Finite Group Databasebeta

← C59×#18333 #28430442

Subgroups — C59×#18333 #28430442

Order 15104.

950 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×#3458C211yesmaximal, characteristic, complemented
2C59×#3215C212yesmaximal, complemented
3C59×#2610C211yesmaximal, characteristic
4C59×#1605C212yesmaximal, complemented
5C59×#1602C212yesmaximal, complemented
6C59×#1599C212yesmaximal, complemented
7C59×#1596C212yesmaximal
8C59×#1506C212yesmaximal, complemented
9C59×#1464C211yesmaximal, characteristic, complemented
10C59×#544—22no—
11C59×#544—22no—
12C59×#544—21no—
13C59×#544C2212yes—
14C59×#543—21no—
15C59×#543C2212yes—
16C59×#533—24no—
17C59×#533—21no—
18C59×#533C2212yes—
19C2×#124×C59C2211yescharacteristic
20C2×#117×C59—21no—
21C2×#117×C59C2211yescharacteristic
22C59×#497—22no—
23C59×#489—22no—
24C59×#464—24no—
25C59×#451C2214yes—
26C59×#450C2214yes—
27C59×#432C2212yes—
28C59×#395C2211yescharacteristic
29C59×#394C2211yescharacteristic
30C59×#393C2211yescharacteristic
31C59×#392C2211yescharacteristic
32C59×#390—21no—
33C59×#388—21no—
34C59×#388—21no—
35C59×#386—21no—
36C59×#376C2211yescharacteristic
37C59×#328C2214yes—
38C59×#328C2214yes—
39C59×#324C2212yes—
40C59×#323C2212yes—
41C22×Q8×C59C2311yescharacteristic
42C22×D4×C59—21no—
43C22×D4×C59C2311yescharacteristic
44C23×C4×C59D411yescharacteristic
45C2×Q16×C59—24no—
46C2×SD16×C59—24no—
47C4⋊Q8×C59—24no—
48C4⋊Q8×C59—21no—
49C4⋊Q8×C59—21no—
50C4⋊Q8×C59—24no—
51C4⋊Q8×C59D412yescomplemented
52C4⋊Q8×C59D412yescomplemented
53#125×C59—24no—
54#125×C59—22no—
55#125×C59—24no—
56#125×C59—22no—
57#124×C59—22no—
58#124×C59—22no—
59C22⋊Q8×C59—24no—
60C22⋊Q8×C59—24no—
61C22⋊Q8×C59—24no—
62C22⋊Q8×C59—22no—
63C22⋊Q8×C59—22no—
64C22⋊Q8×C59—22no—
65C22⋊Q8×C59—24no—
66C22⋊Q8×C59C2314yes—
67C4×Q8×C59—22no—
68C4×Q8×C59—22no—
69C4×Q8×C59—22no—
70C4×Q8×C59D414yescomplemented
71#117×C59—22no—
72#117×C59—22no—
73#117×C59—22no—
74#117×C59—22no—
75#117×C59—22no—
76#117×C59—22no—
77C2×C4⋊C4×C59—21no—
78C2×C4⋊C4×C59—21no—
79C2×C4⋊C4×C59—21no—
80C2×C4⋊C4×C59D411yescharacteristic
81C2×C4⋊C4×C59C2311yescharacteristic
82C2×C22⋊C4×C59—22no—
83C2×C22⋊C4×C59—21no—
84C2×C22⋊C4×C59—21no—
85C2×C22⋊C4×C59—21no—
86C2×C22⋊C4×C59—21no—
87C2×C22⋊C4×C59—21no—
88C2×C22⋊C4×C59—21no—
89C2×C22⋊C4×C59D411yescharacteristic
90C2×C22⋊C4×C59C2311yescharacteristic
91C2×C42×C59—22no—
92C2×C42×C59—21no—
93C2×C42×C59D411yescharacteristic
94C2×C42×C59C2311yescharacteristic
95C4⋊C8×C59—22no—
96#103×C59—24no—
97#102×C59—24no—
98C22⋊C8×C59C2314yes—
99#97×C59—22no—
100#95×C59—21no—
101#95×C59—21no—
102#95×C59—21no—
103#95×C59C2311yescharacteristic
104#95×C59C2311yescharacteristic
105C24×C59—21no—
106C24×C59C2×D411yescharacteristic
107C2×Q8×C59—22no—
108C2×Q8×C59—22no—
109C2×Q8×C59—22no—
110C2×Q8×C59—22no—
111C2×Q8×C59—81no—
112C2×Q8×C59C2×D414yes—
113C2×D4×C59—22no—
114C2×D4×C59—42no—
115C2×D4×C59—42no—
116C2×D4×C59—81no—
117C2×D4×C59—81no—
118C22×C4×C59—22no—
119C22×C4×C59—21no—
120C22×C4×C59—21no—
121C22×C4×C59—22no—
122C22×C4×C59—21no—
123C22×C4×C59—22no—
124C22×C4×C59—22no—
125C22×C4×C59—21no—
126C22×C4×C59—21no—
127C22×C4×C59C2×D411yescharacteristic
128C22×C4×C59C2×D411yescharacteristic
129C22×C4×C59C2×D411yescharacteristic
130C22×C4×C59C2×D411yescharacteristic
131C22×C4×C59C2×D411yescharacteristic
132C22×C4×C59C2411yescharacteristic
133Q16×C59—84no—
134SD16×C59—84no—
135C2×C8×C59—24no—
136C4⋊C4×C59—22no—
137C4⋊C4×C59—22no—
138C4⋊C4×C59—22no—
139C4⋊C4×C59—24no—
140C4⋊C4×C59—24no—
141C4⋊C4×C59—22no—
142C4⋊C4×C59—22no—
143C4⋊C4×C59—22no—
144C4⋊C4×C59—22no—
145C4⋊C4×C59—22no—
146C4⋊C4×C59—24no—
147C4⋊C4×C59—22no—
148C4⋊C4×C59—24no—
149C4⋊C4×C59—81no—
150C4⋊C4×C59C2×D414yes—
151C22⋊C4×C59—24no—
152C22⋊C4×C59—24no—
153C22⋊C4×C59—22no—
154C22⋊C4×C59—22no—
155C22⋊C4×C59—42no—
156C22⋊C4×C59—41no—
157C22⋊C4×C59—41no—
158C22⋊C4×C59—42no—
159C22⋊C4×C59—42no—
160C22⋊C4×C59—81no—
161C22⋊C4×C59—81no—
162C42×C59—24no—
163C42×C59—24no—
164C42×C59—21no—
165C42×C59—21no—
166C42×C59—42no—
167C42×C59C2×D412yes—
168C42×C59C2×D412yes—
169C23×C59—21no—
170C23×C59—21no—
171C23×C59—41no—
172C23×C59—41no—
173C23×C59—41no—
174C23×C59—41no—
175C23×C59—41no—
176C23×C59—41no—
177C23×C59—41no—
178C23×C59—41no—
179C23×C59—41no—
180C23×C59#13712yes—
181C23×C59C22×D411yescharacteristic
182Q8×C59—44no—
183Q8×C59—44no—
184Q8×C59—82no—
185Q8×C59—82no—
186Q8×C59—82no—
187D4×C59—44no—
188D4×C59—84no—
189C2×C4×C59—24no—
190C2×C4×C59—24no—
191C2×C4×C59—21no—
192C2×C4×C59—21no—
193C2×C4×C59—21no—
194C2×C4×C59—21no—
195C2×C4×C59—22no—
196C2×C4×C59—24no—
197C2×C4×C59—21no—
198C2×C4×C59—21no—
199C2×C4×C59—24no—
200C2×C4×C59—41no—
201C2×C4×C59—41no—
202C2×C4×C59—41no—
203C2×C4×C59—41no—
204C2×C4×C59—41no—
205C2×C4×C59—41no—
206C2×C4×C59—41no—
207C2×C4×C59—41no—
208C2×C4×C59—41no—
209C2×C4×C59—41no—
210C2×C4×C59—41no—
211C2×C4×C59—41no—
212C2×C4×C59—82no—
213C2×C4×C59—82no—
214C2×C4×C59#12011yescharacteristic
215C2×C4×C59#12011yescharacteristic
216C2×C4×C59#12012yes—
217C2×C4×C59#13712yes—
218C2×C4×C59C22×D412yes—
219C8×C59—44no—
220#18333C5911yesmaximal, characteristic, direct product factor, Sylow
221C22×C59—21no—
222C22×C59—21no—
223C22×C59—22no—
224C22×C59—42no—
225C22×C59—41no—
226C22×C59—41no—
227C22×C59—81no—
228C22×C59—81no—
229C22×C59—81no—
230C22×C59—81no—
231C22×C59—81no—
232C22×C59—81no—
233C22×C59—81no—
234C22×C59—81no—
235C22×C59C2×#12011yescharacteristic
236C22×C59C2×#13711yescharacteristic
237C22×C59C2×#13711yescharacteristic
238C4×C59—21no—
239C4×C59—21no—
240C4×C59—22no—
241C4×C59—22no—
242C4×C59—22no—
243C4×C59—42no—
244C4×C59—41no—
245C4×C59—44no—
246C4×C59—41no—
247C4×C59—44no—
248C4×C59—81no—
249C4×C59—81no—
250#3458C2×C5911yescharacteristic, complemented
251#3215C2×C5912yescomplemented
252#2610C2×C5911yescharacteristic
253#1605C2×C5912yescomplemented
254#1602C2×C5912yescomplemented
255#1599C2×C5912yescomplemented
256#1596C2×C5912yes—
257#1506C2×C5912yescomplemented
258#1464C2×C5911yescharacteristic, complemented
259C2×C59—21no—
260C2×C59—21no—
261C2×C59—42no—
262C2×C59—161no—
263C2×C59#300411yescharacteristic
264C2×C59#301811yescharacteristic
265C2×C59#302711yescharacteristic
266#544—22no—
267#544—22no—
268#544—21no—
269#544C22×C5912yes—
270#543—21no—
271#543C22×C5912yes—
272#533—24no—
273#533—21no—
274#533C22×C5912yes—
275C2×#124C22×C5911yescharacteristic
276C2×#117—21no—
277C2×#117C22×C5911yescharacteristic
278#497—22no—
279#489—22no—
280#464—24no—
281#451C22×C5914yes—
282#450C22×C5914yes—
283#432C22×C5912yes—
284#395C22×C5911yescharacteristic
285#394C22×C5911yescharacteristic
286#393C22×C5911yescharacteristic
287#392C22×C5911yescharacteristic
288#390—21no—
289#388—21no—
290#388—21no—
291#386—21no—
292#376C22×C5911yescharacteristic
293#328C22×C5914yes—
294#328C22×C5914yes—
295#324C22×C5912yes—
296#323C22×C5912yes—
297C59#1833311yescharacteristic, direct product factor, Sylow
298C22×Q8C23×C5911yescharacteristic
299C22×D4—21no—
300C22×D4C23×C5911yescharacteristic
301C23×C4D4×C5911yescharacteristic
302C2×Q16—24no—
303C2×SD16—24no—
304C4⋊Q8—24no—
305C4⋊Q8—21no—
306C4⋊Q8—21no—
307C4⋊Q8—24no—
308C4⋊Q8D4×C5912yescomplemented
309C4⋊Q8D4×C5912yescomplemented
310#125—24no—
311#125—22no—
312#125—24no—
313#125—22no—
314#124—22no—
315#124—22no—
316C22⋊Q8—24no—
317C22⋊Q8—24no—
318C22⋊Q8—24no—
319C22⋊Q8—22no—
320C22⋊Q8—22no—
321C22⋊Q8—22no—
322C22⋊Q8—24no—
323C22⋊Q8C23×C5914yes—
324C4×Q8—22no—
325C4×Q8—22no—
326C4×Q8—22no—
327C4×Q8D4×C5914yescomplemented
328#117—22no—
329#117—22no—
330#117—22no—
331#117—22no—
332#117—22no—
333#117—22no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4D4×C5911yescharacteristic
338C2×C4⋊C4C23×C5911yescharacteristic
339C2×C22⋊C4—22no—
340C2×C22⋊C4—21no—
341C2×C22⋊C4—21no—
342C2×C22⋊C4—21no—
343C2×C22⋊C4—21no—
344C2×C22⋊C4—21no—
345C2×C22⋊C4—21no—
346C2×C22⋊C4D4×C5911yescharacteristic
347C2×C22⋊C4C23×C5911yescharacteristic
348C2×C42—22no—
349C2×C42—21no—
350C2×C42D4×C5911yescharacteristic
351C2×C42C23×C5911yescharacteristic
352C4⋊C8—22no—
353#103—24no—
354#102—24no—
355C22⋊C8C23×C5914yes—
356#97—22no—
357#95—21no—
358#95—21no—
359#95—21no—
360#95C23×C5911yescharacteristic
361#95C23×C5911yescharacteristic
362C24—21no—
363C24C2×D4×C5911yescharacteristic
364C2×Q8—22no—
365C2×Q8—22no—
366C2×Q8—22no—
367C2×Q8—22no—
368C2×Q8—81no—
369C2×Q8C2×D4×C5914yes—
370C2×D4—22no—
371C2×D4—42no—
372C2×D4—42no—
373C2×D4—81no—
374C2×D4—81no—
375C22×C4—22no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—22no—
379C22×C4—21no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4C2×D4×C5911yescharacteristic
385C22×C4C2×D4×C5911yescharacteristic
386C22×C4C2×D4×C5911yescharacteristic
387C22×C4C2×D4×C5911yescharacteristic
388C22×C4C2×D4×C5911yescharacteristic
389C22×C4C24×C5911yescharacteristic
390Q16—84no—
391SD16—84no—
392C2×C8—24no—
393C4⋊C4—22no—
394C4⋊C4—22no—
395C4⋊C4—22no—
396C4⋊C4—24no—
397C4⋊C4—24no—
398C4⋊C4—22no—
399C4⋊C4—22no—
400C4⋊C4—22no—
401C4⋊C4—22no—
402C4⋊C4—22no—
403C4⋊C4—24no—
404C4⋊C4—22no—
405C4⋊C4—24no—
406C4⋊C4—81no—
407C4⋊C4C2×D4×C5914yes—
408C22⋊C4—24no—
409C22⋊C4—24no—
410C22⋊C4—22no—
411C22⋊C4—22no—
412C22⋊C4—42no—
413C22⋊C4—41no—
414C22⋊C4—41no—
415C22⋊C4—42no—
416C22⋊C4—42no—
417C22⋊C4—81no—
418C22⋊C4—81no—
419C42—24no—
420C42—24no—
421C42—21no—
422C42—21no—
423C42—42no—
424C42C2×D4×C5912yes—
425C42C2×D4×C5912yes—
426C23—21no—
427C23—21no—
428C23—41no—
429C23—41no—
430C23—41no—
431C23—41no—
432C23—41no—
433C23—41no—
434C23—41no—
435C23—41no—
436C23—41no—
437C23#137×C5912yes—
438C23C22×D4×C5911yescharacteristic
439Q8—44no—
440Q8—44no—
441Q8—82no—
442Q8—82no—
443Q8—82no—
444D4—44no—
445D4—84no—
446C2×C4—24no—
447C2×C4—24no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—22no—
453C2×C4—24no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—24no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—82no—
470C2×C4—82no—
471C2×C4#120×C5911yescharacteristic
472C2×C4#120×C5911yescharacteristic
473C2×C4#120×C5912yes—
474C2×C4#137×C5912yes—
475C2×C4C22×D4×C5912yes—
476C8—44no—
477C22—21no—
478C22—21no—
479C22—22no—
480C22—42no—
481C22—41no—
482C22—41no—
483C22—81no—
484C22—81no—
485C22—81no—
486C22—81no—
487C22—81no—
488C22—81no—
489C22—81no—
490C22—81no—
491C22C2×#120×C5911yescharacteristic
492C22C2×#137×C5911yescharacteristic
493C22C2×#137×C5911yescharacteristic
494C4—21no—
495C4—21no—
496C4—22no—
497C4—22no—
498C4—22no—
499C4—42no—
500C4—41no—
501C4—44no—
502C4—41no—
503C4—44no—
504C4—81no—
505C4—81no—
506C2—21no—
507C2—21no—
508C2—42no—
509C2—161no—
510C2C59×#300411yescharacteristic
511C2C59×#301811yescharacteristic
512C2C59×#302711yescharacteristic
subgroupG/H
center, socleC22×C59C2×#120
commutator, Frattini, cosocleC22×C4C24×C59
prime radicalC59×#392C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C59 ◁ C2×C42×C59 ◁ G

Complements

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

NH ≅ G/Ntype
1. C59×#3458C2semidirect
2. C59×#3215C2semidirect
4. C59×#1605C2semidirect
5. C59×#1602C2semidirect
6. C59×#1599C2semidirect
8. C59×#1506C2semidirect
9. C59×#1464C2semidirect
51. C4⋊Q8×C59D4semidirect
52. C4⋊Q8×C59D4semidirect
70. C4×Q8×C59D4semidirect
220. #18333C59direct (N × H)
250. #3458C2×C59semidirect
251. #3215C2×C59semidirect
253. #1605C2×C59semidirect
254. #1602C2×C59semidirect
255. #1599C2×C59semidirect
257. #1506C2×C59semidirect
258. #1464C2×C59semidirect
297. C59#18333direct (N × H)
308. C4⋊Q8D4×C59semidirect
309. C4⋊Q8D4×C59semidirect
327. C4×Q8D4×C59semidirect

Maximal subgroups

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

subgroupindex
C59×#34582
C59×#32152
C59×#26102
C59×#16052
C59×#16022
C59×#15992
C59×#15962
C59×#15062
C59×#14642
#1833359