×C59#54611yescharacteristic
553C22×C59#54611yescharacteristic
554C22×C59#54711yescharacteristic
555C22×C59#54711yescharacteristic
556C22×C59#54811yescharacteristic
557C22×C59#55611yescharacteristic
558C22×C59#55911yescharacteristic
559C22×C59H(3,𝔽4)11yescharacteristic
560C22×C59#56211yescharacteristic
561C22×C59#56211yescharacteristic
562C22×C59#56311yescharacteristic
563C4×C59—24no—
564C4×C59—24no—
565C4×C59—24no—
566C4×C59—42no—
567C4×C59—42no—
568C4×C59—42no—
569C4×C59—42no—
570C4×C59—42no—
571C4×C59—42no—
572C4×C59—81no—
573C4×C59—81no—
574C4×C59—81no—
575C4×C59—81no—
576C22×#124C2×C5911yescharacteristic
577C2×#391C2×C5911yescharacteristic, complemented
578C2×#388C2×C5911yescharacteristic, complemented
579C2×#386C2×C5911yescharacteristic
580C2×#385C2×C5911yescharacteristic, complemented
581#1446C2×C5911yescharacteristic, complemented
582#1440C2×C5911yescharacteristic, complemented
583#1439C2×C5911yescharacteristic, complemented
584#1439C2×C5911yescharacteristic, complemented
585#1439C2×C5911yescharacteristic, complemented
586#1438C2×C5911yescharacteristic
587#1437C2×C5911yescharacteristic, complemented
588C4⋊#95C2×C5911yescharacteristic, complemented
589#1434C2×C5911yescharacteristic, complemented
590C22⋊#95C2×C5911yescharacteristic, complemented
591C2×C59—44no—
592C2×C59—82no—
593C2×C59#231111yescharacteristic
594C2×C59#232611yescharacteristic
595C2×C59#233711yescharacteristic
596C2×C59D4×C22⋊C411yescharacteristic
597C2×C59#233911yescharacteristic
598C2×C59#236711yescharacteristic
599C2×C59#237911yescharacteristic
600C2×C59#267011yescharacteristic
601C2×C59#267211yescharacteristic
602C2×C59#267411yescharacteristic
603C2×C59#267611yescharacteristic
604C2×C59#270011yescharacteristic
605C2×C59#271011yescharacteristic
606C2×C59#271211yescharacteristic
607C2×C59#271511yescharacteristic
608C23×Q8C22×C5911yescharacteristic
609C23×D4C22×C5911yescharacteristic
610C24×C4C22×C5911yescharacteristic
611C2×#124—24no—
612C2×#124—24no—
613C2×#124C4×C5918yescomplemented
614C22×C4⋊C4C22×C5911yescharacteristic
615C22×C4⋊C4C22×C5911yescharacteristic
616C22×C4⋊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×C22⋊C4C22×C5911yescharacteristic
624C22×C22⋊C4C22×C5911yescharacteristic
625C22×C22⋊C4C22×C5911yescharacteristic
626C22×C22⋊C4C22×C5911yescharacteristic
627C22×C22⋊C4C22×C5911yescharacteristic
628C22×C42C22×C5911yescharacteristic
629C22×C42C22×C5911yescharacteristic
630#391—24no—
631#388—24no—
632#386—24no—
633#385—24no—
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
645C2×#95C22×C5911yescharacteristic
646C2×#95C22×C5911yescharacteristic
647C2×#95C22×C5911yescharacteristic
648C2×#95C22×C5911yescharacteristic
649C2×#95C22×C5911yescharacteristic
650C59#1442111yescharacteristic, direct product factor, Sylow
651C25C23×C5911yescharacteristic
652C25C23×C5911yescharacteristic
653C22×Q8—22no—
654C22×Q8—22no—
655C22×Q8—22no—
656C22×Q8—22no—
657C22×Q8—41no—
658C22×Q8—41no—
659C22×Q8C2×C4×C5914yescomplemented
660C22×D4—22no—
661C22×D4—22no—
662C22×D4—22no—
663C22×D4—22no—
664C22×D4—41no—
665C22×D4—41no—
666C22×D4C2×C4×C5914yes—
667C23×C4—22no—
668C23×C4—22no—
669C23×C4—22no—
670C23×C4—41no—
671C23×C4—41no—
672C23×C4—41no—
673C23×C4—41no—
674C23×C4C23×C5911yescharacteristic
675C23×C4C23×C5911yescharacteristic
676C23×C4C23×C5911yescharacteristic
677C23×C4C23×C5911yescharacteristic
678C23×C4C23×C5911yescharacteristic
679C23×C4C23×C5911yescharacteristic
680C23×C4C23×C5911yescharacteristic
681C23×C4C23×C5911yescharacteristic
682C23×C4C23×C5911yescharacteristic
683C23×C4C23×C5911yescharacteristic
684C23×C4C23×C5911yescharacteristic
685C23×C4C23×C5911yescharacteristic
686C23×C4C23×C5911yescharacteristic
687#124—232no—
688C2×C4⋊C4—22no—
689C2×C4⋊C4—22no—
690C2×C4⋊C4—22no—
691C2×C4⋊C4—22no—
692C2×C4⋊C4—22no—
693C2×C4⋊C4—22no—
694C2×C4⋊C4—41no—
695C2×C4⋊C4—41no—
696C2×C4⋊C4—41no—
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—22no—
712C2×C22⋊C4—41no—
713C2×C22⋊C4—41no—
714C2×C22⋊C4—41no—
715C2×C22⋊C4—41no—
716C2×C22⋊C4—41no—
717C2×C22⋊C4—41no—
718C2×C22⋊C4—41no—
719C2×C22⋊C4—41no—
720C2×C22⋊C4—41no—
721C2×C22⋊C4—41no—
722C2×C22⋊C4—41no—
723C2×C22⋊C4—41no—
724C2×C22⋊C4C2×C4×C5914yes—
725C2×C22⋊C4C2×C4×C5914yes—
726C2×C22⋊C4C2×C4×C5914yescomplemented
727C2×C22⋊C4C2×C4×C5914yescomplemented
728C2×C22⋊C4D4×C5914yes—
729C2×C22⋊C4D4×C5914yes—
730C2×C42—22no—
731C2×C42—22no—
732C2×C42—22no—
733C2×C42—22no—
734C2×C42—41no—
735C2×C42C2×C4×C5914yescomplemented
736#95—22no—
737#95—22no—
738#95—22no—
739#95—22no—
740#95—22no—
741#95—22no—
742#95—22no—
743#95—22no—
744#95—22no—
745#95—41no—
746#95—41no—
747#95—41no—
748#95—41no—
749#95—41no—
750#95—41no—
751#95D4×C5914yes—
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—
773C24—21no—
774C24—21no—
775C24—21no—
776C24—21no—
777C24—21no—
778C24C22×C4×C5912yes—
779C24C22×C4×C5912yes—
780C24C2×D4×C5912yes—
781C24C2×D4×C5912yes—
782C24C24×C5911yescharacteristic
783C2×Q8—28no—
784C2×Q8—28no—
785C2×Q8—44no—
786C2×Q8—44no—
787C2×Q8—44no—
788C2×Q8—44no—
789C2×Q8—44no—
790C2×D4—28no—
791C2×D4—28no—
792C2×D4—44no—
793C2×D4—44no—
794C2×D4—44no—
795C2×D4—44no—
796C2×D4—44no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
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—21no—
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—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—44no—
874C22×C4—44no—
875C22×C4—44no—
876C22×C4—44no—
877C22×C4—44no—
878C22×C4—44no—
879C22×C4—44no—
880C22×C4C22×C4×C5912yes—
881C22×C4C22×C4×C5912yes—
882C22×C4C22×C4×C5912yes—
883C22×C4C22×C4×C5912yes—
884C22×C4C22×C4×C5912yes—
885C22×C4C2×D4×C5912yes—
886C22×C4C2×D4×C5912yes—
887C22×C4C2×D4×C5912yes—
888C22×C4C2×D4×C5912yes—
889C22×C4C2×D4×C5912yes—
890C22×C4C2×D4×C5912yes—
891C22×C4C2×D4×C5912yes—
892C22×C4#41×C5912yes—
893C22×C4#41×C5912yes—
894C22×C4#41×C5912yes—
895C4⋊C4—44no—
896C4⋊C4—44no—
897C4⋊C4—44no—
898C22⋊C4—28no—
899C22⋊C4—28no—
900C22⋊C4—28no—
901C22⋊C4—44no—
902C22⋊C4—44no—
903C22⋊C4—44no—
904C22⋊C4—44no—
905C22⋊C4—44no—
906C22⋊C4—44no—
907C22⋊C4—44no—
908C22⋊C4C22⋊C4×C59116yescomplemented
909C42—28no—
910C42—44no—
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—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
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—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23C2×C22⋊C4×C5914yes—
981C23C23×C4×C5911yescharacteristic
982C23C22×D4×C5911yescharacteristic
983C23C22×D4×C5911yescharacteristic
984C23C22×D4×C5911yescharacteristic
985C23C2×#41×C5911yescharacteristic
986C23C2×#41×C5911yescharacteristic
987C23C2×#41×C5911yescharacteristic
988C23H(5,𝔽2)×C5911yescharacteristic
989C23H(5,𝔽2)×C5911yescharacteristic
990C23H(5,𝔽2)×C5911yescharacteristic
991C23H(5,𝔽2)×C5911yescharacteristic
992C23H(5,𝔽2)×C5911yescharacteristic
993C232−1+4×C5911yescharacteristic
994C232−1+4×C5911yescharacteristic
995C232−1+4×C5911yescharacteristic
996Q8—416no—
997D4—416no—
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—22no—
1034C2×C4—416no—
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×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4C2×C22⋊C4×C5914yes—
1088C2×C4C2×C22⋊C4×C5914yes—
1089C2×C4C4×D4×C5914yes—
1090C22—24no—
1091C22—24no—
1092C22—24no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—81no—
1113C22—81no—
1114C22—81no—
1115C22—81no—
1116C22—81no—
1117C22—81no—
1118C22—81no—
1119C22—81no—
1120C22C22×C22⋊C4×C5911yescharacteristic
1121C22C2×C4×D4×C5911yescharacteristic
1122C22C4×#41×C5911yescharacteristic
1123C22C59×#51811yescharacteristic
1124C22C59×#52011yescharacteristic
1125C22C59×#52011yescharacteristic
1126C22C59×#52011yescharacteristic
1127C22C59×#53511yescharacteristic
1128C22C59×#53511yescharacteristic
1129C22C59×#53611yescharacteristic
1130C22C59×#53611yescharacteristic
1131C22C59×#53711yescharacteristic
1132C22C59×#53711yescharacteristic
1133C22C59×#53811yescharacteristic
1134C22C59×#53811yescharacteristic
1135C22C59×#54211yescharacteristic
1136C22C59×#54211yescharacteristic
1137C22C59×#54211yescharacteristic
1138C22C59×#54211yescharacteristic
1139C22D42×C5911yescharacteristic
1140C22D42×C5911yescharacteristic
1141C22C59×#54611yescharacteristic
1142C22C59×#54611yescharacteristic
1143C22C59×#54611yescharacteristic
1144C22C59×#54611yescharacteristic
1145C22C59×#54611yescharacteristic
1146C22C59×#54711yescharacteristic
1147C22C59×#54711yescharacteristic
1148C22C59×#54811yescharacteristic
1149C22C59×#55611yescharacteristic
1150C22C59×#55911yescharacteristic
1151C22C59×H(3,𝔽4)11yescharacteristic
1152C22C59×#56211yescharacteristic
1153C22C59×#56211yescharacteristic
1154C22C59×#56311yescharacteristic
1155C4—24no—
1156C4—24no—
1157C4—24no—
1158C4—42no—
1159C4—42no—
1160C4—42no—
1161C4—42no—
1162C4—42no—
1163C4—42no—
1164C4—81no—
1165C4—81no—
1166C4—81no—
1167C4—81no—
1168C2—44no—
1169C2—82no—
1170C2C59×#231111yescharacteristic
1171C2C59×#232611yescharacteristic
1172C2C59×#233711yescharacteristic
1173C2D4×C22⋊C4×C5911yescharacteristic
1174C2C59×#233911yescharacteristic
1175C2C59×#236711yescharacteristic
1176C2C59×#237911yescharacteristic
1177C2C59×#267011yescharacteristic
1178C2C59×#267211yescharacteristic
1179C2C59×#267411yescharacteristic
1180C2C59×#267611yescharacteristic
1181C2C59×#270011yescharacteristic
1182C2C59×#271011yescharacteristic
1183C2C59×#271211yescharacteristic
1184C2C59×#271511yescharacteristic
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
2. C2×C59×#391C2semidirect
3. C2×C59×#388C2semidirect
5. C2×C59×#385C2semidirect
6. C59×#1446C2semidirect
7. C59×#1440C2semidirect
8. C59×#1439C2semidirect
9. C59×#1439C2semidirect
10. C59×#1439C2semidirect
12. C59×#1437C2semidirect
13. C59×C4⋊#95C2semidirect
14. C59×#1434C2semidirect
15. C59×C22⋊#95C2semidirect
21. C2×#124×C59C4semidirect
66. C22×Q8×C59C2×C4semidirect
133. C2×C22⋊C4×C59C2×C4semidirect
134. C2×C22⋊C4×C59C2×C4semidirect
142. C2×C42×C59C2×C4semidirect
315. C22⋊C4×C59C22⋊C4semidirect
497. #14421C59direct (N × H)
577. C2×#391C2×C59semidirect
578. C2×#388C2×C59semidirect
580. C2×#385C2×C59semidirect
581. #1446C2×C59semidirect
582. #1440C2×C59semidirect
583. #1439C2×C59semidirect
584. #1439C2×C59semidirect
585. #1439C2×C59semidirect
587. #1437C2×C59semidirect
588. C4⋊#95C2×C59semidirect
589. #1434C2×C59semidirect
590. C22⋊#95C2×C59semidirect
613. C2×#124C4×C59semidirect
650. C59#14421direct (N × H)
659. C22×Q8C2×C4×C59semidirect
726. C2×C22⋊C4C2×C4×C59semidirect
727. C2×C22⋊C4C2×C4×C59semidirect
735. C2×C42C2×C4×C59semidirect
908. C22⋊C4C22⋊C4×C59semidirect

Maximal subgroups

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

subgroupindex
C22×#124×C592
C2×C59×#3912
C2×C59×#3882
C2×C59×#3862
C2×C59×#3852
C59×#14462
C59×#14402
C59×#14392
C59×#14382
C59×#14372
C59×C4⋊#952
C59×#14342
C59×C22⋊#952
#1442159