Finite Group Databasebeta

← C59×#18151 #28430260

Subgroups — C59×#18151 #28430260

Order 15104.

994 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3460C211yesmaximal, characteristic
2C59×#3092C212yesmaximal, complemented
3C59×#2487C211yesmaximal, characteristic, complemented
4C59×#1618C214yesmaximal, complemented
5C59×#1617C212yesmaximal, complemented
6C59×#1616C212yesmaximal, complemented
7C59×#1513C212yesmaximal, complemented
8C59×#1465C211yesmaximal, characteristic, complemented
9C59×#544C2211yescharacteristic
10C59×#542—22no—
11C59×#540—22no—
12C59×#538—21no—
13C59×#538C2212yes—
14C59×#537C2211yescharacteristic
15C59×#535—21no—
16C59×#532—22no—
17C59×#529—22no—
18C59×#525—21no—
19C59×#525C2212yes—
20C4×#41×C59—21no—
21C2×C4×D4×C59C2211yescharacteristic
22C22×C4⋊C4×C59C2211yescharacteristic
23C59×#484C2214yes—
24C59×#483—22no—
25C59×#481C2214yes—
26C59×#480—22no—
27C59×#428—22no—
28C59×#417—22no—
29C59×#407C2212yes—
30C59×#400C2212yes—
31C59×#399C2212yes—
32C59×#389—21no—
33C59×#386—21no—
34C59×#385—21no—
35C59×#380—21no—
36C59×#380C2211yescharacteristic
37C59×#328C2214yes—
38C59×#327C2214yes—
39C59×#324C2212yes—
40C59×#323C2212yes—
41C2×#41×C59—21no—
42C2×#41×C59—21no—
43C2×#41×C59D412yes—
44C22×D4×C59D411yescharacteristic
45C23×C4×C59—21no—
46C23×C4×C59D411yescharacteristic
47C23×C4×C59C2311yescharacteristic
48C2×M16×C59—22no—
49C4⋊Q8×C59—22no—
50#127×C59—22no—
51#126×C59—22no—
52#126×C59—22no—
53#125×C59—22no—
54#124×C59—22no—
55#124×C59—22no—
56#124×C59—22no—
57#123×C59—22no—
58#123×C59—22no—
59#123×C59—22no—
60#123×C59—22no—
61C22⋊Q8×C59—21no—
62C22⋊Q8×C59—21no—
63C22⋊Q8×C59—22no—
64C22⋊Q8×C59D412yes—
65C22⋊Q8×C59C2312yes—
66#121×C59—21no—
67#121×C59—22no—
68#121×C59—22no—
69#121×C59—22no—
70#121×C59—22no—
71#121×C59—22no—
72#121×C59—21no—
73#121×C59D412yes—
74#121×C59C2312yes—
75#120×C59—22no—
76#120×C59—22no—
77C4×Q8×C59—21no—
78C4×Q8×C59—21no—
79C4×D4×C59—21no—
80C4×D4×C59—21no—
81C4×D4×C59—22no—
82C4×D4×C59—22no—
83C4×D4×C59—22no—
84C4×D4×C59—22no—
85C4×D4×C59—22no—
86C4×D4×C59—22no—
87#117×C59—22no—
88#117×C59—21no—
89#117×C59—21no—
90#117×C59D412yes—
91C2×C4⋊C4×C59—22no—
92C2×C4⋊C4×C59—22no—
93C2×C4⋊C4×C59—21no—
94C2×C4⋊C4×C59—21no—
95C2×C4⋊C4×C59—22no—
96C2×C4⋊C4×C59C2312yes—
97C2×C4⋊C4×C59C2311yescharacteristic
98C2×C22⋊C4×C59—21no—
99C2×C22⋊C4×C59—22no—
100C2×C22⋊C4×C59D411yescharacteristic
101C2×C22⋊C4×C59C2311yescharacteristic
102C2×C42×C59—22no—
103C2×C42×C59D411yescharacteristic
104#107×C59—24no—
105#106×C59—24no—
106#103×C59—24no—
107#102×C59—24no—
108C22⋊C8×C59—22no—
109C22⋊C8×C59C2314yes—
110#95×C59—22no—
111#95×C59—22no—
112#95×C59C2312yes—
113C24×C59C2×D411yescharacteristic
114C24×C59C2×D411yescharacteristic
115#41×C59—42no—
116#41×C59—44no—
117#41×C59—42no—
118#41×C59—82no—
119C2×Q8×C59—21no—
120C2×Q8×C59—21no—
121C2×Q8×C59C2×D412yes—
122C2×D4×C59—21no—
123C2×D4×C59—22no—
124C2×D4×C59—22no—
125C2×D4×C59—22no—
126C2×D4×C59—22no—
127C2×D4×C59—21no—
128C2×D4×C59—22no—
129C2×D4×C59—22no—
130C2×D4×C59—22no—
131C2×D4×C59—41no—
132C2×D4×C59C2×D412yes—
133C22×C4×C59—22no—
134C22×C4×C59—22no—
135C22×C4×C59—22no—
136C22×C4×C59—21no—
137C22×C4×C59—21no—
138C22×C4×C59—22no—
139C22×C4×C59—22no—
140C22×C4×C59—42no—
141C22×C4×C59—42no—
142C22×C4×C59—42no—
143C22×C4×C59—82no—
144C22×C4×C59C2×D411yescharacteristic
145C22×C4×C59C2×D412yes—
146C22×C4×C59C2×D411yescharacteristic
147C22×C4×C59C2×D411yescharacteristic
148C22×C4×C59C2×D411yescharacteristic
149C22×C4×C59C2×D412yes—
150C22×C4×C59C2411yescharacteristic
151M16×C59—44no—
152C2×C8×C59—24no—
153C4⋊C4×C59—21no—
154C4⋊C4×C59—21no—
155C4⋊C4×C59—22no—
156C4⋊C4×C59—21no—
157C4⋊C4×C59—21no—
158C4⋊C4×C59—22no—
159C4⋊C4×C59—22no—
160C4⋊C4×C59—22no—
161C4⋊C4×C59—22no—
162C4⋊C4×C59—24no—
163C4⋊C4×C59—42no—
164C4⋊C4×C59—41no—
165C4⋊C4×C59—41no—
166C4⋊C4×C59—82no—
167C4⋊C4×C59C2×D412yes—
168C4⋊C4×C59C2×D412yes—
169C22⋊C4×C59—22no—
170C22⋊C4×C59—22no—
171C22⋊C4×C59—22no—
172C22⋊C4×C59—22no—
173C22⋊C4×C59—22no—
174C22⋊C4×C59—22no—
175C22⋊C4×C59—22no—
176C22⋊C4×C59—22no—
177C22⋊C4×C59—22no—
178C22⋊C4×C59—22no—
179C22⋊C4×C59—22no—
180C22⋊C4×C59—42no—
181C22⋊C4×C59—82no—
182C42×C59—22no—
183C42×C59—22no—
184C42×C59—21no—
185C42×C59—22no—
186C42×C59—21no—
187C23×C59—21no—
188C23×C59—21no—
189C23×C59—21no—
190C23×C59—22no—
191C23×C59—21no—
192C23×C59—21no—
193C23×C59—41no—
194C23×C59—41no—
195C23×C59—41no—
196C23×C59—41no—
197C23×C59#12012yes—
198C23×C59C22×D411yescharacteristic
199Q8×C59—42no—
200Q8×C59—42no—
201Q8×C59—81no—
202D4×C59—44no—
203D4×C59—42no—
204D4×C59—42no—
205D4×C59—42no—
206D4×C59—42no—
207D4×C59—82no—
208D4×C59—82no—
209D4×C59—82no—
210D4×C59—81no—
211D4×C59—82no—
212C2×C4×C59—21no—
213C2×C4×C59—21no—
214C2×C4×C59—22no—
215C2×C4×C59—24no—
216C2×C4×C59—21no—
217C2×C4×C59—22no—
218C2×C4×C59—22no—
219C2×C4×C59—22no—
220C2×C4×C59—21no—
221C2×C4×C59—42no—
222C2×C4×C59—41no—
223C2×C4×C59—44no—
224C2×C4×C59—42no—
225C2×C4×C59—44no—
226C2×C4×C59—41no—
227C2×C4×C59—41no—
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—81no—
235C2×C4×C59—82no—
236C2×C4×C59—84no—
237C2×C4×C59#12011yescharacteristic
238C2×C4×C59#12011yescharacteristic
239C2×C4×C59#13712yes—
240C2×C4×C59C22×D412yes—
241C8×C59—44no—
242#18151C5911yesmaximal, characteristic, direct product factor, Sylow
243C22×C59—21no—
244C22×C59—21no—
245C22×C59—22no—
246C22×C59—22no—
247C22×C59—22no—
248C22×C59—42no—
249C22×C59—42no—
250C22×C59—42no—
251C22×C59—42no—
252C22×C59—41no—
253C22×C59—42no—
254C22×C59—41no—
255C22×C59—41no—
256C22×C59—42no—
257C22×C59—81no—
258C22×C59C2×#12011yescharacteristic
259C22×C59C2×#13711yescharacteristic
260C22×C59#57511yescharacteristic
261C4×C59—22no—
262C4×C59—22no—
263C4×C59—21no—
264C4×C59—42no—
265C4×C59—41no—
266C4×C59—42no—
267C4×C59—41no—
268C4×C59—42no—
269C4×C59—82no—
270C4×C59—82no—
271C4×C59#45812yes—
272#3460C2×C5911yescharacteristic
273#3092C2×C5912yescomplemented
274#2487C2×C5911yescharacteristic, complemented
275#1618C2×C5914yescomplemented
276#1617C2×C5912yescomplemented
277#1616C2×C5912yescomplemented
278#1513C2×C5912yescomplemented
279#1465C2×C5911yescharacteristic, complemented
280C2×C59—21no—
281C2×C59—21no—
282C2×C59—42no—
283C2×C59—82no—
284C2×C59—81no—
285C2×C59#300711yescharacteristic
286C2×C59#302111yescharacteristic
287C2×C59C2×#45811yescharacteristic
288#544C22×C5911yescharacteristic
289#542—22no—
290#540—22no—
291#538—21no—
292#538C22×C5912yes—
293#537C22×C5911yescharacteristic
294#535—21no—
295#532—22no—
296#529—22no—
297#525—21no—
298#525C22×C5912yes—
299C4×#41—21no—
300C2×C4×D4C22×C5911yescharacteristic
301C22×C4⋊C4C22×C5911yescharacteristic
302#484C22×C5914yes—
303#483—22no—
304#481C22×C5914yes—
305#480—22no—
306#428—22no—
307#417—22no—
308#407C22×C5912yes—
309#400C22×C5912yes—
310#399C22×C5912yes—
311#389—21no—
312#386—21no—
313#385—21no—
314#380—21no—
315#380C22×C5911yescharacteristic
316#328C22×C5914yes—
317#327C22×C5914yes—
318#324C22×C5912yes—
319#323C22×C5912yes—
320C59#1815111yescharacteristic, direct product factor, Sylow
321C2×#41—21no—
322C2×#41—21no—
323C2×#41D4×C5912yes—
324C22×D4D4×C5911yescharacteristic
325C23×C4—21no—
326C23×C4D4×C5911yescharacteristic
327C23×C4C23×C5911yescharacteristic
328C2×M16—22no—
329C4⋊Q8—22no—
330#127—22no—
331#126—22no—
332#126—22no—
333#125—22no—
334#124—22no—
335#124—22no—
336#124—22no—
337#123—22no—
338#123—22no—
339#123—22no—
340#123—22no—
341C22⋊Q8—21no—
342C22⋊Q8—21no—
343C22⋊Q8—22no—
344C22⋊Q8D4×C5912yes—
345C22⋊Q8C23×C5912yes—
346#121—21no—
347#121—22no—
348#121—22no—
349#121—22no—
350#121—22no—
351#121—22no—
352#121—21no—
353#121D4×C5912yes—
354#121C23×C5912yes—
355#120—22no—
356#120—22no—
357C4×Q8—21no—
358C4×Q8—21no—
359C4×D4—21no—
360C4×D4—21no—
361C4×D4—22no—
362C4×D4—22no—
363C4×D4—22no—
364C4×D4—22no—
365C4×D4—22no—
366C4×D4—22no—
367#117—22no—
368#117—21no—
369#117—21no—
370#117D4×C5912yes—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4C23×C5912yes—
377C2×C4⋊C4C23×C5911yescharacteristic
378C2×C22⋊C4—21no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4D4×C5911yescharacteristic
381C2×C22⋊C4C23×C5911yescharacteristic
382C2×C42—22no—
383C2×C42D4×C5911yescharacteristic
384#107—24no—
385#106—24no—
386#103—24no—
387#102—24no—
388C22⋊C8—22no—
389C22⋊C8C23×C5914yes—
390#95—22no—
391#95—22no—
392#95C23×C5912yes—
393C24C2×D4×C5911yescharacteristic
394C24C2×D4×C5911yescharacteristic
395#41—42no—
396#41—44no—
397#41—42no—
398#41—82no—
399C2×Q8—21no—
400C2×Q8—21no—
401C2×Q8C2×D4×C5912yes—
402C2×D4—21no—
403C2×D4—22no—
404C2×D4—22no—
405C2×D4—22no—
406C2×D4—22no—
407C2×D4—21no—
408C2×D4—22no—
409C2×D4—22no—
410C2×D4—22no—
411C2×D4—41no—
412C2×D4C2×D4×C5912yes—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—42no—
421C22×C4—42no—
422C22×C4—42no—
423C22×C4—82no—
424C22×C4C2×D4×C5911yescharacteristic
425C22×C4C2×D4×C5912yes—
426C22×C4C2×D4×C5911yescharacteristic
427C22×C4C2×D4×C5911yescharacteristic
428C22×C4C2×D4×C5911yescharacteristic
429C22×C4C2×D4×C5912yes—
430C22×C4C24×C5911yescharacteristic
431M16—44no—
432C2×C8—24no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—22no—
436C4⋊C4—21no—
437C4⋊C4—21no—
438C4⋊C4—22no—
439C4⋊C4—22no—
440C4⋊C4—22no—
441C4⋊C4—22no—
442C4⋊C4—24no—
443C4⋊C4—42no—
444C4⋊C4—41no—
445C4⋊C4—41no—
446C4⋊C4—82no—
447C4⋊C4C2×D4×C5912yes—
448C4⋊C4C2×D4×C5912yes—
449C22⋊C4—22no—
450C22⋊C4—22no—
451C22⋊C4—22no—
452C22⋊C4—22no—
453C22⋊C4—22no—
454C22⋊C4—22no—
455C22⋊C4—22no—
456C22⋊C4—22no—
457C22⋊C4—22no—
458C22⋊C4—22no—
459C22⋊C4—22no—
460C22⋊C4—42no—
461C22⋊C4—82no—
462C42—22no—
463C42—22no—
464C42—21no—
465C42—22no—
466C42—21no—
467C23—21no—
468C23—21no—
469C23—21no—
470C23—22no—
471C23—21no—
472C23—21no—
473C23—41no—
474C23—41no—
475C23—41no—
476C23—41no—
477C23#120×C5912yes—
478C23C22×D4×C5911yescharacteristic
479Q8—42no—
480Q8—42no—
481Q8—81no—
482D4—44no—
483D4—42no—
484D4—42no—
485D4—42no—
486D4—42no—
487D4—82no—
488D4—82no—
489D4—82no—
490D4—81no—
491D4—82no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—22no—
495C2×C4—24no—
496C2×C4—21no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—21no—
501C2×C4—42no—
502C2×C4—41no—
503C2×C4—44no—
504C2×C4—42no—
505C2×C4—44no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—81no—
515C2×C4—82no—
516C2×C4—84no—
517C2×C4#120×C5911yescharacteristic
518C2×C4#120×C5911yescharacteristic
519C2×C4#137×C5912yes—
520C2×C4C22×D4×C5912yes—
521C8—44no—
522C22—21no—
523C22—21no—
524C22—22no—
525C22—22no—
526C22—22no—
527C22—42no—
528C22—42no—
529C22—42no—
530C22—42no—
531C22—41no—
532C22—42no—
533C22—41no—
534C22—41no—
535C22—42no—
536C22—81no—
537C22C2×#120×C5911yescharacteristic
538C22C2×#137×C5911yescharacteristic
539C22C59×#57511yescharacteristic
540C4—22no—
541C4—22no—
542C4—21no—
543C4—42no—
544C4—41no—
545C4—42no—
546C4—41no—
547C4—42no—
548C4—82no—
549C4—82no—
550C4C59×#45812yes—
551C2—21no—
552C2—21no—
553C2—42no—
554C2—81no—
555C2—82no—
556C2C59×#300711yescharacteristic
557C2C59×#302111yescharacteristic
558C2C2×C59×#45811yescharacteristic
subgroupG/H
center, socleC22×C59C2×#120
commutator, Frattini, cosocleC22×C4C24×C59
prime radicalC59×#3460C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C59 ◁ C23×C4×C59 ◁ G

Complements

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

NH ≅ G/Ntype
2. C59×#3092C2semidirect
3. C59×#2487C2semidirect
4. C59×#1618C2semidirect
5. C59×#1617C2semidirect
6. C59×#1616C2semidirect
7. C59×#1513C2semidirect
8. C59×#1465C2semidirect
242. #18151C59direct (N × H)
273. #3092C2×C59semidirect
274. #2487C2×C59semidirect
275. #1618C2×C59semidirect
276. #1617C2×C59semidirect
277. #1616C2×C59semidirect
278. #1513C2×C59semidirect
279. #1465C2×C59semidirect
320. C59#18151direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#34602
C59×#30922
C59×#24872
C59×#16182
C59×#16172
C59×#16162
C59×#15132
C59×#14652
#1815159