Finite Group Databasebeta

← C59×#13967 #28426076

Subgroups — C59×#13967 #28426076

Order 15104.

4478 conjugacy classes of subgroups.

The subgroup lattice has 1062 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#120×C59C211yesmaximal, characteristic
2C22×C4×D4×C59C211yesmaximal, characteristic, complemented
3C23×C22⋊C4×C59C211yesmaximal, characteristic, complemented
4C2×C59×#386C212yesmaximal, complemented
5C2×C59×#386C211yesmaximal, characteristic, complemented
6C2×C59×#379C211yesmaximal, characteristic, complemented
7C59×#1439C212yesmaximal, complemented
8C59×#1438C212yesmaximal, complemented
9C59×#1437C212yesmaximal, complemented
10C59×C22⋊#95C211yesmaximal, characteristic, complemented
11C59×C22⋊#95C211yesmaximal, characteristic, complemented
12C26×C59C2211yescharacteristic
13C23×D4×C59C2212yes—
14C23×D4×C59C2211yescharacteristic
15C24×C4×C59C2211yescharacteristic
16C24×C4×C59C2211yescharacteristic
17C24×C4×C59C2211yescharacteristic, complemented
18C2×#120×C59—24no—
19C2×#120×C59—24no—
20C2×#120×C59C418yescomplemented
21C2×C4×D4×C59—24no—
22C2×C4×D4×C59—24no—
23C2×C4×D4×C59—24no—
24C22×C4⋊C4×C59C2211yescharacteristic, complemented
25C22×C22⋊C4×C59—24no—
26C22×C22⋊C4×C59—28no—
27C22×C22⋊C4×C59C2211yescharacteristic
28C22×C22⋊C4×C59C2212yes—
29C22×C22⋊C4×C59C2212yes—
30C22×C22⋊C4×C59C2212yes—
31C22×C22⋊C4×C59C2211yescharacteristic
32C22×C22⋊C4×C59C2212yes—
33C22×C22⋊C4×C59C2211yescharacteristic
34C22×C22⋊C4×C59C2212yes—
35C22×C22⋊C4×C59C2211yescharacteristic, complemented
36C22×C22⋊C4×C59C2212yescomplemented
37C22×C42×C59C2211yescharacteristic, complemented
38C59×#386—24no—
39C59×#386—28no—
40C59×#379—24no—
41C2×#95×C59C2212yescomplemented
42C2×#95×C59C2212yescomplemented
43C2×#95×C59C2212yescomplemented
44C2×#95×C59C2212yescomplemented
45C2×#95×C59C2212yescomplemented
46C25×C59—24no—
47C25×C59—22no—
48C25×C59—24no—
49C25×C59—22no—
50C25×C59—22no—
51C25×C59—22no—
52C25×C59—22no—
53C25×C59—22no—
54C25×C59—42no—
55C25×C59—42no—
56C25×C59C2×C414yescomplemented
57C25×C59C2311yescharacteristic
58C25×C59C2312yes—
59C25×C59C2311yescharacteristic
60C22×D4×C59—22no—
61C22×D4×C59—22no—
62C22×D4×C59—22no—
63C22×D4×C59—22no—
64C22×D4×C59—24no—
65C22×D4×C59—24no—
66C22×D4×C59—24no—
67C22×D4×C59—24no—
68C22×D4×C59—42no—
69C22×D4×C59—42no—
70C22×D4×C59C2×C414yes—
71C22×D4×C59C2×C418yescomplemented
72C22×D4×C59D414yes—
73C22×D4×C59D414yes—
74C23×C4×C59—22no—
75C23×C4×C59—22no—
76C23×C4×C59—22no—
77C23×C4×C59—22no—
78C23×C4×C59—24no—
79C23×C4×C59—24no—
80C23×C4×C59—22no—
81C23×C4×C59—22no—
82C23×C4×C59—22no—
83C23×C4×C59—22no—
84C23×C4×C59—24no—
85C23×C4×C59—42no—
86C23×C4×C59—42no—
87C23×C4×C59—42no—
88C23×C4×C59D414yescomplemented
89C23×C4×C59C2312yes—
90C23×C4×C59C2312yes—
91C23×C4×C59C2312yes—
92C23×C4×C59C2311yescharacteristic
93C23×C4×C59C2311yescharacteristic
94C23×C4×C59C2311yescharacteristic
95C23×C4×C59C2311yescharacteristic
96C23×C4×C59C2311yescharacteristic
97#120×C59—232no—
98C4×D4×C59—232no—
99C2×C4⋊C4×C59—22no—
100C2×C4⋊C4×C59—22no—
101C2×C4⋊C4×C59—22no—
102C2×C22⋊C4×C59—232no—
103C2×C22⋊C4×C59—24no—
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—24no—
110C2×C22⋊C4×C59—24no—
111C2×C22⋊C4×C59—24no—
112C2×C22⋊C4×C59—24no—
113C2×C22⋊C4×C59—24no—
114C2×C22⋊C4×C59—24no—
115C2×C22⋊C4×C59—22no—
116C2×C22⋊C4×C59—22no—
117C2×C22⋊C4×C59—22no—
118C2×C22⋊C4×C59—24no—
119C2×C22⋊C4×C59—22no—
120C2×C22⋊C4×C59—24no—
121C2×C22⋊C4×C59—24no—
122C2×C22⋊C4×C59—22no—
123C2×C22⋊C4×C59—24no—
124C2×C22⋊C4×C59—24no—
125C2×C22⋊C4×C59—24no—
126C2×C22⋊C4×C59—42no—
127C2×C22⋊C4×C59—42no—
128C2×C22⋊C4×C59—42no—
129C2×C22⋊C4×C59C2×C414yescomplemented
130C2×C22⋊C4×C59C2×C418yescomplemented
131C2×C22⋊C4×C59D414yescomplemented
132C2×C22⋊C4×C59D418yescomplemented
133C2×C42×C59—22no—
134C2×C42×C59—22no—
135C2×C42×C59—22no—
136#95×C59—24no—
137#95×C59—24no—
138#95×C59—24no—
139#95×C59—42no—
140#95×C59—42no—
141C24×C59—22no—
142C24×C59—22no—
143C24×C59—22no—
144C24×C59—22no—
145C24×C59—28no—
146C24×C59—28no—
147C24×C59—216no—
148C24×C59—28no—
149C24×C59—216no—
150C24×C59—22no—
151C24×C59—22no—
152C24×C59—22no—
153C24×C59—21no—
154C24×C59—21no—
155C24×C59—22no—
156C24×C59—22no—
157C24×C59—22no—
158C24×C59—21no—
159C24×C59—21no—
160C24×C59—22no—
161C24×C59—22no—
162C24×C59—22no—
163C24×C59—22no—
164C24×C59—22no—
165C24×C59—22no—
166C24×C59—22no—
167C24×C59—22no—
168C24×C59—22no—
169C24×C59—22no—
170C24×C59—28no—
171C24×C59—28no—
172C24×C59—48no—
173C24×C59—48no—
174C24×C59—48no—
175C24×C59—48no—
176C24×C59—48no—
177C24×C59—48no—
178C24×C59—48no—
179C24×C59—48no—
180C24×C59—48no—
181C24×C59—44no—
182C24×C59—44no—
183C24×C59—48no—
184C24×C59—44no—
185C24×C59—44no—
186C24×C59—44no—
187C24×C59—44no—
188C24×C59C22×C412yes—
189C24×C59C22×C414yes—
190C24×C59C22×C412yes—
191C24×C59C2×D412yes—
192C24×C59C2×D412yes—
193C24×C59C2×D414yes—
194C24×C59C2×D412yes—
195C24×C59C2×D412yes—
196C24×C59C2×D412yes—
197C24×C59C2×D412yes—
198C24×C59#4114yes—
199C24×C59#4112yes—
200C24×C59#4112yes—
201C24×C59C2411yescharacteristic
202C2×D4×C59—28no—
203C2×D4×C59—28no—
204C2×D4×C59—28no—
205C2×D4×C59—28no—
206C2×D4×C59—28no—
207C2×D4×C59—28no—
208C2×D4×C59—216no—
209C2×D4×C59—216no—
210C2×D4×C59—48no—
211C2×D4×C59—48no—
212C2×D4×C59—48no—
213C2×D4×C59—48no—
214C2×D4×C59—48no—
215C2×D4×C59C22⋊C4116yescomplemented
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—22no—
223C22×C4×C59—28no—
224C22×C4×C59—28no—
225C22×C4×C59—28no—
226C22×C4×C59—22no—
227C22×C4×C59—22no—
228C22×C4×C59—22no—
229C22×C4×C59—21no—
230C22×C4×C59—21no—
231C22×C4×C59—22no—
232C22×C4×C59—22no—
233C22×C4×C59—22no—
234C22×C4×C59—22no—
235C22×C4×C59—22no—
236C22×C4×C59—21no—
237C22×C4×C59—21no—
238C22×C4×C59—21no—
239C22×C4×C59—21no—
240C22×C4×C59—22no—
241C22×C4×C59—22no—
242C22×C4×C59—22no—
243C22×C4×C59—22no—
244C22×C4×C59—22no—
245C22×C4×C59—22no—
246C22×C4×C59—22no—
247C22×C4×C59—22no—
248C22×C4×C59—22no—
249C22×C4×C59—22no—
250C22×C4×C59—28no—
251C22×C4×C59—22no—
252C22×C4×C59—22no—
253C22×C4×C59—22no—
254C22×C4×C59—22no—
255C22×C4×C59—22no—
256C22×C4×C59—22no—
257C22×C4×C59—22no—
258C22×C4×C59—44no—
259C22×C4×C59—48no—
260C22×C4×C59—48no—
261C22×C4×C59—48no—
262C22×C4×C59—48no—
263C22×C4×C59—48no—
264C22×C4×C59—48no—
265C22×C4×C59—44no—
266C22×C4×C59—44no—
267C22×C4×C59—44no—
268C22×C4×C59—44no—
269C22×C4×C59C22×C414yes—
270C22×C4×C59C22×C412yes—
271C22×C4×C59C2×D414yes—
272C22×C4×C59C2×D412yes—
273C22×C4×C59C2×D412yes—
274C22×C4×C59C2×D412yes—
275C22×C4×C59C2×D412yes—
276C22×C4×C59C2×D412yes—
277C22×C4×C59C2×D414yes—
278C22×C4×C59C2×D412yes—
279C4⋊C4×C59—28no—
280C22⋊C4×C59—216no—
281C22⋊C4×C59—28no—
282C22⋊C4×C59—28no—
283C22⋊C4×C59—28no—
284C22⋊C4×C59—216no—
285C22⋊C4×C59—216no—
286C22⋊C4×C59—48no—
287C22⋊C4×C59—48no—
288C22⋊C4×C59—48no—
289C22⋊C4×C59—44no—
290C42×C59—28no—
291C23×C59—24no—
292C23×C59—24no—
293C23×C59—22no—
294C23×C59—22no—
295C23×C59—24no—
296C23×C59—22no—
297C23×C59—22no—
298C23×C59—24no—
299C23×C59—24no—
300C23×C59—24no—
301C23×C59—24no—
302C23×C59—24no—
303C23×C59—24no—
304C23×C59—24no—
305C23×C59—24no—
306C23×C59—24no—
307C23×C59—232no—
308C23×C59—24no—
309C23×C59—24no—
310C23×C59—22no—
311C23×C59—22no—
312C23×C59—24no—
313C23×C59—24no—
314C23×C59—24no—
315C23×C59—24no—
316C23×C59—24no—
317C23×C59—24no—
318C23×C59—24no—
319C23×C59—22no—
320C23×C59—22no—
321C23×C59—22no—
322C23×C59—22no—
323C23×C59—24no—
324C23×C59—24no—
325C23×C59—24no—
326C23×C59—24no—
327C23×C59—24no—
328C23×C59—24no—
329C23×C59—24no—
330C23×C59—24no—
331C23×C59—24no—
332C23×C59—24no—
333C23×C59—24no—
334C23×C59—24no—
335C23×C59—24no—
336C23×C59—24no—
337C23×C59—24no—
338C23×C59—432no—
339C23×C59—432no—
340C23×C59—416no—
341C23×C59—416no—
342C23×C59—416no—
343C23×C59—416no—
344C23×C59—432no—
345C23×C59—432no—
346C23×C59—416no—
347C23×C59—41no—
348C23×C59—42no—
349C23×C59—42no—
350C23×C59—42no—
351C23×C59—42no—
352C23×C59—41no—
353C23×C59—42no—
354C23×C59—41no—
355C23×C59—42no—
356C23×C59—41no—
357C23×C59—42no—
358C23×C59—42no—
359C23×C59—42no—
360C23×C59—42no—
361C23×C59—42no—
362C23×C59—42no—
363C23×C59—42no—
364C23×C59—42no—
365C23×C59—42no—
366C23×C59—42no—
367C23×C59—42no—
368C23×C59—42no—
369C23×C59—42no—
370C23×C59—42no—
371C23×C59—42no—
372C23×C59—42no—
373C23×C59—416no—
374C23×C59C2×C22⋊C414yes—
375C23×C59C2×C22⋊C414yescomplemented
376C23×C59C4×D414yes—
377C23×C59C4×D414yes—
378C23×C59C4×D418yescomplemented
379C23×C59#12014yes—
380C23×C59#12114yes—
381C23×C59#12114yes—
382C23×C59#12314yes—
383C23×C59C23×C411yescharacteristic
384C23×C59C22×D411yescharacteristic
385C23×C59C22×D411yescharacteristic
386C23×C59C22×D411yescharacteristic
387C23×C59C22×D411yescharacteristic
388C23×C59C22×D412yes—
389C23×C59C2×#4111yescharacteristic
390C23×C59C2×#4111yescharacteristic
391C23×C59C2×#4112yes—
392C23×C59H(5,𝔽2)12yes—
393C23×C59H(5,𝔽2)12yes—
394D4×C59—232no—
395D4×C59—432no—
396C2×C4×C59—22no—
397C2×C4×C59—22no—
398C2×C4×C59—22no—
399C2×C4×C59—22no—
400C2×C4×C59—22no—
401C2×C4×C59—22no—
402C2×C4×C59—22no—
403C2×C4×C59—22no—
404C2×C4×C59—24no—
405C2×C4×C59—24no—
406C2×C4×C59—24no—
407C2×C4×C59—24no—
408C2×C4×C59—24no—
409C2×C4×C59—22no—
410C2×C4×C59—22no—
411C2×C4×C59—24no—
412C2×C4×C59—22no—
413C2×C4×C59—22no—
414C2×C4×C59—22no—
415C2×C4×C59—24no—
416C2×C4×C59—24no—
417C2×C4×C59—24no—
418C2×C4×C59—24no—
419C2×C4×C59—416no—
420C2×C4×C59—416no—
421C2×C4×C59—416no—
422C2×C4×C59—41no—
423C2×C4×C59—42no—
424C2×C4×C59—41no—
425C2×C4×C59—41no—
426C2×C4×C59—41no—
427C2×C4×C59—42no—
428C2×C4×C59—42no—
429C2×C4×C59—42no—
430C2×C4×C59—42no—
431C2×C4×C59—42no—
432C2×C4×C59—42no—
433C2×C4×C59—42no—
434C2×C4×C59—42no—
435C2×C4×C59—42no—
436C2×C4×C59—42no—
437C2×C4×C59—42no—
438C2×C4×C59—42no—
439C2×C4×C59—42no—
440C2×C4×C59—42no—
441C2×C4×C59—42no—
442C2×C4×C59—42no—
443C2×C4×C59—42no—
444C2×C4×C59—42no—
445C2×C4×C59C2×C22⋊C414yescomplemented
446C2×C4×C59#12014yescomplemented
447#13967C5911yesmaximal, characteristic, direct product factor, Sylow
448C22×C59—24no—
449C22×C59—28no—
450C22×C59—28no—
451C22×C59—24no—
452C22×C59—24no—
453C22×C59—24no—
454C22×C59—28no—
455C22×C59—28no—
456C22×C59—24no—
457C22×C59—24no—
458C22×C59—28no—
459C22×C59—28no—
460C22×C59—28no—
461C22×C59—24no—
462C22×C59—28no—
463C22×C59—464no—
464C22×C59—42no—
465C22×C59—44no—
466C22×C59—44no—
467C22×C59—44no—
468C22×C59—44no—
469C22×C59—42no—
470C22×C59—44no—
471C22×C59—42no—
472C22×C59—44no—
473C22×C59—42no—
474C22×C59—44no—
475C22×C59—44no—
476C22×C59—44no—
477C22×C59—44no—
478C22×C59—44no—
479C22×C59—44no—
480C22×C59—44no—
481C22×C59—42no—
482C22×C59—44no—
483C22×C59—44no—
484C22×C59—42no—
485C22×C59#38618yescomplemented
486C22×C59C22×C22⋊C411yescharacteristic
487C22×C59C2×C4×D411yescharacteristic
488C22×C59C2×C4×D412yes—
489C22×C59C2×C4×D411yescharacteristic
490C22×C59#51812yes—
491C22×C59C2×#12011yescharacteristic
492C22×C59C2×#12011yescharacteristic
493C22×C59C2×#12111yescharacteristic
494C22×C59C2×#12111yescharacteristic
495C22×C59C2×#12311yescharacteristic
496C22×C59#52511yescharacteristic
497C22×C59#52512yes—
498C22×C59#53411yescharacteristic
499C22×C59#53511yescharacteristic
500C22×C59#53812yes—
501C22×C59D4212yes—
502C22×C59D4212yes—
503C22×C59D4212yes—
504C22×C59#54612yes—
505C22×C59#54612yes—
506C22×C59#54612yes—
507C22×C59#54612yes—
508C22×C59#55112yes—
509C4×C59—24no—
510C4×C59—24no—
511C4×C59—44no—
512C4×C59—42no—
513C4×C59—42no—
514C4×C59—42no—
515C4×C59—44no—
516C4×C59—82no—
517C22×#120C2×C5911yescharacteristic
518C22×C4×D4C2×C5911yescharacteristic, complemented
519C23×C22⋊C4C2×C5911yescharacteristic, complemented
520C2×#386C2×C5912yescomplemented
521C2×#386C2×C5911yescharacteristic, complemented
522C2×#379C2×C5911yescharacteristic, complemented
523#1439C2×C5912yescomplemented
524#1438C2×C5912yescomplemented
525#1437C2×C5912yescomplemented
526C22⋊#95C2×C5911yescharacteristic, complemented
527C22⋊#95C2×C5911yescharacteristic, complemented
528C2×C59—28no—
529C2×C59—44no—
530C2×C59—48no—
531C2×C59C2×#38611yescharacteristic
532C2×C59C4×#12011yescharacteristic
533C2×C59#232111yescharacteristic
534C2×C59D4×C22⋊C412yes—
535C2×C59#235812yes—
536C2×C59#240311yescharacteristic
537C2×C59#240411yescharacteristic
538C2×C59#240811yescharacteristic
539C2×C59#241812yes—
540C2×C59#242412yes—
541C2×C59#253411yescharacteristic
542C26C22×C5911yescharacteristic
543C23×D4C22×C5912yes—
544C23×D4C22×C5911yescharacteristic
545C24×C4C22×C5911yescharacteristic
546C24×C4C22×C5911yescharacteristic
547C24×C4C22×C5911yescharacteristic, complemented
548C2×#120—24no—
549C2×#120—24no—
550C2×#120C4×C5918yescomplemented
551C2×C4×D4—24no—
552C2×C4×D4—24no—
553C2×C4×D4—24no—
554C22×C4⋊C4C22×C5911yescharacteristic, complemented
555C22×C22⋊C4—24no—
556C22×C22⋊C4—28no—
557C22×C22⋊C4C22×C5912yes—
558C22×C22⋊C4C22×C5911yescharacteristic
559C22×C22⋊C4C22×C5912yes—
560C22×C22⋊C4C22×C5912yes—
561C22×C22⋊C4C22×C5911yescharacteristic
562C22×C22⋊C4C22×C5912yes—
563C22×C22⋊C4C22×C5912yes—
564C22×C22⋊C4C22×C5911yescharacteristic
565C22×C22⋊C4C22×C5911yescharacteristic, complemented
566C22×C22⋊C4C22×C5912yescomplemented
567C22×C42C22×C5911yescharacteristic, complemented
568#386—24no—
569#386—28no—
570#379—24no—
571C2×#95C22×C5912yescomplemented
572C2×#95C22×C5912yescomplemented
573C2×#95C22×C5912yescomplemented
574C2×#95C22×C5912yescomplemented
575C2×#95C22×C5912yescomplemented
576C59#1396711yescharacteristic, direct product factor, Sylow
577C25—24no—
578C25—22no—
579C25—24no—
580C25—22no—
581C25—22no—
582C25—22no—
583C25—22no—
584C25—22no—
585C25—42no—
586C25—42no—
587C25C2×C4×C5914yescomplemented
588C25C23×C5911yescharacteristic
589C25C23×C5912yes—
590C25C23×C5911yescharacteristic
591C22×D4—22no—
592C22×D4—22no—
593C22×D4—22no—
594C22×D4—22no—
595C22×D4—24no—
596C22×D4—24no—
597C22×D4—24no—
598C22×D4—24no—
599C22×D4—42no—
600C22×D4—42no—
601C22×D4C2×C4×C5914yes—
602C22×D4C2×C4×C5918yescomplemented
603C22×D4D4×C5914yes—
604C22×D4D4×C5914yes—
605C23×C4—22no—
606C23×C4—22no—
607C23×C4—22no—
608C23×C4—22no—
609C23×C4—24no—
610C23×C4—24no—
611C23×C4—22no—
612C23×C4—22no—
613C23×C4—22no—
614C23×C4—22no—
615C23×C4—24no—
616C23×C4—42no—
617C23×C4—42no—
618C23×C4—42no—
619C23×C4D4×C5914yescomplemented
620C23×C4C23×C5912yes—
621C23×C4C23×C5912yes—
622C23×C4C23×C5911yescharacteristic
623C23×C4C23×C5911yescharacteristic
624C23×C4C23×C5911yescharacteristic
625C23×C4C23×C5912yes—
626C23×C4C23×C5911yescharacteristic
627C23×C4C23×C5911yescharacteristic
628#120—232no—
629C4×D4—232no—
630C2×C4⋊C4—22no—
631C2×C4⋊C4—22no—
632C2×C4⋊C4—22no—
633C2×C22⋊C4—232no—
634C2×C22⋊C4—24no—
635C2×C22⋊C4—22no—
636C2×C22⋊C4—22no—
637C2×C22⋊C4—22no—
638C2×C22⋊C4—22no—
639C2×C22⋊C4—22no—
640C2×C22⋊C4—24no—
641C2×C22⋊C4—24no—
642C2×C22⋊C4—24no—
643C2×C22⋊C4—24no—
644C2×C22⋊C4—24no—
645C2×C22⋊C4—24no—
646C2×C22⋊C4—22no—
647C2×C22⋊C4—22no—
648C2×C22⋊C4—22no—
649C2×C22⋊C4—24no—
650C2×C22⋊C4—22no—
651C2×C22⋊C4—24no—
652C2×C22⋊C4—24no—
653C2×C22⋊C4—22no—
654C2×C22⋊C4—24no—
655C2×C22⋊C4—24no—
656C2×C22⋊C4—24no—
657C2×C22⋊C4—42no—
658C2×C22⋊C4—42no—
659C2×C22⋊C4—42no—
660C2×C22⋊C4C2×C4×C5914yescomplemented
661C2×C22⋊C4C2×C4×C5918yescomplemented
662C2×C22⋊C4D4×C5918yescomplemented
663C2×C22⋊C4D4×C5914yescomplemented
664C2×C42—22no—
665C2×C42—22no—
666C2×C42—22no—
667#95—24no—
668#95—24no—
669#95—24no—
670#95—42no—
671#95—42no—
672C24—22no—
673C24—22no—
674C24—22no—
675C24—22no—
676C24—28no—
677C24—28no—
678C24—216no—
679C24—28no—
680C24—216no—
681C24—22no—
682C24—22no—
683C24—22no—
684C24—21no—
685C24—21no—
686C24—22no—
687C24—22no—
688C24—22no—
689C24—21no—
690C24—21no—
691C24—22no—
692C24—22no—
693C24—22no—
694C24—22no—
695C24—22no—
696C24—22no—
697C24—22no—
698C24—22no—
699C24—22no—
700C24—22no—
701C24—28no—
702C24—28no—
703C24—48no—
704C24—48no—
705C24—48no—
706C24—48no—
707C24—48no—
708C24—48no—
709C24—48no—
710C24—48no—
711C24—48no—
712C24—44no—
713C24—44no—
714C24—48no—
715C24—44no—
716C24—44no—
717C24—44no—
718C24—44no—
719C24C22×C4×C5912yes—
720C24C22×C4×C5914yes—
721C24C22×C4×C5912yes—
722C24C2×D4×C5912yes—
723C24C2×D4×C5912yes—
724C24C2×D4×C5914yes—
725C24C2×D4×C5912yes—
726C24C2×D4×C5912yes—
727C24C2×D4×C5912yes—
728C24C2×D4×C5912yes—
729C24#41×C5914yes—
730C24#41×C5912yes—
731C24#41×C5912yes—
732C24C24×C5911yescharacteristic
733C2×D4—28no—
734C2×D4—28no—
735C2×D4—28no—
736C2×D4—28no—
737C2×D4—28no—
738C2×D4—28no—
739C2×D4—216no—
740C2×D4—216no—
741C2×D4—48no—
742C2×D4—48no—
743C2×D4—48no—
744C2×D4—48no—
745C2×D4—48no—
746C2×D4C22⋊C4×C59116yescomplemented
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—22no—
754C22×C4—28no—
755C22×C4—28no—
756C22×C4—28no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—28no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—44no—
790C22×C4—48no—
791C22×C4—48no—
792C22×C4—48no—
793C22×C4—48no—
794C22×C4—48no—
795C22×C4—48no—
796C22×C4—44no—
797C22×C4—44no—
798C22×C4—44no—
799C22×C4—44no—
800C22×C4C22×C4×C5914yes—
801C22×C4C22×C4×C5912yes—
802C22×C4C2×D4×C5914yes—
803C22×C4C2×D4×C5912yes—
804C22×C4C2×D4×C5912yes—
805C22×C4C2×D4×C5912yes—
806C22×C4C2×D4×C5912yes—
807C22×C4C2×D4×C5912yes—
808C22×C4C2×D4×C5914yes—
809C22×C4C2×D4×C5912yes—
810C4⋊C4—28no—
811C22⋊C4—216no—
812C22⋊C4—28no—
813C22⋊C4—28no—
814C22⋊C4—28no—
815C22⋊C4—216no—
816C22⋊C4—216no—
817C22⋊C4—48no—
818C22⋊C4—48no—
819C22⋊C4—48no—
820C22⋊C4—44no—
821C42—28no—
822C23—24no—
823C23—24no—
824C23—22no—
825C23—22no—
826C23—24no—
827C23—22no—
828C23—22no—
829C23—24no—
830C23—24no—
831C23—24no—
832C23—24no—
833C23—24no—
834C23—24no—
835C23—24no—
836C23—24no—
837C23—24no—
838C23—232no—
839C23—24no—
840C23—22no—
841C23—22no—
842C23—24no—
843C23—24no—
844C23—24no—
845C23—24no—
846C23—24no—
847C23—24no—
848C23—24no—
849C23—24no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—24no—
855C23—24no—
856C23—24no—
857C23—24no—
858C23—24no—
859C23—24no—
860C23—24no—
861C23—24no—
862C23—24no—
863C23—24no—
864C23—24no—
865C23—24no—
866C23—24no—
867C23—24no—
868C23—24no—
869C23—432no—
870C23—432no—
871C23—416no—
872C23—416no—
873C23—416no—
874C23—416no—
875C23—416no—
876C23—432no—
877C23—432no—
878C23—416no—
879C23—41no—
880C23—42no—
881C23—42no—
882C23—42no—
883C23—42no—
884C23—41no—
885C23—42no—
886C23—41no—
887C23—42no—
888C23—41no—
889C23—42no—
890C23—42no—
891C23—42no—
892C23—42no—
893C23—42no—
894C23—42no—
895C23—42no—
896C23—42no—
897C23—42no—
898C23—42no—
899C23—42no—
900C23—42no—
901C23—42no—
902C23—42no—
903C23—42no—
904C23—42no—
905C23C2×C22⋊C4×C5914yes—
906C23C2×C22⋊C4×C5914yescomplemented
907C23C4×D4×C5914yes—
908C23C4×D4×C5914yes—
909C23C4×D4×C5918yescomplemented
910C23#120×C5914yes—
911C23#121×C5914yes—
912C23#121×C5914yes—
913C23#123×C5914yes—
914C23C23×C4×C5911yescharacteristic
915C23C22×D4×C5911yescharacteristic
916C23C22×D4×C5911yescharacteristic
917C23C22×D4×C5911yescharacteristic
918C23C22×D4×C5911yescharacteristic
919C23C22×D4×C5912yes—
920C23C2×#41×C5911yescharacteristic
921C23C2×#41×C5911yescharacteristic
922C23C2×#41×C5912yes—
923C23H(5,𝔽2)×C5912yes—
924C23H(5,𝔽2)×C5912yes—
925D4—232no—
926D4—432no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—24no—
936C2×C4—24no—
937C2×C4—24no—
938C2×C4—24no—
939C2×C4—24no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—24no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—24no—
947C2×C4—24no—
948C2×C4—24no—
949C2×C4—24no—
950C2×C4—416no—
951C2×C4—416no—
952C2×C4—416no—
953C2×C4—41no—
954C2×C4—42no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—42no—
959C2×C4—42no—
960C2×C4—42no—
961C2×C4—42no—
962C2×C4—42no—
963C2×C4—42no—
964C2×C4—42no—
965C2×C4—42no—
966C2×C4—42no—
967C2×C4—42no—
968C2×C4—42no—
969C2×C4—42no—
970C2×C4—42no—
971C2×C4—42no—
972C2×C4—42no—
973C2×C4—42no—
974C2×C4—42no—
975C2×C4—42no—
976C2×C4C2×C22⋊C4×C5914yescomplemented
977C2×C4#120×C5914yescomplemented
978C22—24no—
979C22—24no—
980C22—24no—
981C22—28no—
982C22—28no—
983C22—24no—
984C22—24no—
985C22—24no—
986C22—28no—
987C22—28no—
988C22—24no—
989C22—28no—
990C22—28no—
991C22—28no—
992C22—28no—
993C22—464no—
994C22—44no—
995C22—42no—
996C22—44no—
997C22—42no—
998C22—44no—
999C22—42no—
1000C22—44no—
1001C22—44no—
1002C22—44no—
1003C22—42no—
1004C22—44no—
1005C22—44no—
1006C22—42no—
1007C22—44no—
1008C22—42no—
1009C22—44no—
1010C22—44no—
1011C22—44no—
1012C22—44no—
1013C22—44no—
1014C22—44no—
1015C22C59×#38618yescomplemented
1016C22C22×C22⋊C4×C5911yescharacteristic
1017C22C2×C4×D4×C5911yescharacteristic
1018C22C2×C4×D4×C5911yescharacteristic
1019C22C2×C4×D4×C5912yes—
1020C22C59×#51812yes—
1021C22C2×#120×C5911yescharacteristic
1022C22C2×#120×C5911yescharacteristic
1023C22C2×#121×C5911yescharacteristic
1024C22C2×#121×C5911yescharacteristic
1025C22C2×#123×C5911yescharacteristic
1026C22C59×#52511yescharacteristic
1027C22C59×#52512yes—
1028C22C59×#53411yescharacteristic
1029C22C59×#53511yescharacteristic
1030C22C59×#53812yes—
1031C22D42×C5912yes—
1032C22D42×C5912yes—
1033C22D42×C5912yes—
1034C22C59×#54612yes—
1035C22C59×#54612yes—
1036C22C59×#54612yes—
1037C22C59×#54612yes—
1038C22C59×#55112yes—
1039C4—24no—
1040C4—24no—
1041C4—44no—
1042C4—42no—
1043C4—42no—
1044C4—42no—
1045C4—44no—
1046C4—82no—
1047C2—28no—
1048C2—48no—
1049C2—44no—
1050C2C2×C59×#38611yescharacteristic
1051C2C4×#120×C5911yescharacteristic
1052C2C59×#232111yescharacteristic
1053C2D4×C22⋊C4×C5912yes—
1054C2C59×#235812yes—
1055C2C59×#240311yescharacteristic
1056C2C59×#240411yescharacteristic
1057C2C59×#240811yescharacteristic
1058C2C59×#241812yes—
1059C2C59×#242412yes—
1060C2C59×#253411yescharacteristic
subgroupG/H
center, socleC24×C59C24
commutatorC23C23×C4×C59
Frattini, cosocleC24C24×C59
prime radicalC22×#120×C59C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C59 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C4×D4×C59C2semidirect
3. C23×C22⋊C4×C59C2semidirect
4. C2×C59×#386C2semidirect
5. C2×C59×#386C2semidirect
6. C2×C59×#379C2semidirect
7. C59×#1439C2semidirect
8. C59×#1438C2semidirect
9. C59×#1437C2semidirect
10. C59×C22⋊#95C2semidirect
11. C59×C22⋊#95C2semidirect
17. C24×C4×C59C22semidirect
20. C2×#120×C59C4semidirect
24. C22×C4⋊C4×C59C22semidirect
35. C22×C22⋊C4×C59C22semidirect
36. C22×C22⋊C4×C59C22semidirect
37. C22×C42×C59C22semidirect
41. C2×#95×C59C22semidirect
42. C2×#95×C59C22semidirect
43. C2×#95×C59C22semidirect
44. C2×#95×C59C22semidirect
45. C2×#95×C59C22semidirect
56. C25×C59C2×C4semidirect
71. C22×D4×C59C2×C4semidirect
88. C23×C4×C59D4semidirect
129. C2×C22⋊C4×C59C2×C4semidirect
130. C2×C22⋊C4×C59C2×C4semidirect
131. C2×C22⋊C4×C59D4semidirect
132. C2×C22⋊C4×C59D4semidirect
215. C2×D4×C59C22⋊C4semidirect
375. C23×C59C2×C22⋊C4semidirect
378. C23×C59C4×D4semidirect
445. C2×C4×C59C2×C22⋊C4semidirect
446. C2×C4×C59#120semidirect
447. #13967C59direct (N × H)
485. C22×C59#386semidirect
518. C22×C4×D4C2×C59semidirect
519. C23×C22⋊C4C2×C59semidirect
520. C2×#386C2×C59semidirect
521. C2×#386C2×C59semidirect
522. C2×#379C2×C59semidirect
523. #1439C2×C59semidirect
524. #1438C2×C59semidirect
525. #1437C2×C59semidirect
526. C22⋊#95C2×C59semidirect
527. C22⋊#95C2×C59semidirect
547. C24×C4C22×C59semidirect
550. C2×#120C4×C59semidirect
554. C22×C4⋊C4C22×C59semidirect
565. C22×C22⋊C4C22×C59semidirect
566. C22×C22⋊C4C22×C59semidirect
567. C22×C42C22×C59semidirect
571. C2×#95C22×C59semidirect
572. C2×#95C22×C59semidirect
573. C2×#95C22×C59semidirect
574. C2×#95C22×C59semidirect
575. C2×#95C22×C59semidirect
576. C59#13967direct (N × H)
587. C25C2×C4×C59semidirect
602. C22×D4C2×C4×C59semidirect
619. C23×C4D4×C59semidirect
660. C2×C22⋊C4C2×C4×C59semidirect
661. C2×C22⋊C4C2×C4×C59semidirect
662. C2×C22⋊C4D4×C59semidirect
663. C2×C22⋊C4D4×C59semidirect
746. C2×D4C22⋊C4×C59semidirect
906. C23C2×C22⋊C4×C59semidirect
909. C23C4×D4×C59semidirect
976. C2×C4C2×C22⋊C4×C59semidirect
977. C2×C4#120×C59semidirect
1015. C22C59×#386semidirect

Maximal subgroups

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

subgroupindex
C22×#120×C592
C22×C4×D4×C592
C23×C22⋊C4×C592
C2×C59×#3862
C2×C59×#3792
C59×#14392
C59×#14382
C59×#14372
C59×C22⋊#952
#1396759