Finite Group Databasebeta

← C59×#24102 #28436211

Subgroups — C59×#24102 #28436211

Order 15104.

1132 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×#553C211yesmaximal, characteristic
2C2×C59×#480C211yesmaximal, characteristic, complemented
3C2×C59×#428C211yesmaximal, characteristic, complemented
4C59×#2487C211yesmaximal, characteristic, complemented
5C59×#2059C212yesmaximal, complemented
6C59×#2034C212yesmaximal, complemented
7C59×#1895C211yesmaximal, characteristic, complemented
8C59×#1870C211yesmaximal, characteristic, complemented
9C59×#1862C212yesmaximal, complemented
10C59×#1852C212yesmaximal, complemented
11C59×#1825C211yesmaximal, characteristic, complemented
12C22×M16×C59C2211yescharacteristic
13C59×#553—24no—
14C59×#553—24no—
15C2×#126×C59—21no—
16C2×#125×C59C2211yescharacteristic
17C2×#123×C59—21no—
18C2×#121×C59—21no—
19C2×#121×C59C2211yescharacteristic
20C2×#121×C59C2211yescharacteristic
21C2×C4×D4×C59—21no—
22C2×C4×D4×C59C2211yescharacteristic
23C2×C4×D4×C59C2211yescharacteristic
24C2×#117×C59C2211yescharacteristic
25C22×C4⋊C4×C59C2211yescharacteristic
26C22×C4⋊C4×C59C2211yescharacteristic
27C59×#480—24no—
28C59×#428—24no—
29C2×#107×C59C2212yes—
30C2×#107×C59C2212yes—
31C2×#106×C59C2212yes—
32C2×#102×C59C2212yes—
33C2×#102×C59C2212yes—
34C2×C22⋊C8×C59C2212yes—
35C2×C22⋊C8×C59C2211yescharacteristic
36C59×#400—21no—
37C59×#399—21no—
38C59×#389C2212yes—
39C59×#386—21no—
40C59×#385—21no—
41C59×#380C2212yes—
42C59×#380C2211yescharacteristic
43C59×#340C2212yes—
44C59×#340C2212yes—
45C59×#340C2212yes—
46C59×#336C2212yes—
47C22×D4×C59—21no—
48C22×D4×C59—21no—
49C22×D4×C59D411yescharacteristic
50C22×D4×C59C2311yescharacteristic
51C23×C4×C59—21no—
52C23×C4×C59—21no—
53C23×C4×C59—21no—
54C23×C4×C59C2311yescharacteristic
55C23×C4×C59C2311yescharacteristic
56C2×M16×C59—22no—
57C2×M16×C59—24no—
58C22×C8×C59C2312yes—
59C22×C8×C59C2312yes—
60#126×C59—28no—
61#125×C59—22no—
62#125×C59—22no—
63#123×C59—28no—
64#121×C59—28no—
65#121×C59—22no—
66#121×C59—22no—
67#121×C59—22no—
68#121×C59D414yes—
69C4×D4×C59—28no—
70C4×D4×C59—22no—
71C4×D4×C59—22no—
72C4×D4×C59—22no—
73C4×D4×C59—22no—
74#117×C59—22no—
75#117×C59D414yes—
76C2×C4⋊C4×C59—21no—
77C2×C4⋊C4×C59—21no—
78C2×C4⋊C4×C59—21no—
79C2×C4⋊C4×C59—22no—
80C2×C4⋊C4×C59—22no—
81C2×C4⋊C4×C59—22no—
82C2×C4⋊C4×C59—22no—
83C2×C4⋊C4×C59—21no—
84C2×C4⋊C4×C59—22no—
85C2×C4⋊C4×C59D411yescharacteristic
86C2×C4⋊C4×C59C2312yes—
87C2×C4⋊C4×C59C2312yes—
88C2×C4⋊C4×C59C2311yescharacteristic
89C2×C4⋊C4×C59C2311yescharacteristic
90C2×C4⋊C4×C59C2311yescharacteristic
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×C59—22no—
97C2×C22⋊C4×C59D411yescharacteristic
98C2×C22⋊C4×C59D411yescharacteristic
99C2×C42×C59—21no—
100C2×C42×C59C2311yescharacteristic
101#107×C59—24no—
102#107×C59—24no—
103#106×C59—24no—
104#102×C59—24no—
105#102×C59—24no—
106C22⋊C8×C59—22no—
107C22⋊C8×C59—24no—
108#95×C59—22no—
109#95×C59—21no—
110#95×C59—22no—
111C24×C59—21no—
112C24×C59C2×D411yescharacteristic
113C24×C59C2×D411yescharacteristic
114C2×D4×C59—24no—
115C2×D4×C59—22no—
116C2×D4×C59—22no—
117C2×D4×C59—24no—
118C2×D4×C59—21no—
119C2×D4×C59—22no—
120C2×D4×C59—22no—
121C2×D4×C59—41no—
122C2×D4×C59—42no—
123C2×D4×C59—42no—
124C2×D4×C59—82no—
125C2×D4×C59C2×D412yes—
126C22×C4×C59—22no—
127C22×C4×C59—22no—
128C22×C4×C59—21no—
129C22×C4×C59—21no—
130C22×C4×C59—21no—
131C22×C4×C59—24no—
132C22×C4×C59—24no—
133C22×C4×C59—21no—
134C22×C4×C59—21no—
135C22×C4×C59—22no—
136C22×C4×C59—22no—
137C22×C4×C59—22no—
138C22×C4×C59—22no—
139C22×C4×C59—42no—
140C22×C4×C59—82no—
141C22×C4×C59—82no—
142C22×C4×C59—82no—
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
150M16×C59—28no—
151C2×C8×C59—22no—
152C2×C8×C59—22no—
153C2×C8×C59—22no—
154C2×C8×C59—22no—
155C2×C8×C59—22no—
156C2×C8×C59#4114yes—
157C4⋊C4×C59—24no—
158C4⋊C4×C59—24no—
159C4⋊C4×C59—24no—
160C4⋊C4×C59—22no—
161C4⋊C4×C59—21no—
162C4⋊C4×C59—21no—
163C4⋊C4×C59—21no—
164C4⋊C4×C59—22no—
165C4⋊C4×C59—22no—
166C4⋊C4×C59—22no—
167C4⋊C4×C59—22no—
168C4⋊C4×C59—42no—
169C4⋊C4×C59—82no—
170C4⋊C4×C59C2×D412yes—
171C4⋊C4×C59C2×D412yes—
172C4⋊C4×C59C2×D412yes—
173C22⋊C4×C59—24no—
174C22⋊C4×C59—24no—
175C22⋊C4×C59—24no—
176C22⋊C4×C59—22no—
177C22⋊C4×C59—24no—
178C22⋊C4×C59—22no—
179C22⋊C4×C59—42no—
180C22⋊C4×C59—82no—
181C42×C59—24no—
182C42×C59—21no—
183C42×C59—21no—
184C23×C59—21no—
185C23×C59—22no—
186C23×C59—22no—
187C23×C59—21no—
188C23×C59—21no—
189C23×C59—21no—
190C23×C59—22no—
191C23×C59—22no—
192C23×C59—22no—
193C23×C59—42no—
194C23×C59—41no—
195C23×C59—41no—
196C23×C59—42no—
197C23×C59#12012yes—
198C23×C59#13712yes—
199C23×C59C22×D411yescharacteristic
200D4×C59—24no—
201D4×C59—44no—
202D4×C59—48no—
203D4×C59—41no—
204D4×C59—41no—
205D4×C59—84no—
206C2×C4×C59—22no—
207C2×C4×C59—22no—
208C2×C4×C59—22no—
209C2×C4×C59—24no—
210C2×C4×C59—21no—
211C2×C4×C59—22no—
212C2×C4×C59—21no—
213C2×C4×C59—22no—
214C2×C4×C59—21no—
215C2×C4×C59—22no—
216C2×C4×C59—22no—
217C2×C4×C59—21no—
218C2×C4×C59—21no—
219C2×C4×C59—22no—
220C2×C4×C59—41no—
221C2×C4×C59—41no—
222C2×C4×C59—42no—
223C2×C4×C59—42no—
224C2×C4×C59—41no—
225C2×C4×C59—41no—
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—84no—
234C2×C4×C59—84no—
235C2×C4×C59—84no—
236C2×C4×C59#12012yes—
237C2×C4×C59C22×D411yescharacteristic
238C2×C4×C59C22×D411yescharacteristic
239C2×C4×C59C2×#4112yes—
240C2×C4×C592−1+412yes—
241C8×C59—24no—
242C8×C59—42no—
243#24102C5911yesmaximal, characteristic, direct product factor, Sylow
244C22×C59—24no—
245C22×C59—22no—
246C22×C59—22no—
247C22×C59—22no—
248C22×C59—22no—
249C22×C59—42no—
250C22×C59—42no—
251C22×C59—42no—
252C22×C59—41no—
253C22×C59—41no—
254C22×C59—42no—
255C22×C59—42no—
256C22×C59—42no—
257C22×C59—82no—
258C22×C59—82no—
259C22×C59C2×#12011yescharacteristic
260C22×C59#54712yes—
261C22×C59C2×#13711yescharacteristic
262C22×C59#57511yescharacteristic
263C22×C59#57612yes—
264C4×C59—22no—
265C4×C59—41no—
266C4×C59—41no—
267C4×C59—42no—
268C4×C59—41no—
269C4×C59—42no—
270C4×C59—42no—
271C4×C59—82no—
272C4×C59—82no—
273C4×C59#52511yescharacteristic
274C4×C59#53611yescharacteristic
275C4×C59#54712yes—
276C2×#553C2×C5911yescharacteristic
277C2×#480C2×C5911yescharacteristic, complemented
278C2×#428C2×C5911yescharacteristic, complemented
279#2487C2×C5911yescharacteristic, complemented
280#2059C2×C5912yescomplemented
281#2034C2×C5912yescomplemented
282#1895C2×C5911yescharacteristic, complemented
283#1870C2×C5911yescharacteristic, complemented
284#1862C2×C5912yescomplemented
285#1852C2×C5912yescomplemented
286#1825C2×C5911yescharacteristic, complemented
287C2×C59—42no—
288C2×C59—42no—
289C2×C59—82no—
290C2×C59#240611yescharacteristic
291C2×C59#300711yescharacteristic
292C2×C59#300811yescharacteristic
293C2×C59#334612yes—
294C2×C59#335512yes—
295C22×M16C22×C5911yescharacteristic
296#553—24no—
297#553—24no—
298C2×#126—21no—
299C2×#125C22×C5911yescharacteristic
300C2×#123—21no—
301C2×#121—21no—
302C2×#121C22×C5911yescharacteristic
303C2×#121C22×C5911yescharacteristic
304C2×C4×D4—21no—
305C2×C4×D4C22×C5911yescharacteristic
306C2×C4×D4C22×C5911yescharacteristic
307C2×#117C22×C5911yescharacteristic
308C22×C4⋊C4C22×C5911yescharacteristic
309C22×C4⋊C4C22×C5911yescharacteristic
310#480—24no—
311#428—24no—
312C2×#107C22×C5912yes—
313C2×#107C22×C5912yes—
314C2×#106C22×C5912yes—
315C2×#102C22×C5912yes—
316C2×#102C22×C5912yes—
317C2×C22⋊C8C22×C5911yescharacteristic
318C2×C22⋊C8C22×C5912yes—
319#400—21no—
320#399—21no—
321#389C22×C5912yes—
322#386—21no—
323#385—21no—
324#380C22×C5911yescharacteristic
325#380C22×C5912yes—
326#340C22×C5912yes—
327#340C22×C5912yes—
328#340C22×C5912yes—
329#336C22×C5912yes—
330C59#2410211yescharacteristic, direct product factor, Sylow
331C22×D4—21no—
332C22×D4—21no—
333C22×D4D4×C5911yescharacteristic
334C22×D4C23×C5911yescharacteristic
335C23×C4—21no—
336C23×C4—21no—
337C23×C4—21no—
338C23×C4C23×C5911yescharacteristic
339C23×C4C23×C5911yescharacteristic
340C2×M16—22no—
341C2×M16—24no—
342C22×C8C23×C5912yes—
343C22×C8C23×C5912yes—
344#126—28no—
345#125—22no—
346#125—22no—
347#123—28no—
348#121—28no—
349#121—22no—
350#121—22no—
351#121—22no—
352#121D4×C5914yes—
353C4×D4—28no—
354C4×D4—22no—
355C4×D4—22no—
356C4×D4—22no—
357C4×D4—22no—
358#117—22no—
359#117D4×C5914yes—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4D4×C5911yescharacteristic
370C2×C4⋊C4C23×C5912yes—
371C2×C4⋊C4C23×C5912yes—
372C2×C4⋊C4C23×C5911yescharacteristic
373C2×C4⋊C4C23×C5911yescharacteristic
374C2×C4⋊C4C23×C5911yescharacteristic
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4D4×C5911yescharacteristic
382C2×C22⋊C4D4×C5911yescharacteristic
383C2×C42—21no—
384C2×C42C23×C5911yescharacteristic
385#107—24no—
386#107—24no—
387#106—24no—
388#102—24no—
389#102—24no—
390C22⋊C8—22no—
391C22⋊C8—24no—
392#95—22no—
393#95—21no—
394#95—22no—
395C24—21no—
396C24C2×D4×C5911yescharacteristic
397C24C2×D4×C5911yescharacteristic
398C2×D4—24no—
399C2×D4—22no—
400C2×D4—22no—
401C2×D4—24no—
402C2×D4—21no—
403C2×D4—22no—
404C2×D4—22no—
405C2×D4—41no—
406C2×D4—42no—
407C2×D4—42no—
408C2×D4—82no—
409C2×D4C2×D4×C5912yes—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—24no—
416C22×C4—24no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—42no—
424C22×C4—82no—
425C22×C4—82no—
426C22×C4—82no—
427C22×C4C2×D4×C5911yescharacteristic
428C22×C4C2×D4×C5911yescharacteristic
429C22×C4C2×D4×C5911yescharacteristic
430C22×C4C2×D4×C5911yescharacteristic
431C22×C4C2×D4×C5912yes—
432C22×C4C2×D4×C5912yes—
433C22×C4C24×C5911yescharacteristic
434M16—28no—
435C2×C8—22no—
436C2×C8—22no—
437C2×C8—22no—
438C2×C8—22no—
439C2×C8—22no—
440C2×C8#41×C5914yes—
441C4⋊C4—24no—
442C4⋊C4—24no—
443C4⋊C4—24no—
444C4⋊C4—22no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—22no—
449C4⋊C4—22no—
450C4⋊C4—22no—
451C4⋊C4—22no—
452C4⋊C4—42no—
453C4⋊C4—82no—
454C4⋊C4C2×D4×C5912yes—
455C4⋊C4C2×D4×C5912yes—
456C4⋊C4C2×D4×C5912yes—
457C22⋊C4—24no—
458C22⋊C4—24no—
459C22⋊C4—24no—
460C22⋊C4—22no—
461C22⋊C4—24no—
462C22⋊C4—22no—
463C22⋊C4—42no—
464C22⋊C4—82no—
465C42—24no—
466C42—21no—
467C42—21no—
468C23—21no—
469C23—22no—
470C23—22no—
471C23—21no—
472C23—21no—
473C23—21no—
474C23—22no—
475C23—22no—
476C23—22no—
477C23—42no—
478C23—41no—
479C23—41no—
480C23—42no—
481C23#120×C5912yes—
482C23#137×C5912yes—
483C23C22×D4×C5911yescharacteristic
484D4—24no—
485D4—44no—
486D4—48no—
487D4—41no—
488D4—41no—
489D4—84no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—24no—
494C2×C4—21no—
495C2×C4—22no—
496C2×C4—21no—
497C2×C4—22no—
498C2×C4—21no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—22no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—84no—
518C2×C4—84no—
519C2×C4—84no—
520C2×C4#120×C5912yes—
521C2×C4C22×D4×C5911yescharacteristic
522C2×C4C22×D4×C5911yescharacteristic
523C2×C4C2×#41×C5912yes—
524C2×C42−1+4×C5912yes—
525C8—24no—
526C8—42no—
527C22—22no—
528C22—22no—
529C22—22no—
530C22—24no—
531C22—22no—
532C22—41no—
533C22—42no—
534C22—42no—
535C22—42no—
536C22—41no—
537C22—42no—
538C22—42no—
539C22—42no—
540C22—82no—
541C22—82no—
542C22C2×#120×C5911yescharacteristic
543C22C59×#54712yes—
544C22C2×#137×C5911yescharacteristic
545C22C59×#57511yescharacteristic
546C22C59×#57612yes—
547C4—22no—
548C4—41no—
549C4—42no—
550C4—41no—
551C4—42no—
552C4—42no—
553C4—41no—
554C4—82no—
555C4—82no—
556C4C59×#52511yescharacteristic
557C4C59×#53611yescharacteristic
558C4C59×#54712yes—
559C2—42no—
560C2—42no—
561C2—82no—
562C2C59×#240611yescharacteristic
563C2C59×#300711yescharacteristic
564C2C59×#300811yescharacteristic
565C2C59×#334612yes—
566C2C59×#335512yes—
subgroupG/H
center, socleC23×C59C22×D4
commutator, Frattini, cosocleC22×C4C24×C59
prime radicalC2×C59×#553C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C59 ◁ C2×C4×D4×C59 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C59×#480C2semidirect
3. C2×C59×#428C2semidirect
4. C59×#2487C2semidirect
5. C59×#2059C2semidirect
6. C59×#2034C2semidirect
7. C59×#1895C2semidirect
8. C59×#1870C2semidirect
9. C59×#1862C2semidirect
10. C59×#1852C2semidirect
11. C59×#1825C2semidirect
243. #24102C59direct (N × H)
277. C2×#480C2×C59semidirect
278. C2×#428C2×C59semidirect
279. #2487C2×C59semidirect
280. #2059C2×C59semidirect
281. #2034C2×C59semidirect
282. #1895C2×C59semidirect
283. #1870C2×C59semidirect
284. #1862C2×C59semidirect
285. #1852C2×C59semidirect
286. #1825C2×C59semidirect
330. C59#24102direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C59×#5532
C2×C59×#4802
C2×C59×#4282
C59×#24872
C59×#20592
C59×#20342
C59×#18952
C59×#18702
C59×#18622
C59×#18522
C59×#18252
#2410259