Finite Group Databasebeta

← C59×#24069 #28436178

Subgroups — C59×#24069 #28436178

Order 15104.

1130 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×#540C211yesmaximal, characteristic
2C2×C59×#481C211yesmaximal, characteristic, complemented
3C2×C59×#480C211yesmaximal, characteristic, complemented
4C59×#2317C211yesmaximal, characteristic, complemented
5C59×#2059C212yesmaximal, complemented
6C59×#2041C212yesmaximal, complemented
7C59×#1875C211yesmaximal, characteristic, complemented
8C59×#1875C211yesmaximal, characteristic, complemented
9C59×#1864C212yesmaximal, complemented
10C59×#1862C212yesmaximal, complemented
11C59×#1818C211yesmaximal, characteristic, complemented
12C59×#540—24no—
13C59×#540—24no—
14C2×#127×C59C2211yescharacteristic
15C2×#125×C59C2211yescharacteristic
16C2×#123×C59—21no—
17C2×#123×C59—21no—
18C2×#121×C59—21no—
19C2×#121×C59—21no—
20C2×#121×C59C2211yescharacteristic
21C2×#121×C59C2211yescharacteristic
22C2×C4×D4×C59C2211yescharacteristic
23C2×C4×D4×C59C2211yescharacteristic
24C2×#117×C59C2211yescharacteristic
25C2×#117×C59C2211yescharacteristic
26C22×C4⋊C4×C59C2211yescharacteristic
27C59×#481—24no—
28C59×#480—24no—
29C2×#107×C59C2212yes—
30C2×#106×C59C2212yes—
31C2×#102×C59C2212yes—
32C2×#102×C59C2212yes—
33C2×#102×C59C2212yes—
34C2×#102×C59C2212yes—
35C2×C22⋊C8×C59C2211yescharacteristic
36C2×C22⋊C8×C59C2211yescharacteristic
37C59×#389C2212yes—
38C59×#389C2212yes—
39C59×#385—21no—
40C59×#385—21no—
41C59×#384—21no—
42C59×#382—21no—
43C59×#340C2212yes—
44C59×#340C2212yes—
45C59×#336C2212yes—
46C59×#336C2212yes—
47C22×D4×C59—21no—
48C22×D4×C59—21no—
49C22×D4×C59—21no—
50C22×D4×C59—21no—
51C22×D4×C59C2311yescharacteristic
52C22×D4×C59C2311yescharacteristic
53C23×C4×C59—21no—
54C23×C4×C59—21no—
55C23×C4×C59—21no—
56C23×C4×C59C2311yescharacteristic
57C22×C8×C59C2312yes—
58C22×C8×C59C2312yes—
59#127×C59—22no—
60#127×C59—22no—
61#125×C59—22no—
62#125×C59—22no—
63#123×C59—28no—
64#123×C59—28no—
65#121×C59—28no—
66#121×C59—28no—
67#121×C59—22no—
68#121×C59—22no—
69#121×C59D414yes—
70#121×C59D414yes—
71C4×D4×C59—22no—
72C4×D4×C59—22no—
73C4×D4×C59—22no—
74C4×D4×C59—22no—
75#117×C59—22no—
76#117×C59—22no—
77#117×C59—24no—
78C2×C4⋊C4×C59—21no—
79C2×C4⋊C4×C59—21no—
80C2×C4⋊C4×C59—22no—
81C2×C4⋊C4×C59—22no—
82C2×C4⋊C4×C59—21no—
83C2×C4⋊C4×C59—22no—
84C2×C4⋊C4×C59—22no—
85C2×C4⋊C4×C59D411yescharacteristic
86C2×C4⋊C4×C59D411yescharacteristic
87C2×C4⋊C4×C59C2312yes—
88C2×C4⋊C4×C59C2311yescharacteristic
89C2×C4⋊C4×C59C2311yescharacteristic
90C2×C4⋊C4×C59C2312yes—
91C2×C22⋊C4×C59—21no—
92C2×C22⋊C4×C59—21no—
93C2×C22⋊C4×C59—21no—
94C2×C22⋊C4×C59—21no—
95C2×C22⋊C4×C59—21no—
96C2×C22⋊C4×C59D411yescharacteristic
97C2×C22⋊C4×C59D411yescharacteristic
98C2×C42×C59—21no—
99C2×C42×C59C2311yescharacteristic
100C2×C42×C59C2311yescharacteristic
101#107×C59—24no—
102#106×C59—24no—
103#102×C59—24no—
104#102×C59—24no—
105#102×C59—24no—
106#102×C59—24no—
107C22⋊C8×C59—22no—
108C22⋊C8×C59—22no—
109#95×C59—22no—
110#95×C59—22no—
111C24×C59—21no—
112C24×C59—21no—
113C24×C59C2×D411yescharacteristic
114C2×D4×C59—24no—
115C2×D4×C59—24no—
116C2×D4×C59—24no—
117C2×D4×C59—24no—
118C2×D4×C59—21no—
119C2×D4×C59—21no—
120C2×D4×C59—22no—
121C2×D4×C59—22no—
122C2×D4×C59—22no—
123C2×D4×C59—22no—
124C2×D4×C59—82no—
125C2×D4×C59—82no—
126C2×D4×C59—82no—
127C2×D4×C59—82no—
128C2×D4×C59C2×D412yes—
129C2×D4×C59C2×D412yes—
130C22×C4×C59—22no—
131C22×C4×C59—22no—
132C22×C4×C59—22no—
133C22×C4×C59—21no—
134C22×C4×C59—21no—
135C22×C4×C59—24no—
136C22×C4×C59—24no—
137C22×C4×C59—22no—
138C22×C4×C59—42no—
139C22×C4×C59—82no—
140C22×C4×C59—82no—
141C22×C4×C59—82no—
142C22×C4×C59C2×D411yescharacteristic
143C22×C4×C59C2×D411yescharacteristic
144C22×C4×C59C2×D411yescharacteristic
145C22×C4×C59C2×D411yescharacteristic
146C22×C4×C59C2×D411yescharacteristic
147C22×C4×C59C2×D412yes—
148C22×C4×C59C2×D412yes—
149C22×C4×C59C2411yescharacteristic
150C2×C8×C59—22no—
151C2×C8×C59—22no—
152C2×C8×C59—22no—
153C2×C8×C59—22no—
154C2×C8×C59—22no—
155C2×C8×C59—22no—
156C4⋊C4×C59—24no—
157C4⋊C4×C59—24no—
158C4⋊C4×C59—22no—
159C4⋊C4×C59—22no—
160C4⋊C4×C59—21no—
161C4⋊C4×C59—21no—
162C4⋊C4×C59—22no—
163C4⋊C4×C59—22no—
164C4⋊C4×C59—22no—
165C4⋊C4×C59—42no—
166C4⋊C4×C59—82no—
167C4⋊C4×C59—82no—
168C4⋊C4×C59C2×D412yes—
169C4⋊C4×C59C2×D412yes—
170C4⋊C4×C59#4114yes—
171C22⋊C4×C59—24no—
172C22⋊C4×C59—24no—
173C22⋊C4×C59—24no—
174C22⋊C4×C59—22no—
175C22⋊C4×C59—22no—
176C22⋊C4×C59—24no—
177C22⋊C4×C59—24no—
178C42×C59—24no—
179C42×C59—21no—
180C42×C59—21no—
181C42×C59—21no—
182C42×C59—21no—
183C23×C59—21no—
184C23×C59—21no—
185C23×C59—22no—
186C23×C59—22no—
187C23×C59—22no—
188C23×C59—22no—
189C23×C59—41no—
190C23×C59—41no—
191C23×C59—41no—
192C23×C59—41no—
193C23×C59—42no—
194C23×C59—42no—
195C23×C59—42no—
196C23×C59—42no—
197C23×C59#12012yes—
198C23×C59C22×D411yescharacteristic
199D4×C59—24no—
200D4×C59—24no—
201D4×C59—42no—
202D4×C59—42no—
203D4×C59—84no—
204D4×C59—84no—
205D4×C59—84no—
206D4×C59—84no—
207C2×C4×C59—21no—
208C2×C4×C59—21no—
209C2×C4×C59—24no—
210C2×C4×C59—24no—
211C2×C4×C59—21no—
212C2×C4×C59—21no—
213C2×C4×C59—21no—
214C2×C4×C59—21no—
215C2×C4×C59—22no—
216C2×C4×C59—22no—
217C2×C4×C59—24no—
218C2×C4×C59—22no—
219C2×C4×C59—22no—
220C2×C4×C59—22no—
221C2×C4×C59—22no—
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—84no—
230C2×C4×C59—84no—
231C2×C4×C59—84no—
232C2×C4×C59#12012yes—
233C2×C4×C59C22×D411yescharacteristic
234C2×C4×C59C22×D411yescharacteristic
235C2×C4×C59C2×#4112yes—
236C2×C4×C592−1+412yes—
237C8×C59—42no—
238C8×C59—42no—
239#24069C5911yesmaximal, characteristic, direct product factor, Sylow
240C22×C59—22no—
241C22×C59—22no—
242C22×C59—22no—
243C22×C59—42no—
244C22×C59—42no—
245C22×C59—42no—
246C22×C59—42no—
247C22×C59—42no—
248C22×C59—42no—
249C22×C59—42no—
250C22×C59—42no—
251C22×C59—82no—
252C22×C59—82no—
253C22×C59—82no—
254C22×C59—82no—
255C22×C59C2×#12011yescharacteristic
256C22×C59#52511yescharacteristic
257C22×C59#53611yescharacteristic
258C22×C59#57612yes—
259C22×C59#57712yes—
260C4×C59—22no—
261C4×C59—44no—
262C4×C59—41no—
263C4×C59—41no—
264C4×C59—42no—
265C4×C59—41no—
266C4×C59—41no—
267C4×C59—42no—
268C4×C59—82no—
269C4×C59#54712yes—
270C4×C59#54712yes—
271C2×#540C2×C5911yescharacteristic
272C2×#481C2×C5911yescharacteristic, complemented
273C2×#480C2×C5911yescharacteristic, complemented
274#2317C2×C5911yescharacteristic, complemented
275#2059C2×C5912yescomplemented
276#2041C2×C5912yescomplemented
277#1875C2×C5911yescharacteristic, complemented
278#1875C2×C5911yescharacteristic, complemented
279#1864C2×C5912yescomplemented
280#1862C2×C5912yescomplemented
281#1818C2×C5911yescharacteristic, complemented
282C2×C59—42no—
283C2×C59—82no—
284C2×C59—82no—
285C2×C59#240611yescharacteristic
286C2×C59#300811yescharacteristic
287C2×C59#300911yescharacteristic
288C2×C59#311912yes—
289C2×C59#324112yes—
290#540—24no—
291#540—24no—
292C2×#127C22×C5911yescharacteristic
293C2×#125C22×C5911yescharacteristic
294C2×#123—21no—
295C2×#123—21no—
296C2×#121—21no—
297C2×#121—21no—
298C2×#121C22×C5911yescharacteristic
299C2×#121C22×C5911yescharacteristic
300C2×C4×D4C22×C5911yescharacteristic
301C2×C4×D4C22×C5911yescharacteristic
302C2×#117C22×C5911yescharacteristic
303C2×#117C22×C5911yescharacteristic
304C22×C4⋊C4C22×C5911yescharacteristic
305#481—24no—
306#480—24no—
307C2×#107C22×C5912yes—
308C2×#106C22×C5912yes—
309C2×#102C22×C5912yes—
310C2×#102C22×C5912yes—
311C2×#102C22×C5912yes—
312C2×#102C22×C5912yes—
313C2×C22⋊C8C22×C5911yescharacteristic
314C2×C22⋊C8C22×C5911yescharacteristic
315#389C22×C5912yes—
316#389C22×C5912yes—
317#385—21no—
318#385—21no—
319#384—21no—
320#382—21no—
321#340C22×C5912yes—
322#340C22×C5912yes—
323#336C22×C5912yes—
324#336C22×C5912yes—
325C59#2406911yescharacteristic, direct product factor, Sylow
326C22×D4—21no—
327C22×D4—21no—
328C22×D4—21no—
329C22×D4—21no—
330C22×D4C23×C5911yescharacteristic
331C22×D4C23×C5911yescharacteristic
332C23×C4—21no—
333C23×C4—21no—
334C23×C4—21no—
335C23×C4C23×C5911yescharacteristic
336C22×C8C23×C5912yes—
337C22×C8C23×C5912yes—
338#127—22no—
339#127—22no—
340#125—22no—
341#125—22no—
342#123—28no—
343#123—28no—
344#121—28no—
345#121—28no—
346#121—22no—
347#121—22no—
348#121D4×C5914yes—
349#121D4×C5914yes—
350C4×D4—22no—
351C4×D4—22no—
352C4×D4—22no—
353C4×D4—22no—
354#117—22no—
355#117—22no—
356#117—24no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4D4×C5911yescharacteristic
365C2×C4⋊C4D4×C5911yescharacteristic
366C2×C4⋊C4C23×C5912yes—
367C2×C4⋊C4C23×C5911yescharacteristic
368C2×C4⋊C4C23×C5911yescharacteristic
369C2×C4⋊C4C23×C5912yes—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4D4×C5911yescharacteristic
376C2×C22⋊C4D4×C5911yescharacteristic
377C2×C42—21no—
378C2×C42C23×C5911yescharacteristic
379C2×C42C23×C5911yescharacteristic
380#107—24no—
381#106—24no—
382#102—24no—
383#102—24no—
384#102—24no—
385#102—24no—
386C22⋊C8—22no—
387C22⋊C8—22no—
388#95—22no—
389#95—22no—
390C24—21no—
391C24—21no—
392C24C2×D4×C5911yescharacteristic
393C2×D4—24no—
394C2×D4—24no—
395C2×D4—24no—
396C2×D4—24no—
397C2×D4—21no—
398C2×D4—21no—
399C2×D4—22no—
400C2×D4—22no—
401C2×D4—22no—
402C2×D4—22no—
403C2×D4—82no—
404C2×D4—82no—
405C2×D4—82no—
406C2×D4—82no—
407C2×D4C2×D4×C5912yes—
408C2×D4C2×D4×C5912yes—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—24no—
415C22×C4—24no—
416C22×C4—22no—
417C22×C4—42no—
418C22×C4—82no—
419C22×C4—82no—
420C22×C4—82no—
421C22×C4C2×D4×C5911yescharacteristic
422C22×C4C2×D4×C5911yescharacteristic
423C22×C4C2×D4×C5911yescharacteristic
424C22×C4C2×D4×C5911yescharacteristic
425C22×C4C2×D4×C5911yescharacteristic
426C22×C4C2×D4×C5912yes—
427C22×C4C2×D4×C5912yes—
428C22×C4C24×C5911yescharacteristic
429C2×C8—22no—
430C2×C8—22no—
431C2×C8—22no—
432C2×C8—22no—
433C2×C8—22no—
434C2×C8—22no—
435C4⋊C4—24no—
436C4⋊C4—24no—
437C4⋊C4—22no—
438C4⋊C4—22no—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—22no—
442C4⋊C4—22no—
443C4⋊C4—22no—
444C4⋊C4—42no—
445C4⋊C4—82no—
446C4⋊C4—82no—
447C4⋊C4C2×D4×C5912yes—
448C4⋊C4C2×D4×C5912yes—
449C4⋊C4#41×C5914yes—
450C22⋊C4—24no—
451C22⋊C4—24no—
452C22⋊C4—24no—
453C22⋊C4—22no—
454C22⋊C4—22no—
455C22⋊C4—24no—
456C22⋊C4—24no—
457C42—24no—
458C42—21no—
459C42—21no—
460C42—21no—
461C42—21no—
462C23—21no—
463C23—21no—
464C23—22no—
465C23—22no—
466C23—22no—
467C23—22no—
468C23—41no—
469C23—41no—
470C23—41no—
471C23—41no—
472C23—42no—
473C23—42no—
474C23—42no—
475C23—42no—
476C23#120×C5912yes—
477C23C22×D4×C5911yescharacteristic
478D4—24no—
479D4—24no—
480D4—42no—
481D4—42no—
482D4—84no—
483D4—84no—
484D4—84no—
485D4—84no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—24no—
489C2×C4—24no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—24no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—84no—
509C2×C4—84no—
510C2×C4—84no—
511C2×C4#120×C5912yes—
512C2×C4C22×D4×C5911yescharacteristic
513C2×C4C22×D4×C5911yescharacteristic
514C2×C4C2×#41×C5912yes—
515C2×C42−1+4×C5912yes—
516C8—42no—
517C8—42no—
518C22—22no—
519C22—22no—
520C22—22no—
521C22—42no—
522C22—42no—
523C22—42no—
524C22—42no—
525C22—42no—
526C22—42no—
527C22—42no—
528C22—42no—
529C22—82no—
530C22—82no—
531C22—82no—
532C22—82no—
533C22C2×#120×C5911yescharacteristic
534C22C59×#52511yescharacteristic
535C22C59×#53611yescharacteristic
536C22C59×#57612yes—
537C22C59×#57712yes—
538C4—22no—
539C4—41no—
540C4—41no—
541C4—42no—
542C4—41no—
543C4—41no—
544C4—42no—
545C4—44no—
546C4—82no—
547C4C59×#54712yes—
548C4C59×#54712yes—
549C2—42no—
550C2—82no—
551C2—82no—
552C2C59×#240611yescharacteristic
553C2C59×#300811yescharacteristic
554C2C59×#300911yescharacteristic
555C2C59×#311912yes—
556C2C59×#324112yes—
subgroupG/H
center, socleC23×C59C22×D4
commutator, Frattini, cosocleC22×C4C24×C59
prime radicalC2×C59×#540C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C59 ◁ C2×#117×C59 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C59×#481C2semidirect
3. C2×C59×#480C2semidirect
4. C59×#2317C2semidirect
5. C59×#2059C2semidirect
6. C59×#2041C2semidirect
7. C59×#1875C2semidirect
8. C59×#1875C2semidirect
9. C59×#1864C2semidirect
10. C59×#1862C2semidirect
11. C59×#1818C2semidirect
239. #24069C59direct (N × H)
272. C2×#481C2×C59semidirect
273. C2×#480C2×C59semidirect
274. #2317C2×C59semidirect
275. #2059C2×C59semidirect
276. #2041C2×C59semidirect
277. #1875C2×C59semidirect
278. #1875C2×C59semidirect
279. #1864C2×C59semidirect
280. #1862C2×C59semidirect
281. #1818C2×C59semidirect
325. C59#24069direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C59×#5402
C2×C59×#4812
C2×C59×#4802
C59×#23172
C59×#20592
C59×#20412
C59×#18752
C59×#18642
C59×#18622
C59×#18182
#2406959