Finite Group Databasebeta

← C59×#16988 #28429097

Subgroups — C59×#16988 #28429097

Order 15104.

1146 conjugacy classes of subgroups.

The subgroup lattice has 550 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×#1444C211yesmaximal, characteristic
4C59×#1444C211yesmaximal, characteristic
5C59×#1444C212yesmaximal
6C59×#1442C212yesmaximal
7C59×#1442C211yesmaximal, characteristic
8C59×#1442C211yesmaximal, characteristic
9C59×#1441C212yesmaximal
10C59×#1441C212yesmaximal
11C59×#1434C211yesmaximal, characteristic
12C22×C4⋊C4×C59C2211yescharacteristic
13C22×C4⋊C4×C59C2211yescharacteristic
14C22×C4⋊C4×C59C2211yescharacteristic
15C22×C4⋊C4×C59C2212yes—
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×C59C2212yes—
28C2×#95×C59C2212yes—
29C2×#95×C59C2212yes—
30C2×#95×C59C2212yes—
31C2×#95×C59C2212yes—
32C2×#95×C59C2212yes—
33C2×#95×C59C2212yes—
34C2×#95×C59C2212yes—
35C2×#95×C59C2211yescharacteristic
36C2×#95×C59C2211yescharacteristic
37C23×C4×C59C2311yescharacteristic
38C23×C4×C59C2311yescharacteristic
39C23×C4×C59C2312yes—
40C23×C4×C59C2311yescharacteristic
41C23×C4×C59C2311yescharacteristic
42C23×C4×C59C2312yes—
43C23×C4×C59C2312yes—
44C23×C4×C59C2311yescharacteristic
45C23×C4×C59C2312yes—
46C23×C4×C59C2311yescharacteristic
47C23×C4×C59C2311yescharacteristic
48C2×C4⋊C4×C59—22no—
49C2×C4⋊C4×C59—22no—
50C2×C4⋊C4×C59—24no—
51C2×C4⋊C4×C59—22no—
52C2×C4⋊C4×C59—22no—
53C2×C4⋊C4×C59—22no—
54C2×C4⋊C4×C59—24no—
55C2×C4⋊C4×C59—22no—
56C2×C4⋊C4×C59—24no—
57C2×C4⋊C4×C59—24no—
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×C59—42no—
66C2×C42×C59—42no—
67C2×C42×C59D414yes—
68#95×C59—22no—
69#95×C59—22no—
70#95×C59—22no—
71#95×C59—22no—
72#95×C59—24no—
73#95×C59—24no—
74#95×C59—24no—
75#95×C59—42no—
76#95×C59—42no—
77#95×C59—42no—
78#95×C59—42no—
79#95×C59—42no—
80#95×C59—42no—
81#95×C59Q814yes—
82#95×C59Q814yes—
83C24×C59C2411yescharacteristic
84C22×C4×C59—22no—
85C22×C4×C59—22no—
86C22×C4×C59—21no—
87C22×C4×C59—21no—
88C22×C4×C59—22no—
89C22×C4×C59—22no—
90C22×C4×C59—22no—
91C22×C4×C59—22no—
92C22×C4×C59—21no—
93C22×C4×C59—21no—
94C22×C4×C59—22no—
95C22×C4×C59—21no—
96C22×C4×C59—21no—
97C22×C4×C59—22no—
98C22×C4×C59—22no—
99C22×C4×C59—21no—
100C22×C4×C59—22no—
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—22no—
111C22×C4×C59—22no—
112C22×C4×C59—22no—
113C22×C4×C59—22no—
114C22×C4×C59—22no—
115C22×C4×C59—21no—
116C22×C4×C59—22no—
117C22×C4×C59—22no—
118C22×C4×C59—22no—
119C22×C4×C59—22no—
120C22×C4×C59—21no—
121C22×C4×C59—21no—
122C22×C4×C59—22no—
123C22×C4×C59—22no—
124C22×C4×C59—22no—
125C22×C4×C59—22no—
126C22×C4×C59—21no—
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—21no—
134C22×C4×C59—22no—
135C22×C4×C59—21no—
136C22×C4×C59—21no—
137C22×C4×C59C2×D412yes—
138C22×C4×C59C2×D412yes—
139C22×C4×C59C2×D412yes—
140C22×C4×C59C2×Q814yes—
141C22×C4×C59C2×Q814yes—
142C22×C4×C59C2×Q812yes—
143C22×C4×C59C2×Q812yes—
144C22×C4×C59#4112yes—
145C22×C4×C59#4114yes—
146C22×C4×C59#4112yes—
147C4⋊C4×C59—28no—
148C4⋊C4×C59—28no—
149C4⋊C4×C59—44no—
150C4⋊C4×C59—44no—
151C4⋊C4×C59—48no—
152C4⋊C4×C59—48no—
153C4⋊C4×C59—48no—
154C42×C59—44no—
155C23×C59C22×D411yescharacteristic
156C23×C59C22×Q811yescharacteristic
157C23×C59C22×Q811yescharacteristic
158C23×C59C2×#4111yescharacteristic
159C23×C59C2×#4112yes—
160C23×C59C2×#4111yescharacteristic
161C23×C59H(5,𝔽2)12yes—
162C23×C59H(5,𝔽2)12yes—
163C23×C59H(5,𝔽2)11yescharacteristic
164C23×C592−1+412yes—
165C23×C592−1+411yescharacteristic
166C2×C4×C59—22no—
167C2×C4×C59—22no—
168C2×C4×C59—24no—
169C2×C4×C59—24no—
170C2×C4×C59—22no—
171C2×C4×C59—22no—
172C2×C4×C59—22no—
173C2×C4×C59—24no—
174C2×C4×C59—22no—
175C2×C4×C59—22no—
176C2×C4×C59—22no—
177C2×C4×C59—22no—
178C2×C4×C59—22no—
179C2×C4×C59—24no—
180C2×C4×C59—24no—
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—24no—
189C2×C4×C59—41no—
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—42no—
205C2×C4×C59—42no—
206C2×C4×C59—42no—
207C2×C4×C59—42no—
208C2×C4×C59—42no—
209C2×C4×C59—42no—
210C2×C4×C59—42no—
211C2×C4×C59—42no—
212C2×C4×C59—41no—
213C2×C4×C59—42no—
214C2×C4×C59—41no—
215C2×C4×C59—42no—
216C2×C4×C59—41no—
217C2×C4×C59—41no—
218C2×C4×C59—41no—
219C2×C4×C59—41no—
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×C59C4⋊Q814yes—
229#16988C5911yesmaximal, characteristic, direct product factor, Sylow
230C22×C59#52511yescharacteristic
231C22×C59#52511yescharacteristic
232C22×C59C2×C4⋊Q811yescharacteristic
233C22×C59#53411yescharacteristic
234C22×C59#53511yescharacteristic
235C22×C59#53611yescharacteristic
236C22×C59#53711yescharacteristic
237C22×C59#53812yes—
238C22×C59#53812yes—
239C22×C59#53912yes—
240C22×C59#54012yes—
241C22×C59#54412yes—
242C22×C59#54412yes—
243C22×C59#55212yes—
244C22×C59#55412yes—
245C22×C59#55412yes—
246C22×C59#55411yescharacteristic
247C22×C59#55411yescharacteristic
248C22×C59#55612yes—
249C22×C59#55711yescharacteristic
250C22×C59#55711yescharacteristic
251C22×C59#56212yes—
252C22×C59#56312yes—
253C4×C59—24no—
254C4×C59—42no—
255C4×C59—42no—
256C4×C59—42no—
257C4×C59—44no—
258C4×C59—44no—
259C4×C59—44no—
260C4×C59—42no—
261C4×C59—82no—
262C4×C59—81no—
263C4×C59—81no—
264C2×#389C2×C5911yescharacteristic
265C2×#387C2×C5911yescharacteristic
266#1444C2×C5911yescharacteristic
267#1444C2×C5912yes—
268#1444C2×C5911yescharacteristic
269#1442C2×C5911yescharacteristic
270#1442C2×C5912yes—
271#1442C2×C5911yescharacteristic
272#1441C2×C5912yes—
273#1441C2×C5912yes—
274#1434C2×C5911yescharacteristic
275C2×C59#258311yescharacteristic
276C2×C59#258411yescharacteristic
277C2×C59#259911yescharacteristic
278C2×C59#263511yescharacteristic
279C2×C59#263611yescharacteristic
280C2×C59#266011yescharacteristic
281C2×C59#276812yes—
282C2×C59#278812yes—
283C2×C59#279112yes—
284C2×C59#280512yes—
285C2×C59#281411yescharacteristic
286C22×C4⋊C4C22×C5911yescharacteristic
287C22×C4⋊C4C22×C5911yescharacteristic
288C22×C4⋊C4C22×C5911yescharacteristic
289C22×C4⋊C4C22×C5912yes—
290C22×C4⋊C4C22×C5912yes—
291C22×C4⋊C4C22×C5912yes—
292C22×C4⋊C4C22×C5911yescharacteristic
293C22×C42C22×C5911yescharacteristic
294#389—24no—
295#387—24no—
296C2×#95C22×C5911yescharacteristic
297C2×#95C22×C5912yes—
298C2×#95C22×C5912yes—
299C2×#95C22×C5912yes—
300C2×#95C22×C5911yescharacteristic
301C2×#95C22×C5911yescharacteristic
302C2×#95C22×C5911yescharacteristic
303C2×#95C22×C5912yes—
304C2×#95C22×C5912yes—
305C2×#95C22×C5912yes—
306C2×#95C22×C5912yes—
307C2×#95C22×C5912yes—
308C2×#95C22×C5912yes—
309C2×#95C22×C5911yescharacteristic
310C2×#95C22×C5911yescharacteristic
311C59#1698811yescharacteristic, direct product factor, Sylow
312C23×C4C23×C5912yes—
313C23×C4C23×C5911yescharacteristic
314C23×C4C23×C5911yescharacteristic
315C23×C4C23×C5911yescharacteristic
316C23×C4C23×C5911yescharacteristic
317C23×C4C23×C5912yes—
318C23×C4C23×C5912yes—
319C23×C4C23×C5911yescharacteristic
320C23×C4C23×C5912yes—
321C23×C4C23×C5911yescharacteristic
322C23×C4C23×C5911yescharacteristic
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—24no—
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×C42—42no—
342C2×C42D4×C5914yes—
343#95—22no—
344#95—22no—
345#95—22no—
346#95—22no—
347#95—24no—
348#95—24no—
349#95—24no—
350#95—42no—
351#95—42no—
352#95—42no—
353#95—42no—
354#95—42no—
355#95—42no—
356#95Q8×C5914yes—
357#95Q8×C5914yes—
358C24C24×C5911yescharacteristic
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—22no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—21no—
375C22×C4—22no—
376C22×C4—22no—
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—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—21no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—21no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—21no—
409C22×C4—22no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4C2×D4×C5912yes—
413C22×C4C2×D4×C5912yes—
414C22×C4C2×D4×C5912yes—
415C22×C4C2×Q8×C5914yes—
416C22×C4C2×Q8×C5914yes—
417C22×C4C2×Q8×C5912yes—
418C22×C4C2×Q8×C5912yes—
419C22×C4#41×C5912yes—
420C22×C4#41×C5914yes—
421C22×C4#41×C5912yes—
422C4⋊C4—28no—
423C4⋊C4—28no—
424C4⋊C4—44no—
425C4⋊C4—44no—
426C4⋊C4—48no—
427C4⋊C4—48no—
428C4⋊C4—48no—
429C42—44no—
430C23C22×D4×C5911yescharacteristic
431C23C22×Q8×C5911yescharacteristic
432C23C22×Q8×C5911yescharacteristic
433C23C2×#41×C5911yescharacteristic
434C23C2×#41×C5912yes—
435C23C2×#41×C5911yescharacteristic
436C23H(5,𝔽2)×C5912yes—
437C23H(5,𝔽2)×C5912yes—
438C23H(5,𝔽2)×C5911yescharacteristic
439C232−1+4×C5912yes—
440C232−1+4×C5911yescharacteristic
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—24no—
444C2×C4—24no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—24no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—24no—
455C2×C4—24no—
456C2×C4—24no—
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—41no—
466C2×C4—42no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—42no—
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—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
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×C4C4⋊Q8×C5914yes—
504C22C59×#52511yescharacteristic
505C22C59×#52511yescharacteristic
506C22C2×C4⋊Q8×C5911yescharacteristic
507C22C59×#53411yescharacteristic
508C22C59×#53511yescharacteristic
509C22C59×#53611yescharacteristic
510C22C59×#53711yescharacteristic
511C22C59×#53812yes—
512C22C59×#53812yes—
513C22C59×#53912yes—
514C22C59×#54012yes—
515C22C59×#54412yes—
516C22C59×#54412yes—
517C22C59×#55212yes—
518C22C59×#55411yescharacteristic
519C22C59×#55412yes—
520C22C59×#55411yescharacteristic
521C22C59×#55412yes—
522C22C59×#55612yes—
523C22C59×#55711yescharacteristic
524C22C59×#55711yescharacteristic
525C22C59×#56212yes—
526C22C59×#56312yes—
527C4—24no—
528C4—44no—
529C4—44no—
530C4—42no—
531C4—42no—
532C4—42no—
533C4—42no—
534C4—44no—
535C4—81no—
536C4—82no—
537C4—81no—
538C2C59×#258311yescharacteristic
539C2C59×#258411yescharacteristic
540C2C59×#259911yescharacteristic
541C2C59×#263511yescharacteristic
542C2C59×#263611yescharacteristic
543C2C59×#266011yescharacteristic
544C2C59×#276812yes—
545C2C59×#278812yes—
546C2C59×#279112yes—
547C2C59×#280512yes—
548C2C59×#281411yescharacteristic
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
229. #16988C59direct (N × H)
311. C59#16988direct (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×#14442
C59×#14422
C59×#14412
C59×#14342
#1698859