Finite Group Databasebeta

← C59×#16830 #28428939

Subgroups — C59×#16830 #28428939

Order 15104.

1346 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×#399C211yesmaximal, characteristic
2C2×C59×#397C211yesmaximal, characteristic
3C59×#1443C212yesmaximal, complemented
4C59×#1442C212yesmaximal, complemented
5C59×#1442C212yesmaximal, complemented
6C59×#1441C212yesmaximal, complemented
7C59×#1440C212yesmaximal
8C59×C22⋊#95C211yesmaximal, characteristic
9C59×C22⋊#95C212yesmaximal
10C24×C4×C59C2211yescharacteristic
11C22×C4⋊C4×C59C2212yes—
12C22×C4⋊C4×C59C2211yescharacteristic
13C22×C4⋊C4×C59C2211yescharacteristic
14C22×C22⋊C4×C59C2212yes—
15C22×C22⋊C4×C59C2212yes—
16C22×C22⋊C4×C59C2211yescharacteristic
17C22×C22⋊C4×C59C2211yescharacteristic
18C59×#399—24no—
19C59×#397—24no—
20C2×#95×C59C2211yescharacteristic
21C2×#95×C59C2212yes—
22C2×#95×C59C2211yescharacteristic
23C2×#95×C59C2212yes—
24C2×#95×C59C2212yes—
25C2×#95×C59C2212yes—
26C2×#95×C59C2212yes—
27C2×#95×C59C2212yes—
28C2×#95×C59C2212yes—
29C2×#95×C59C2212yes—
30C2×#95×C59C2212yes—
31C2×#95×C59C2212yes—
32C2×#95×C59C2212yes—
33C25×C59C2311yescharacteristic
34C23×C4×C59—22no—
35C23×C4×C59—24no—
36C23×C4×C59—41no—
37C23×C4×C59—42no—
38C23×C4×C59—41no—
39C23×C4×C59C2312yes—
40C23×C4×C59C2312yes—
41C23×C4×C59C2312yes—
42C23×C4×C59C2312yes—
43C23×C4×C59C2311yescharacteristic
44C23×C4×C59C2311yescharacteristic
45C23×C4×C59C2312yes—
46C23×C4×C59C2312yes—
47C2×C4⋊C4×C59—22no—
48C2×C4⋊C4×C59—24no—
49C2×C4⋊C4×C59—22no—
50C2×C4⋊C4×C59—24no—
51C2×C4⋊C4×C59—42no—
52C2×C4⋊C4×C59—41no—
53C2×C4⋊C4×C59—41no—
54C2×C4⋊C4×C59—41no—
55C2×C4⋊C4×C59—41no—
56C2×C22⋊C4×C59—24no—
57C2×C22⋊C4×C59—24no—
58C2×C22⋊C4×C59—22no—
59C2×C22⋊C4×C59—24no—
60C2×C22⋊C4×C59—24no—
61C2×C22⋊C4×C59—24no—
62C2×C22⋊C4×C59—41no—
63C2×C22⋊C4×C59—41no—
64C2×C22⋊C4×C59—42no—
65C2×C22⋊C4×C59—41no—
66C2×C22⋊C4×C59—41no—
67C2×C22⋊C4×C59D414yes—
68#95×C59—22no—
69#95×C59—24no—
70#95×C59—22no—
71#95×C59—24no—
72#95×C59—24no—
73#95×C59—24no—
74#95×C59—42no—
75#95×C59—42no—
76#95×C59—42no—
77#95×C59—42no—
78#95×C59—42no—
79#95×C59—42no—
80#95×C59—42no—
81C24×C59—22no—
82C24×C59—22no—
83C24×C59—21no—
84C24×C59—21no—
85C24×C59—21no—
86C24×C59—22no—
87C24×C59—21no—
88C24×C59—22no—
89C24×C59C2×D412yes—
90C24×C59#4112yes—
91C24×C59#4112yes—
92C24×C59C2411yescharacteristic
93C22×C4×C59—22no—
94C22×C4×C59—22no—
95C22×C4×C59—22no—
96C22×C4×C59—22no—
97C22×C4×C59—22no—
98C22×C4×C59—22no—
99C22×C4×C59—22no—
100C22×C4×C59—22no—
101C22×C4×C59—22no—
102C22×C4×C59—22no—
103C22×C4×C59—22no—
104C22×C4×C59—22no—
105C22×C4×C59—21no—
106C22×C4×C59—21no—
107C22×C4×C59—21no—
108C22×C4×C59—21no—
109C22×C4×C59—22no—
110C22×C4×C59—22no—
111C22×C4×C59—22no—
112C22×C4×C59—22no—
113C22×C4×C59—22no—
114C22×C4×C59—22no—
115C22×C4×C59—22no—
116C22×C4×C59—22no—
117C22×C4×C59—22no—
118C22×C4×C59—22no—
119C22×C4×C59—22no—
120C22×C4×C59—22no—
121C22×C4×C59—22no—
122C22×C4×C59—22no—
123C22×C4×C59—22no—
124C22×C4×C59—22no—
125C22×C4×C59—22no—
126C22×C4×C59—22no—
127C22×C4×C59—22no—
128C22×C4×C59—22no—
129C22×C4×C59—22no—
130C22×C4×C59—22no—
131C22×C4×C59—22no—
132C22×C4×C59—22no—
133C22×C4×C59—22no—
134C22×C4×C59—22no—
135C22×C4×C59—22no—
136C22×C4×C59—22no—
137C22×C4×C59—22no—
138C22×C4×C59—22no—
139C22×C4×C59—22no—
140C22×C4×C59—22no—
141C22×C4×C59—44no—
142C22×C4×C59—48no—
143C22×C4×C59—48no—
144C22×C4×C59—44no—
145C22×C4×C59—44no—
146C22×C4×C59C2×D412yes—
147C22×C4×C59C2×D412yes—
148C22×C4×C59#4114yes—
149C22×C4×C59#4114yes—
150C4⋊C4×C59—48no—
151C4⋊C4×C59—44no—
152C4⋊C4×C59—44no—
153C22⋊C4×C59—44no—
154C22⋊C4×C59—48no—
155C22⋊C4×C59—44no—
156C22⋊C4×C59—48no—
157C23×C59—24no—
158C23×C59—22no—
159C23×C59—22no—
160C23×C59—22no—
161C23×C59—22no—
162C23×C59—22no—
163C23×C59—22no—
164C23×C59—24no—
165C23×C59—24no—
166C23×C59—24no—
167C23×C59—24no—
168C23×C59—24no—
169C23×C59—42no—
170C23×C59—42no—
171C23×C59—42no—
172C23×C59—42no—
173C23×C59—41no—
174C23×C59—42no—
175C23×C59—41no—
176C23×C59—41no—
177C23×C59—42no—
178C23×C59—41no—
179C23×C59#12414yes—
180C23×C59C22×D411yescharacteristic
181C23×C59C2×#4111yescharacteristic
182C23×C59C2×#4111yescharacteristic
183C23×C59C2×#4112yes—
184C23×C59C2×#4112yes—
185C23×C59H(5,𝔽2)11yescharacteristic
186C23×C59H(5,𝔽2)11yescharacteristic
187C23×C59H(5,𝔽2)11yescharacteristic
188C23×C59H(5,𝔽2)12yes—
189C23×C592−1+411yescharacteristic
190C23×C592−1+412yes—
191C2×C4×C59—22no—
192C2×C4×C59—22no—
193C2×C4×C59—24no—
194C2×C4×C59—24no—
195C2×C4×C59—24no—
196C2×C4×C59—24no—
197C2×C4×C59—24no—
198C2×C4×C59—24no—
199C2×C4×C59—24no—
200C2×C4×C59—24no—
201C2×C4×C59—416no—
202C2×C4×C59—42no—
203C2×C4×C59—42no—
204C2×C4×C59—42no—
205C2×C4×C59—42no—
206C2×C4×C59—42no—
207C2×C4×C59—42no—
208C2×C4×C59—42no—
209C2×C4×C59—41no—
210C2×C4×C59—42no—
211C2×C4×C59—41no—
212C2×C4×C59—41no—
213C2×C4×C59—42no—
214C2×C4×C59—42no—
215C2×C4×C59—41no—
216C2×C4×C59—42no—
217C2×C4×C59—42no—
218C2×C4×C59—42no—
219C2×C4×C59—42no—
220C2×C4×C59—42no—
221C2×C4×C59—42no—
222C2×C4×C59—42no—
223C2×C4×C59—42no—
224C2×C4×C59—42no—
225C2×C4×C59—42no—
226C2×C4×C59—42no—
227C2×C4×C59—42no—
228C2×C4×C59—42no—
229C2×C4×C59—42no—
230C2×C4×C59—42no—
231C2×C4×C59—42no—
232C2×C4×C59—42no—
233C2×C4×C59—42no—
234C2×C4×C59—42no—
235C2×C4×C59—42no—
236C2×C4×C59—42no—
237C2×C4×C59—42no—
238C2×C4×C59—42no—
239C2×C4×C59—42no—
240C2×C4×C59—42no—
241C2×C4×C59—42no—
242C2×C4×C59—42no—
243C2×C4×C59—42no—
244#16830C5911yesmaximal, characteristic, direct product factor, Sylow
245C22×C59—24no—
246C22×C59—28no—
247C22×C59—42no—
248C22×C59—44no—
249C22×C59—44no—
250C22×C59—42no—
251C22×C59—42no—
252C22×C59—42no—
253C22×C59—44no—
254C22×C59—42no—
255C22×C59—42no—
256C22×C59C2×#12411yescharacteristic
257C22×C59#52912yes—
258C22×C59#53411yescharacteristic
259C22×C59#53711yescharacteristic
260C22×C59#53811yescharacteristic
261C22×C59#53811yescharacteristic
262C22×C59#53812yes—
263C22×C59#53911yescharacteristic
264C22×C59#53912yes—
265C22×C59#53911yescharacteristic
266C22×C59#53912yes—
267C22×C59#54012yes—
268C22×C59#54212yes—
269C22×C59#54612yes—
270C22×C59#54712yes—
271C22×C59#55111yescharacteristic
272C22×C59#55112yes—
273C22×C59#55212yes—
274C22×C59#55212yes—
275C22×C59#55911yescharacteristic
276C22×C59#56011yescharacteristic
277C22×C59#56312yes—
278C22×C59#56311yescharacteristic
279C4×C59—44no—
280C4×C59—42no—
281C4×C59—42no—
282C4×C59—44no—
283C4×C59—82no—
284C4×C59—82no—
285C4×C59—82no—
286C4×C59—82no—
287C2×#399C2×C5911yescharacteristic
288C2×#397C2×C5911yescharacteristic
289#1443C2×C5912yescomplemented
290#1442C2×C5912yescomplemented
291#1442C2×C5912yescomplemented
292#1441C2×C5912yescomplemented
293#1440C2×C5912yes—
294C22⋊#95C2×C5912yes—
295C22⋊#95C2×C5911yescharacteristic
296C2×C59—44no—
297C2×C59#248812yes—
298C2×C59#251711yescharacteristic
299C2×C59#263911yescharacteristic
300C2×C59#264912yes—
301C2×C59#269512yes—
302C2×C59#270911yescharacteristic
303C2×C59#271711yescharacteristic
304C2×C59#273511yescharacteristic
305C2×C59#273812yes—
306C2×C59#277111yescharacteristic
307C2×C59#283411yescharacteristic
308C24×C4C22×C5911yescharacteristic
309C22×C4⋊C4C22×C5912yes—
310C22×C4⋊C4C22×C5911yescharacteristic
311C22×C4⋊C4C22×C5911yescharacteristic
312C22×C22⋊C4C22×C5912yes—
313C22×C22⋊C4C22×C5912yes—
314C22×C22⋊C4C22×C5911yescharacteristic
315C22×C22⋊C4C22×C5911yescharacteristic
316#399—24no—
317#397—24no—
318C2×#95C22×C5911yescharacteristic
319C2×#95C22×C5912yes—
320C2×#95C22×C5911yescharacteristic
321C2×#95C22×C5912yes—
322C2×#95C22×C5912yes—
323C2×#95C22×C5912yes—
324C2×#95C22×C5912yes—
325C2×#95C22×C5912yes—
326C2×#95C22×C5912yes—
327C2×#95C22×C5912yes—
328C2×#95C22×C5912yes—
329C2×#95C22×C5912yes—
330C2×#95C22×C5912yes—
331C59#1683011yescharacteristic, direct product factor, Sylow
332C25C23×C5911yescharacteristic
333C23×C4—22no—
334C23×C4—24no—
335C23×C4—41no—
336C23×C4—42no—
337C23×C4—41no—
338C23×C4C23×C5912yes—
339C23×C4C23×C5912yes—
340C23×C4C23×C5912yes—
341C23×C4C23×C5912yes—
342C23×C4C23×C5911yescharacteristic
343C23×C4C23×C5911yescharacteristic
344C23×C4C23×C5912yes—
345C23×C4C23×C5912yes—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—42no—
351C2×C4⋊C4—41no—
352C2×C4⋊C4—41no—
353C2×C4⋊C4—41no—
354C2×C4⋊C4—41no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—22no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—41no—
362C2×C22⋊C4—41no—
363C2×C22⋊C4—42no—
364C2×C22⋊C4—41no—
365C2×C22⋊C4—41no—
366C2×C22⋊C4D4×C5914yes—
367#95—22no—
368#95—24no—
369#95—22no—
370#95—24no—
371#95—24no—
372#95—24no—
373#95—42no—
374#95—42no—
375#95—42no—
376#95—42no—
377#95—42no—
378#95—42no—
379#95—42no—
380C24—22no—
381C24—22no—
382C24—21no—
383C24—21no—
384C24—21no—
385C24—22no—
386C24—21no—
387C24—22no—
388C24C2×D4×C5912yes—
389C24#41×C5912yes—
390C24#41×C5912yes—
391C24C24×C5911yescharacteristic
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—44no—
441C22×C4—48no—
442C22×C4—48no—
443C22×C4—44no—
444C22×C4—44no—
445C22×C4C2×D4×C5912yes—
446C22×C4C2×D4×C5912yes—
447C22×C4#41×C5914yes—
448C22×C4#41×C5914yes—
449C4⋊C4—48no—
450C4⋊C4—44no—
451C4⋊C4—44no—
452C22⋊C4—44no—
453C22⋊C4—48no—
454C22⋊C4—44no—
455C22⋊C4—48no—
456C23—24no—
457C23—22no—
458C23—22no—
459C23—22no—
460C23—22no—
461C23—24no—
462C23—22no—
463C23—22no—
464C23—24no—
465C23—24no—
466C23—24no—
467C23—24no—
468C23—42no—
469C23—42no—
470C23—42no—
471C23—42no—
472C23—41no—
473C23—42no—
474C23—41no—
475C23—41no—
476C23—42no—
477C23—41no—
478C23#124×C5914yes—
479C23C22×D4×C5911yescharacteristic
480C23C2×#41×C5911yescharacteristic
481C23C2×#41×C5911yescharacteristic
482C23C2×#41×C5912yes—
483C23C2×#41×C5912yes—
484C23H(5,𝔽2)×C5911yescharacteristic
485C23H(5,𝔽2)×C5911yescharacteristic
486C23H(5,𝔽2)×C5911yescharacteristic
487C23H(5,𝔽2)×C5912yes—
488C232−1+4×C5911yescharacteristic
489C232−1+4×C5912yes—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—24no—
493C2×C4—24no—
494C2×C4—24no—
495C2×C4—24no—
496C2×C4—24no—
497C2×C4—24no—
498C2×C4—24no—
499C2×C4—24no—
500C2×C4—416no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—41no—
509C2×C4—42no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—41no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C22—28no—
544C22—24no—
545C22—44no—
546C22—42no—
547C22—42no—
548C22—42no—
549C22—44no—
550C22—44no—
551C22—42no—
552C22—42no—
553C22—42no—
554C22C2×#124×C5911yescharacteristic
555C22C59×#52912yes—
556C22C59×#53411yescharacteristic
557C22C59×#53711yescharacteristic
558C22C59×#53811yescharacteristic
559C22C59×#53811yescharacteristic
560C22C59×#53812yes—
561C22C59×#53911yescharacteristic
562C22C59×#53912yes—
563C22C59×#53912yes—
564C22C59×#53911yescharacteristic
565C22C59×#54012yes—
566C22C59×#54212yes—
567C22C59×#54612yes—
568C22C59×#54712yes—
569C22C59×#55112yes—
570C22C59×#55111yescharacteristic
571C22C59×#55212yes—
572C22C59×#55212yes—
573C22C59×#55911yescharacteristic
574C22C59×#56011yescharacteristic
575C22C59×#56312yes—
576C22C59×#56311yescharacteristic
577C4—44no—
578C4—42no—
579C4—42no—
580C4—44no—
581C4—82no—
582C4—82no—
583C4—82no—
584C4—82no—
585C2—44no—
586C2C59×#248812yes—
587C2C59×#251711yescharacteristic
588C2C59×#263911yescharacteristic
589C2C59×#264912yes—
590C2C59×#269512yes—
591C2C59×#270911yescharacteristic
592C2C59×#271711yescharacteristic
593C2C59×#273511yescharacteristic
594C2C59×#273812yes—
595C2C59×#277111yescharacteristic
596C2C59×#283411yescharacteristic
subgroupG/H
center, socleC24×C59C24
commutator, Frattini, cosocleC24C24×C59
prime radicalC25×C59C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C59 ◁ G

Complements

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

NH ≅ G/Ntype
3. C59×#1443C2semidirect
4. C59×#1442C2semidirect
5. C59×#1442C2semidirect
6. C59×#1441C2semidirect
244. #16830C59direct (N × H)
289. #1443C2×C59semidirect
290. #1442C2×C59semidirect
291. #1442C2×C59semidirect
292. #1441C2×C59semidirect
331. C59#16830direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C59×#3992
C2×C59×#3972
C59×#14432
C59×#14422
C59×#14412
C59×#14402
C59×C22⋊#952
#1683059