Finite Group Databasebeta

← C59×#24024 #28436133

Subgroups — C59×#24024 #28436133

Order 15104.

1274 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3487C211yesmaximal, characteristic
2C59×#3092C212yesmaximal, complemented
3C59×#2311C211yesmaximal, characteristic, complemented
4C59×#2037C214yesmaximal, complemented
5C59×#1897C212yesmaximal, complemented
6C59×#1857C212yesmaximal, complemented
7C59×#1793C212yesmaximal, complemented
8C59×#1785C211yesmaximal, characteristic, complemented
9C2×2−1+4×C59C2211yescharacteristic
10C22×#41×C59C2211yescharacteristic
11C59×#550—22no—
12C59×#550—22no—
13C59×#548—22no—
14C59×#548—22no—
15C59×#535—22no—
16C59×#535C2212yes—
17C59×#525—22no—
18C59×#525C2212yes—
19C59×#519C2211yescharacteristic
20C2×#117×C59C2211yescharacteristic
21C22×C4⋊C4×C59C2211yescharacteristic
22C59×#484—22no—
23C59×#483—22no—
24C59×#481—22no—
25C59×#480—22no—
26C59×#428C2214yes—
27C2×#104×C59C2214yes—
28C59×#417C2214yes—
29C2×#101×C59C2212yes—
30C2×#100×C59C2212yes—
31C59×#407C2212yes—
32C59×#391C2212yes—
33C59×#390C2212yes—
34C59×#386—22no—
35C59×#380—22no—
36C59×#339C2214yes—
372−1+4×C59—24no—
382−1+4×C59—42no—
39C2×#41×C59—24no—
40C2×#41×C59—22no—
41C2×#41×C59—22no—
42C2×#41×C59—22no—
43C2×#41×C59—22no—
44C2×#41×C59—42no—
45C2×#41×C59C2312yes—
46C22×Q8×C59—22no—
47C22×Q8×C59C2311yescharacteristic
48C22×D4×C59D412yes—
49C22×D4×C59C2311yescharacteristic
50C23×C4×C59—21no—
51C23×C4×C59D412yes—
52C23×C4×C59C2311yescharacteristic
53C2×M16×C59C2314yes—
54#127×C59—24no—
55#127×C59—22no—
56#124×C59—24no—
57#124×C59—22no—
58#123×C59—22no—
59C22⋊Q8×C59—22no—
60C22⋊Q8×C59—22no—
61C22⋊Q8×C59D412yes—
62C22⋊Q8×C59D412yes—
63#121×C59—22no—
64#121×C59—22no—
65#121×C59—24no—
66#121×C59—24no—
67#121×C59—22no—
68#121×C59—22no—
69#121×C59D412yes—
70#121×C59D412yes—
71#120×C59—24no—
72#120×C59—22no—
73C4×Q8×C59—22no—
74C4×Q8×C59—22no—
75C4×D4×C59—24no—
76C4×D4×C59—24no—
77C4×D4×C59—22no—
78C4×D4×C59—22no—
79#117×C59—22no—
80#117×C59—42no—
81#117×C59C2312yes—
82C2×C4⋊C4×C59—22no—
83C2×C4⋊C4×C59—22no—
84C2×C4⋊C4×C59—21no—
85C2×C4⋊C4×C59—21no—
86C2×C4⋊C4×C59C2312yes—
87C2×C22⋊C4×C59—21no—
88C2×C22⋊C4×C59—24no—
89C2×C42×C59C2312yes—
90#107×C59—24no—
91#106×C59—24no—
92#104×C59—44no—
93#103×C59—24no—
94#102×C59—24no—
95#101×C59—24no—
96#100×C59—42no—
97C22⋊C8×C59—22no—
98C22⋊C8×C59—22no—
99#95×C59—24no—
100C24×C59C2×D412yes—
101C24×C59C2×D411yescharacteristic
102#41×C59—24no—
103#41×C59—24no—
104#41×C59—48no—
105#41×C59—48no—
106#41×C59—44no—
107#41×C59—48no—
108#41×C59—44no—
109C2×Q8×C59—22no—
110C2×Q8×C59—22no—
111C2×Q8×C59—22no—
112C2×Q8×C59—48no—
113C2×Q8×C59C2×D412yes—
114C2×Q8×C59#4114yes—
115C2×D4×C59—22no—
116C2×D4×C59—24no—
117C2×D4×C59—22no—
118C2×D4×C59—24no—
119C2×D4×C59—24no—
120C2×D4×C59—22no—
121C2×D4×C59—22no—
122C2×D4×C59—24no—
123C2×D4×C59—22no—
124C2×D4×C59—22no—
125C2×D4×C59—22no—
126C2×D4×C59—42no—
127C2×D4×C59C2×D412yes—
128C22×C4×C59—22no—
129C22×C4×C59—22no—
130C22×C4×C59—24no—
131C22×C4×C59—22no—
132C22×C4×C59—22no—
133C22×C4×C59—24no—
134C22×C4×C59—22no—
135C22×C4×C59—22no—
136C22×C4×C59—22no—
137C22×C4×C59—42no—
138C22×C4×C59—42no—
139C22×C4×C59—82no—
140C22×C4×C59C2×D411yescharacteristic
141C22×C4×C59C2×D412yes—
142C22×C4×C59C2×D412yes—
143C22×C4×C59C2×D412yes—
144C22×C4×C59C2411yescharacteristic
145M16×C59—24no—
146M16×C59—24no—
147C2×C8×C59—24no—
148C4⋊C4×C59—22no—
149C4⋊C4×C59—22no—
150C4⋊C4×C59—22no—
151C4⋊C4×C59—22no—
152C4⋊C4×C59—24no—
153C4⋊C4×C59—42no—
154C4⋊C4×C59—41no—
155C4⋊C4×C59—41no—
156C4⋊C4×C59C2×D412yes—
157C4⋊C4×C59C2×D412yes—
158C22⋊C4×C59—24no—
159C22⋊C4×C59—24no—
160C22⋊C4×C59—22no—
161C22⋊C4×C59—22no—
162C22⋊C4×C59—22no—
163C22⋊C4×C59—22no—
164C22⋊C4×C59—22no—
165C22⋊C4×C59—42no—
166C22⋊C4×C59—84no—
167C42×C59—24no—
168C42×C59—22no—
169C42×C59—24no—
170C23×C59—21no—
171C23×C59—21no—
172C23×C59—22no—
173C23×C59—22no—
174C23×C59—22no—
175C23×C59—22no—
176C23×C59—41no—
177C23×C59—41no—
178C23×C59—42no—
179C23×C59—42no—
180C23×C59#12012yes—
181C23×C59C22×D411yescharacteristic
182Q8×C59—28no—
183Q8×C59—24no—
184Q8×C59—44no—
185D4×C59—24no—
186D4×C59—48no—
187D4×C59—44no—
188D4×C59—42no—
189D4×C59—42no—
190D4×C59—44no—
191D4×C59—82no—
192D4×C59—82no—
193D4×C59—84no—
194D4×C59—84no—
195C2×C4×C59—22no—
196C2×C4×C59—21no—
197C2×C4×C59—21no—
198C2×C4×C59—22no—
199C2×C4×C59—24no—
200C2×C4×C59—24no—
201C2×C4×C59—22no—
202C2×C4×C59—22no—
203C2×C4×C59—22no—
204C2×C4×C59—44no—
205C2×C4×C59—44no—
206C2×C4×C59—48no—
207C2×C4×C59—44no—
208C2×C4×C59—42no—
209C2×C4×C59—44no—
210C2×C4×C59—42no—
211C2×C4×C59—42no—
212C2×C4×C59—42no—
213C2×C4×C59—84no—
214C2×C4×C59#12011yescharacteristic
215C2×C4×C59#12011yescharacteristic
216C2×C4×C59#12314yes—
217C2×C4×C59C22×D412yes—
218C2×C4×C59C2×#4112yes—
219C2×C4×C59H(5,𝔽2)12yes—
220C8×C59—44no—
221#24024C5911yesmaximal, characteristic, direct product factor, Sylow
222C22×C59—21no—
223C22×C59—21no—
224C22×C59—22no—
225C22×C59—22no—
226C22×C59—22no—
227C22×C59—42no—
228C22×C59—42no—
229C22×C59—44no—
230C22×C59—42no—
231C22×C59—42no—
232C22×C59—42no—
233C22×C59—42no—
234C22×C59—42no—
235C22×C59—42no—
236C22×C59—82no—
237C22×C59C2×#12011yescharacteristic
238C22×C59C2×#12311yescharacteristic
239C22×C59#53411yescharacteristic
240C4×C59—21no—
241C4×C59—21no—
242C4×C59—24no—
243C4×C59—42no—
244C4×C59—42no—
245C4×C59—42no—
246C4×C59—82no—
247C4×C59—82no—
248C4×C59#54614yes—
249#3487C2×C5911yescharacteristic
250#3092C2×C5912yescomplemented
251#2311C2×C5911yescharacteristic, complemented
252#2037C2×C5914yescomplemented
253#1897C2×C5912yescomplemented
254#1857C2×C5912yescomplemented
255#1793C2×C5912yescomplemented
256#1785C2×C5911yescharacteristic, complemented
257C2×C59—21no—
258C2×C59—21no—
259C2×C59—42no—
260C2×C59—82no—
261C2×C59—82no—
262C2×C59#240511yescharacteristic
263C2×C59#302111yescharacteristic
264C2×C59#302211yescharacteristic
265C2×2−1+4C22×C5911yescharacteristic
266C22×#41C22×C5911yescharacteristic
267#550—22no—
268#550—22no—
269#548—22no—
270#548—22no—
271#535—22no—
272#535C22×C5912yes—
273#525—22no—
274#525C22×C5912yes—
275#519C22×C5911yescharacteristic
276C2×#117C22×C5911yescharacteristic
277C22×C4⋊C4C22×C5911yescharacteristic
278#484—22no—
279#483—22no—
280#481—22no—
281#480—22no—
282#428C22×C5914yes—
283C2×#104C22×C5914yes—
284#417C22×C5914yes—
285C2×#101C22×C5912yes—
286C2×#100C22×C5912yes—
287#407C22×C5912yes—
288#391C22×C5912yes—
289#390C22×C5912yes—
290#386—22no—
291#380—22no—
292#339C22×C5914yes—
293C59#2402411yescharacteristic, direct product factor, Sylow
2942−1+4—24no—
2952−1+4—42no—
296C2×#41—24no—
297C2×#41—22no—
298C2×#41—22no—
299C2×#41—22no—
300C2×#41—22no—
301C2×#41—42no—
302C2×#41C23×C5912yes—
303C22×Q8—22no—
304C22×Q8C23×C5911yescharacteristic
305C22×D4D4×C5912yes—
306C22×D4C23×C5911yescharacteristic
307C23×C4—21no—
308C23×C4D4×C5912yes—
309C23×C4C23×C5911yescharacteristic
310C2×M16C23×C5914yes—
311#127—24no—
312#127—22no—
313#124—24no—
314#124—22no—
315#123—22no—
316C22⋊Q8—22no—
317C22⋊Q8—22no—
318C22⋊Q8D4×C5912yes—
319C22⋊Q8D4×C5912yes—
320#121—22no—
321#121—22no—
322#121—24no—
323#121—24no—
324#121—22no—
325#121—22no—
326#121D4×C5912yes—
327#121D4×C5912yes—
328#120—24no—
329#120—22no—
330C4×Q8—22no—
331C4×Q8—22no—
332C4×D4—24no—
333C4×D4—24no—
334C4×D4—22no—
335C4×D4—22no—
336#117—22no—
337#117—42no—
338#117C23×C5912yes—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4C23×C5912yes—
344C2×C22⋊C4—21no—
345C2×C22⋊C4—24no—
346C2×C42C23×C5912yes—
347#107—24no—
348#106—24no—
349#104—44no—
350#103—24no—
351#102—24no—
352#101—24no—
353#100—42no—
354C22⋊C8—22no—
355C22⋊C8—22no—
356#95—24no—
357C24C2×D4×C5912yes—
358C24C2×D4×C5911yescharacteristic
359#41—24no—
360#41—24no—
361#41—48no—
362#41—48no—
363#41—44no—
364#41—48no—
365#41—44no—
366C2×Q8—22no—
367C2×Q8—22no—
368C2×Q8—22no—
369C2×Q8—48no—
370C2×Q8C2×D4×C5912yes—
371C2×Q8#41×C5914yes—
372C2×D4—22no—
373C2×D4—24no—
374C2×D4—22no—
375C2×D4—24no—
376C2×D4—24no—
377C2×D4—22no—
378C2×D4—22no—
379C2×D4—24no—
380C2×D4—22no—
381C2×D4—22no—
382C2×D4—22no—
383C2×D4—42no—
384C2×D4C2×D4×C5912yes—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—24no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—24no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—42no—
395C22×C4—42no—
396C22×C4—82no—
397C22×C4C2×D4×C5911yescharacteristic
398C22×C4C2×D4×C5912yes—
399C22×C4C2×D4×C5912yes—
400C22×C4C2×D4×C5912yes—
401C22×C4C24×C5911yescharacteristic
402M16—24no—
403M16—24no—
404C2×C8—24no—
405C4⋊C4—22no—
406C4⋊C4—22no—
407C4⋊C4—22no—
408C4⋊C4—22no—
409C4⋊C4—24no—
410C4⋊C4—42no—
411C4⋊C4—41no—
412C4⋊C4—41no—
413C4⋊C4C2×D4×C5912yes—
414C4⋊C4C2×D4×C5912yes—
415C22⋊C4—24no—
416C22⋊C4—24no—
417C22⋊C4—22no—
418C22⋊C4—22no—
419C22⋊C4—22no—
420C22⋊C4—22no—
421C22⋊C4—22no—
422C22⋊C4—42no—
423C22⋊C4—84no—
424C42—24no—
425C42—22no—
426C42—24no—
427C23—21no—
428C23—21no—
429C23—22no—
430C23—22no—
431C23—22no—
432C23—22no—
433C23—41no—
434C23—41no—
435C23—42no—
436C23—42no—
437C23#120×C5912yes—
438C23C22×D4×C5911yescharacteristic
439Q8—28no—
440Q8—24no—
441Q8—44no—
442D4—24no—
443D4—48no—
444D4—44no—
445D4—42no—
446D4—42no—
447D4—44no—
448D4—82no—
449D4—82no—
450D4—84no—
451D4—84no—
452C2×C4—22no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—22no—
456C2×C4—24no—
457C2×C4—24no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—44no—
462C2×C4—44no—
463C2×C4—48no—
464C2×C4—44no—
465C2×C4—42no—
466C2×C4—44no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—84no—
471C2×C4#120×C5911yescharacteristic
472C2×C4#120×C5911yescharacteristic
473C2×C4#123×C5914yes—
474C2×C4C22×D4×C5912yes—
475C2×C4C2×#41×C5912yes—
476C2×C4H(5,𝔽2)×C5912yes—
477C8—44no—
478C22—21no—
479C22—21no—
480C22—22no—
481C22—22no—
482C22—22no—
483C22—42no—
484C22—42no—
485C22—44no—
486C22—42no—
487C22—42no—
488C22—42no—
489C22—42no—
490C22—42no—
491C22—42no—
492C22—82no—
493C22C2×#120×C5911yescharacteristic
494C22C2×#123×C5911yescharacteristic
495C22C59×#53411yescharacteristic
496C4—21no—
497C4—21no—
498C4—24no—
499C4—42no—
500C4—42no—
501C4—42no—
502C4—82no—
503C4—82no—
504C4C59×#54614yes—
505C2—21no—
506C2—21no—
507C2—42no—
508C2—82no—
509C2—82no—
510C2C59×#240511yescharacteristic
511C2C59×#302111yescharacteristic
512C2C59×#302211yescharacteristic
subgroupG/H
center, socleC22×C59C2×#120
commutator, Frattini, cosocleC22×C4C24×C59
prime radicalC59×#3487C2
LCSG ▷ C22×C4 ▷ C2 ▷ 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×#2311C2semidirect
4. C59×#2037C2semidirect
5. C59×#1897C2semidirect
6. C59×#1857C2semidirect
7. C59×#1793C2semidirect
8. C59×#1785C2semidirect
221. #24024C59direct (N × H)
250. #3092C2×C59semidirect
251. #2311C2×C59semidirect
252. #2037C2×C59semidirect
253. #1897C2×C59semidirect
254. #1857C2×C59semidirect
255. #1793C2×C59semidirect
256. #1785C2×C59semidirect
293. C59#24024direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#34872
C59×#30922
C59×#23112
C59×#20372
C59×#18972
C59×#18572
C59×#17932
C59×#17852
#2402459