Finite Group Databasebeta

← C59×#16900 #28429009

Subgroups — C59×#16900 #28429009

Order 15104.

1146 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×#389C211yesmaximal, characteristic
2C2×C59×#387C211yesmaximal, characteristic
3C59×#1445C211yesmaximal, characteristic
4C59×#1445C211yesmaximal, characteristic
5C59×#1444C211yesmaximal, characteristic
6C59×#1444C212yesmaximal
7C59×#1442C212yesmaximal
8C59×#1442C211yesmaximal, characteristic
9C59×#1441C212yesmaximal
10C59×#1441C212yesmaximal
11C59×C4⋊#95C211yesmaximal, characteristic
12C22×C4⋊C4×C59C2212yes—
13C22×C4⋊C4×C59C2211yescharacteristic
14C22×C4⋊C4×C59C2211yescharacteristic
15C22×C4⋊C4×C59C2211yescharacteristic
16C22×C4⋊C4×C59C2211yescharacteristic
17C22×C4⋊C4×C59C2212yes—
18C22×C4⋊C4×C59C2212yes—
19C22×C42×C59C2211yescharacteristic
20C59×#389—24no—
21C59×#387—24no—
22C2×#95×C59C2211yescharacteristic
23C2×#95×C59C2211yescharacteristic
24C2×#95×C59C2211yescharacteristic
25C2×#95×C59C2211yescharacteristic
26C2×#95×C59C2212yes—
27C2×#95×C59C2211yescharacteristic
28C2×#95×C59C2211yescharacteristic
29C2×#95×C59C2212yes—
30C2×#95×C59C2212yes—
31C2×#95×C59C2212yes—
32C2×#95×C59C2212yes—
33C2×#95×C59C2212yes—
34C2×#95×C59C2212yes—
35C2×#95×C59C2212yes—
36C2×#95×C59C2212yes—
37C23×C4×C59C2311yescharacteristic
38C23×C4×C59C2312yes—
39C23×C4×C59C2311yescharacteristic
40C23×C4×C59C2312yes—
41C23×C4×C59C2311yescharacteristic
42C23×C4×C59C2311yescharacteristic
43C23×C4×C59C2311yescharacteristic
44C23×C4×C59C2312yes—
45C23×C4×C59C2312yes—
46C23×C4×C59C2311yescharacteristic
47C23×C4×C59C2311yescharacteristic
48C2×C4⋊C4×C59—22no—
49C2×C4⋊C4×C59—22no—
50C2×C4⋊C4×C59—22no—
51C2×C4⋊C4×C59—22no—
52C2×C4⋊C4×C59—22no—
53C2×C4⋊C4×C59—24no—
54C2×C4⋊C4×C59—22no—
55C2×C4⋊C4×C59—24no—
56C2×C4⋊C4×C59—24no—
57C2×C4⋊C4×C59—42no—
58C2×C4⋊C4×C59—42no—
59C2×C4⋊C4×C59—42no—
60C2×C4⋊C4×C59—42no—
61C2×C4⋊C4×C59—42no—
62C2×C4⋊C4×C59—42no—
63C2×C4⋊C4×C59—42no—
64C2×C4⋊C4×C59—42no—
65C2×C4⋊C4×C59Q814yes—
66C2×C4⋊C4×C59Q814yes—
67C2×C42×C59—42no—
68C2×C42×C59D414yes—
69#95×C59—22no—
70#95×C59—22no—
71#95×C59—22no—
72#95×C59—22no—
73#95×C59—24no—
74#95×C59—24no—
75#95×C59—22no—
76#95×C59—24no—
77#95×C59—22no—
78#95×C59—42no—
79#95×C59—42no—
80#95×C59—42no—
81#95×C59—42no—
82#95×C59—42no—
83#95×C59—42no—
84C24×C59C2411yescharacteristic
85C22×C4×C59—22no—
86C22×C4×C59—22no—
87C22×C4×C59—22no—
88C22×C4×C59—22no—
89C22×C4×C59—21no—
90C22×C4×C59—21no—
91C22×C4×C59—22no—
92C22×C4×C59—22no—
93C22×C4×C59—22no—
94C22×C4×C59—22no—
95C22×C4×C59—22no—
96C22×C4×C59—21no—
97C22×C4×C59—21no—
98C22×C4×C59—22no—
99C22×C4×C59—22no—
100C22×C4×C59—21no—
101C22×C4×C59—22no—
102C22×C4×C59—22no—
103C22×C4×C59—22no—
104C22×C4×C59—22no—
105C22×C4×C59—22no—
106C22×C4×C59—22no—
107C22×C4×C59—22no—
108C22×C4×C59—22no—
109C22×C4×C59—22no—
110C22×C4×C59—21no—
111C22×C4×C59—22no—
112C22×C4×C59—22no—
113C22×C4×C59—21no—
114C22×C4×C59—21no—
115C22×C4×C59—22no—
116C22×C4×C59—22no—
117C22×C4×C59—22no—
118C22×C4×C59—22no—
119C22×C4×C59—22no—
120C22×C4×C59—21no—
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—21no—
132C22×C4×C59—22no—
133C22×C4×C59—21no—
134C22×C4×C59—21no—
135C22×C4×C59—22no—
136C22×C4×C59—22no—
137C22×C4×C59C2×D412yes—
138C22×C4×C59C2×D412yes—
139C22×C4×C59C2×D412yes—
140C22×C4×C59C2×Q812yes—
141C22×C4×C59C2×Q812yes—
142C22×C4×C59C2×Q814yes—
143C22×C4×C59C2×Q812yes—
144C22×C4×C59C2×Q812yes—
145C22×C4×C59#4114yes—
146C22×C4×C59#4112yes—
147C22×C4×C59#4112yes—
148C4⋊C4×C59—28no—
149C4⋊C4×C59—28no—
150C4⋊C4×C59—48no—
151C4⋊C4×C59—44no—
152C4⋊C4×C59—44no—
153C4⋊C4×C59—48no—
154C4⋊C4×C59—48no—
155C42×C59—44no—
156C23×C59C22×D411yescharacteristic
157C23×C59C22×Q811yescharacteristic
158C23×C59C22×Q811yescharacteristic
159C23×C59C2×#4111yescharacteristic
160C23×C59C2×#4111yescharacteristic
161C23×C59C2×#4112yes—
162C23×C59H(5,𝔽2)12yes—
163C23×C59H(5,𝔽2)12yes—
164C23×C59H(5,𝔽2)11yescharacteristic
165C23×C592−1+412yes—
166C23×C592−1+411yescharacteristic
167C2×C4×C59—22no—
168C2×C4×C59—22no—
169C2×C4×C59—22no—
170C2×C4×C59—22no—
171C2×C4×C59—24no—
172C2×C4×C59—24no—
173C2×C4×C59—24no—
174C2×C4×C59—24no—
175C2×C4×C59—22no—
176C2×C4×C59—24no—
177C2×C4×C59—22no—
178C2×C4×C59—22no—
179C2×C4×C59—22no—
180C2×C4×C59—22no—
181C2×C4×C59—24no—
182C2×C4×C59—24no—
183C2×C4×C59—24no—
184C2×C4×C59—24no—
185C2×C4×C59—24no—
186C2×C4×C59—24no—
187C2×C4×C59—24no—
188C2×C4×C59—41no—
189C2×C4×C59—42no—
190C2×C4×C59—41no—
191C2×C4×C59—42no—
192C2×C4×C59—41no—
193C2×C4×C59—41no—
194C2×C4×C59—42no—
195C2×C4×C59—42no—
196C2×C4×C59—42no—
197C2×C4×C59—42no—
198C2×C4×C59—42no—
199C2×C4×C59—42no—
200C2×C4×C59—42no—
201C2×C4×C59—42no—
202C2×C4×C59—42no—
203C2×C4×C59—42no—
204C2×C4×C59—41no—
205C2×C4×C59—41no—
206C2×C4×C59—42no—
207C2×C4×C59—42no—
208C2×C4×C59—41no—
209C2×C4×C59—41no—
210C2×C4×C59—41no—
211C2×C4×C59—41no—
212C2×C4×C59—42no—
213C2×C4×C59—42no—
214C2×C4×C59—42no—
215C2×C4×C59—42no—
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×C59C22⋊Q814yes—
229C2×C4×C59C22⋊Q814yes—
230#16900C5911yesmaximal, characteristic, direct product factor, Sylow
231C22×C59C2×C22⋊Q811yescharacteristic
232C22×C59C2×C22⋊Q811yescharacteristic
233C22×C59#53211yescharacteristic
234C22×C59#53411yescharacteristic
235C22×C59#53511yescharacteristic
236C22×C59#53611yescharacteristic
237C22×C59#53711yescharacteristic
238C22×C59#53912yes—
239C22×C59#53912yes—
240C22×C59#54112yes—
241C22×C59#54212yes—
242C22×C59#54412yes—
243C22×C59#54412yes—
244C22×C59#55112yes—
245C22×C59#55312yes—
246C22×C59#55412yes—
247C22×C59#55412yes—
248C22×C59#55711yescharacteristic
249C22×C59#55711yescharacteristic
250C22×C59Q8211yescharacteristic
251C22×C59#55911yescharacteristic
252C22×C59#56012yes—
253C22×C59#56212yes—
254C4×C59—24no—
255C4×C59—24no—
256C4×C59—42no—
257C4×C59—44no—
258C4×C59—42no—
259C4×C59—44no—
260C4×C59—42no—
261C4×C59—81no—
262C4×C59—82no—
263C4×C59—82no—
264C4×C59—81no—
265C2×#389C2×C5911yescharacteristic
266C2×#387C2×C5911yescharacteristic
267#1445C2×C5911yescharacteristic
268#1445C2×C5911yescharacteristic
269#1444C2×C5912yes—
270#1444C2×C5911yescharacteristic
271#1442C2×C5911yescharacteristic
272#1442C2×C5912yes—
273#1441C2×C5912yes—
274#1441C2×C5912yes—
275C4⋊#95C2×C5911yescharacteristic
276C2×C59#256411yescharacteristic
277C2×C59#256611yescharacteristic
278C2×C59#258211yescharacteristic
279C2×C59#262711yescharacteristic
280C2×C59#262811yescharacteristic
281C2×C59#266411yescharacteristic
282C2×C59#275512yes—
283C2×C59#279212yes—
284C2×C59#279612yes—
285C2×C59#280212yes—
286C2×C59#281311yescharacteristic
287C22×C4⋊C4C22×C5912yes—
288C22×C4⋊C4C22×C5911yescharacteristic
289C22×C4⋊C4C22×C5911yescharacteristic
290C22×C4⋊C4C22×C5911yescharacteristic
291C22×C4⋊C4C22×C5912yes—
292C22×C4⋊C4C22×C5911yescharacteristic
293C22×C4⋊C4C22×C5912yes—
294C22×C42C22×C5911yescharacteristic
295#389—24no—
296#387—24no—
297C2×#95C22×C5911yescharacteristic
298C2×#95C22×C5911yescharacteristic
299C2×#95C22×C5911yescharacteristic
300C2×#95C22×C5912yes—
301C2×#95C22×C5912yes—
302C2×#95C22×C5912yes—
303C2×#95C22×C5911yescharacteristic
304C2×#95C22×C5911yescharacteristic
305C2×#95C22×C5911yescharacteristic
306C2×#95C22×C5912yes—
307C2×#95C22×C5912yes—
308C2×#95C22×C5912yes—
309C2×#95C22×C5912yes—
310C2×#95C22×C5912yes—
311C2×#95C22×C5912yes—
312C59#1690011yescharacteristic, direct product factor, Sylow
313C23×C4C23×C5911yescharacteristic
314C23×C4C23×C5912yes—
315C23×C4C23×C5912yes—
316C23×C4C23×C5911yescharacteristic
317C23×C4C23×C5911yescharacteristic
318C23×C4C23×C5911yescharacteristic
319C23×C4C23×C5912yes—
320C23×C4C23×C5911yescharacteristic
321C23×C4C23×C5912yes—
322C23×C4C23×C5911yescharacteristic
323C23×C4C23×C5911yescharacteristic
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—42no—
334C2×C4⋊C4—42no—
335C2×C4⋊C4—42no—
336C2×C4⋊C4—42no—
337C2×C4⋊C4—42no—
338C2×C4⋊C4—42no—
339C2×C4⋊C4—42no—
340C2×C4⋊C4—42no—
341C2×C4⋊C4Q8×C5914yes—
342C2×C4⋊C4Q8×C5914yes—
343C2×C42—42no—
344C2×C42D4×C5914yes—
345#95—22no—
346#95—22no—
347#95—22no—
348#95—22no—
349#95—24no—
350#95—24no—
351#95—22no—
352#95—24no—
353#95—22no—
354#95—42no—
355#95—42no—
356#95—42no—
357#95—42no—
358#95—42no—
359#95—42no—
360C24C24×C5911yescharacteristic
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—21no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—21no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—21no—
408C22×C4—22no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4C2×D4×C5912yes—
414C22×C4C2×D4×C5912yes—
415C22×C4C2×D4×C5912yes—
416C22×C4C2×Q8×C5912yes—
417C22×C4C2×Q8×C5912yes—
418C22×C4C2×Q8×C5914yes—
419C22×C4C2×Q8×C5912yes—
420C22×C4C2×Q8×C5912yes—
421C22×C4#41×C5914yes—
422C22×C4#41×C5912yes—
423C22×C4#41×C5912yes—
424C4⋊C4—28no—
425C4⋊C4—28no—
426C4⋊C4—48no—
427C4⋊C4—44no—
428C4⋊C4—44no—
429C4⋊C4—48no—
430C4⋊C4—48no—
431C42—44no—
432C23C22×D4×C5911yescharacteristic
433C23C22×Q8×C5911yescharacteristic
434C23C22×Q8×C5911yescharacteristic
435C23C2×#41×C5911yescharacteristic
436C23C2×#41×C5911yescharacteristic
437C23C2×#41×C5912yes—
438C23H(5,𝔽2)×C5912yes—
439C23H(5,𝔽2)×C5912yes—
440C23H(5,𝔽2)×C5911yescharacteristic
441C232−1+4×C5912yes—
442C232−1+4×C5911yescharacteristic
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—24no—
448C2×C4—24no—
449C2×C4—24no—
450C2×C4—24no—
451C2×C4—22no—
452C2×C4—24no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—24no—
458C2×C4—24no—
459C2×C4—24no—
460C2×C4—24no—
461C2×C4—24no—
462C2×C4—24no—
463C2×C4—24no—
464C2×C4—41no—
465C2×C4—42no—
466C2×C4—41no—
467C2×C4—42no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—42no—
488C2×C4—41no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4C22⋊Q8×C5914yes—
505C2×C4C22⋊Q8×C5914yes—
506C22C2×C22⋊Q8×C5911yescharacteristic
507C22C2×C22⋊Q8×C5911yescharacteristic
508C22C59×#53211yescharacteristic
509C22C59×#53411yescharacteristic
510C22C59×#53511yescharacteristic
511C22C59×#53611yescharacteristic
512C22C59×#53711yescharacteristic
513C22C59×#53912yes—
514C22C59×#53912yes—
515C22C59×#54112yes—
516C22C59×#54212yes—
517C22C59×#54412yes—
518C22C59×#54412yes—
519C22C59×#55112yes—
520C22C59×#55312yes—
521C22C59×#55412yes—
522C22C59×#55412yes—
523C22C59×#55711yescharacteristic
524C22C59×#55711yescharacteristic
525C22Q82×C5911yescharacteristic
526C22C59×#55911yescharacteristic
527C22C59×#56012yes—
528C22C59×#56212yes—
529C4—24no—
530C4—24no—
531C4—44no—
532C4—42no—
533C4—42no—
534C4—44no—
535C4—42no—
536C4—82no—
537C4—82no—
538C4—81no—
539C4—81no—
540C2C59×#256411yescharacteristic
541C2C59×#256611yescharacteristic
542C2C59×#258211yescharacteristic
543C2C59×#262711yescharacteristic
544C2C59×#262811yescharacteristic
545C2C59×#266411yescharacteristic
546C2C59×#275512yes—
547C2C59×#279212yes—
548C2C59×#279612yes—
549C2C59×#280212yes—
550C2C59×#281311yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C59C24
commutator, Frattini, cosocleC24C24×C59
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C59 ◁ G

Complements

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

NH ≅ G/Ntype
230. #16900C59direct (N × H)
312. C59#16900direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C59×#3892
C2×C59×#3872
C59×#14452
C59×#14442
C59×#14422
C59×#14412
C59×C4⋊#952
#1690059