Finite Group Databasebeta

← C59×#60027 #28472136

Subgroups — C59×#60027 #28472136

Order 15104.

1674 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#2787C213yesmaximal, complemented
2C59×#2736C211yesmaximal, characteristic
3C59×#2574C213yesmaximal, complemented
4C59×#2527C213yesmaximal, complemented
5C59×#2515C213yesmaximal, complemented
6C59×#2494C213yesmaximal, complemented
7C59×#2480C213yesmaximal
8C59×#2478C213yesmaximal, complemented
9C59×#2373C213yesmaximal, complemented
10C59×#2342C213yesmaximal
11C59×#2298C213yesmaximal, complemented
12C2×#126×C59C2213yes—
13C2×#117×C59C2213yes—
14C22×C22⋊C4×C59C2213yes—
15C59×#401C2211yescharacteristic, complemented
16C59×#401C2213yescomplemented
17C59×#400C2213yescomplemented
18C59×#398C2213yescomplemented
19C59×#398C2213yescomplemented
20C59×#397C2213yes—
21C59×#397C2213yes—
22C59×#397C2213yes—
23C59×#397C2213yes—
24C59×#396C2213yes—
25C59×#395C2211yescharacteristic, complemented
26C59×#393C2213yes—
27C59×#391C2213yescomplemented
28C59×#389C2213yescomplemented
29C59×#389C2213yescomplemented
30C59×#388C2213yes—
31C59×#388C2213yes—
32C59×#388C2213yes—
33C59×#388C2213yes—
34C59×#388C2213yes—
35C59×#388C2213yes—
36C59×#388C2213yes—
37C59×#388C2213yes—
38C59×#388C2213yes—
39C59×#387C2213yescomplemented
40C59×#387C2213yescomplemented
41C59×#387C2213yescomplemented
42C59×#387C2213yescomplemented
43C59×#387C2213yescomplemented
44C59×#387C2213yescomplemented
45C59×#387C2213yescomplemented
46C59×#387C2213yescomplemented
47C59×#385C2213yes—
48C59×#385C2213yes—
49C59×#385C2213yes—
50C59×#385C2213yes—
51C59×#383C2211yescharacteristic, complemented
52C59×#382C2213yescomplemented
53C59×#381C2213yes—
54C59×#380C2213yes—
55C59×#380C2213yes—
56C59×#379C2213yes—
57C59×#379C2211yescharacteristic
58C4×C4⋊C4×C59C2213yescomplemented
59C4×C4⋊C4×C59C2213yescomplemented
60C4×C4⋊C4×C59C2213yescomplemented
61C4×C22⋊C4×C59C2213yes—
62C4×C22⋊C4×C59C2213yes—
63C4×C22⋊C4×C59C2213yes—
64C4×C22⋊C4×C59C2213yes—
65C59×#376C2213yescomplemented
66C43×C59C2211yescharacteristic, complemented
67C25×C59C2311yescharacteristic
68C22×Q8×C59C2311yescharacteristic
69C23×C4×C59C2313yes—
70C23×C4×C59C2313yes—
71#126×C59—212no—
72#117×C59—212no—
73C2×C4⋊C4×C59C2313yes—
74C2×C4⋊C4×C59C2313yes—
75C2×C4⋊C4×C59C2313yes—
76C2×C4⋊C4×C59C2313yes—
77C2×C4⋊C4×C59C2313yes—
78C2×C4⋊C4×C59C2313yes—
79C2×C4⋊C4×C59C2313yes—
80C2×C4⋊C4×C59C2313yes—
81C2×C4⋊C4×C59C2313yes—
82C2×C4⋊C4×C59C2313yes—
83C2×C4⋊C4×C59C2313yes—
84C2×C22⋊C4×C59—212no—
85C2×C22⋊C4×C59C2313yes—
86C2×C22⋊C4×C59C2313yes—
87C2×C22⋊C4×C59C2313yes—
88C2×C22⋊C4×C59C2313yes—
89C2×C22⋊C4×C59C2313yes—
90C2×C22⋊C4×C59C2313yes—
91C2×C22⋊C4×C59C2313yes—
92C2×C22⋊C4×C59C2313yes—
93C2×C22⋊C4×C59C2313yes—
94C2×C22⋊C4×C59C2313yes—
95C2×C22⋊C4×C59C2313yes—
96C2×C22⋊C4×C59C2313yes—
97C2×C42×C59C2313yes—
98C2×C42×C59C2313yes—
99C2×C42×C59C2313yes—
100C2×C42×C59C2313yes—
101C2×C42×C59C2311yescharacteristic
102C2×C42×C59C2313yes—
103C2×C42×C59C2313yes—
104C2×C42×C59C2311yescharacteristic
105#95×C59C2313yes—
106#95×C59C2313yes—
107#95×C59C2313yes—
108#95×C59C2313yes—
109#95×C59C2313yes—
110#95×C59C2313yes—
111#95×C59C2313yes—
112#95×C59C2313yes—
113#95×C59C2313yes—
114#95×C59C2313yes—
115#95×C59C2313yes—
116#95×C59C2313yes—
117#95×C59C2313yes—
118#95×C59C2313yes—
119#95×C59C2313yes—
120#95×C59C2313yes—
121#95×C59C2313yes—
122#95×C59C2313yes—
123#95×C59C2313yes—
124#95×C59C2311yescharacteristic
125C24×C59—26no—
126C24×C59—43no—
127C24×C59—41no—
128C24×C59C2413yes—
129C2×Q8×C59—43no—
130C22×C4×C59—26no—
131C22×C4×C59—26no—
132C22×C4×C59—26no—
133C22×C4×C59—43no—
134C22×C4×C59—43no—
135C22×C4×C59—43no—
136C22×C4×C59C2413yes—
137C22×C4×C59C2413yes—
138C22×C4×C59C2413yes—
139C22×C4×C59C2413yes—
140C22×C4×C59C2413yes—
141C22×C4×C59C2411yescharacteristic
142C22×C4×C59C2413yes—
143C22×C4×C59C2413yes—
144C22×C4×C59C2413yes—
145C22×C4×C59C2413yes—
146C4⋊C4×C59—26no—
147C4⋊C4×C59—26no—
148C4⋊C4×C59—26no—
149C4⋊C4×C59—26no—
150C4⋊C4×C59—26no—
151C4⋊C4×C59—43no—
152C4⋊C4×C59—43no—
153C4⋊C4×C59—43no—
154C4⋊C4×C59—43no—
155C4⋊C4×C59—43no—
156C4⋊C4×C59—43no—
157C22⋊C4×C59—26no—
158C22⋊C4×C59—26no—
159C22⋊C4×C59—26no—
160C22⋊C4×C59—26no—
161C22⋊C4×C59—26no—
162C22⋊C4×C59—26no—
163C22⋊C4×C59—43no—
164C22⋊C4×C59—43no—
165C22⋊C4×C59—43no—
166C22⋊C4×C59—43no—
167C22⋊C4×C59—43no—
168C22⋊C4×C59#41112yes—
169C42×C59—26no—
170C42×C59—26no—
171C42×C59—26no—
172C42×C59—43no—
173C42×C59—43no—
174C42×C59—43no—
175C42×C59—41no—
176C42×C59—41no—
177C23×C59—23no—
178C23×C59—23no—
179C23×C59—23no—
180C23×C59—23no—
181C23×C59—23no—
182C23×C59—23no—
183C23×C59—412no—
184C23×C59—86no—
185C23×C59—82no—
186C23×C59C2×#4116yes—
187C23×C59C2511yescharacteristic
188Q8×C59—82no—
189C2×C4×C59—23no—
190C2×C4×C59—23no—
191C2×C4×C59—23no—
192C2×C4×C59—23no—
193C2×C4×C59—23no—
194C2×C4×C59—23no—
195C2×C4×C59—23no—
196C2×C4×C59—23no—
197C2×C4×C59—23no—
198C2×C4×C59—23no—
199C2×C4×C59—23no—
200C2×C4×C59—23no—
201C2×C4×C59—23no—
202C2×C4×C59—23no—
203C2×C4×C59—23no—
204C2×C4×C59—23no—
205C2×C4×C59—23no—
206C2×C4×C59—23no—
207C2×C4×C59—23no—
208C2×C4×C59—23no—
209C2×C4×C59—23no—
210C2×C4×C59—23no—
211C2×C4×C59—23no—
212C2×C4×C59—23no—
213C2×C4×C59—23no—
214C2×C4×C59—23no—
215C2×C4×C59—412no—
216C2×C4×C59—86no—
217C2×C4×C59C2×#4116yes—
218C2×C4×C59C2×#4116yes—
219#60027C5911yesmaximal, characteristic, direct product factor, Sylow
220C22×C59—26no—
221C22×C59—26no—
222C22×C59—26no—
223C22×C59—43no—
224C22×C59—43no—
225C22×C59—43no—
226C22×C59—43no—
227C22×C59—88no—
228C22×C59C22×#4113yes—
229C22×C59#58513yes—
230C22×C59#58511yescharacteristic
231C4×C59—26no—
232C4×C59—26no—
233C4×C59—43no—
234C4×C59—43no—
235C4×C59—43no—
236C4×C59—43no—
237C4×C59—43no—
238C4×C59—43no—
239C4×C59—41no—
240C4×C59—43no—
241#2787C2×C5913yescomplemented
242#2736C2×C5911yescharacteristic
243#2574C2×C5913yescomplemented
244#2527C2×C5913yescomplemented
245#2515C2×C5913yescomplemented
246#2494C2×C5913yescomplemented
247#2480C2×C5913yes—
248#2478C2×C5913yescomplemented
249#2373C2×C5913yescomplemented
250#2342C2×C5913yes—
251#2298C2×C5913yescomplemented
252C2×C59—46no—
253C2×C59#347513yes—
254C2×C59#352113yes—
255C2×C59#356811yescharacteristic
256C2×#126C22×C5913yes—
257C2×#117C22×C5913yes—
258C22×C22⋊C4C22×C5913yes—
259#401C22×C5911yescharacteristic, complemented
260#401C22×C5913yescomplemented
261#400C22×C5913yescomplemented
262#398C22×C5913yescomplemented
263#398C22×C5913yescomplemented
264#397C22×C5913yes—
265#397C22×C5913yes—
266#397C22×C5913yes—
267#397C22×C5913yes—
268#396C22×C5913yes—
269#395C22×C5911yescharacteristic, complemented
270#393C22×C5913yes—
271#391C22×C5913yescomplemented
272#389C22×C5913yescomplemented
273#389C22×C5913yescomplemented
274#388C22×C5913yes—
275#388C22×C5913yes—
276#388C22×C5913yes—
277#388C22×C5913yes—
278#388C22×C5913yes—
279#388C22×C5913yes—
280#388C22×C5913yes—
281#388C22×C5913yes—
282#388C22×C5913yes—
283#387C22×C5913yescomplemented
284#387C22×C5913yescomplemented
285#387C22×C5913yescomplemented
286#387C22×C5913yescomplemented
287#387C22×C5913yescomplemented
288#387C22×C5913yescomplemented
289#387C22×C5913yescomplemented
290#387C22×C5913yescomplemented
291#385C22×C5913yes—
292#385C22×C5913yes—
293#385C22×C5913yes—
294#385C22×C5913yes—
295#383C22×C5911yescharacteristic, complemented
296#382C22×C5913yescomplemented
297#381C22×C5913yes—
298#380C22×C5913yes—
299#380C22×C5913yes—
300#379C22×C5913yes—
301#379C22×C5911yescharacteristic
302C4×C4⋊C4C22×C5913yescomplemented
303C4×C4⋊C4C22×C5913yescomplemented
304C4×C4⋊C4C22×C5913yescomplemented
305C4×C22⋊C4C22×C5913yes—
306C4×C22⋊C4C22×C5913yes—
307C4×C22⋊C4C22×C5913yes—
308C4×C22⋊C4C22×C5913yes—
309#376C22×C5913yescomplemented
310C43C22×C5911yescharacteristic, complemented
311C59#6002711yescharacteristic, direct product factor, Sylow
312C25C23×C5911yescharacteristic
313C22×Q8C23×C5911yescharacteristic
314C23×C4C23×C5913yes—
315C23×C4C23×C5913yes—
316#126—212no—
317#117—212no—
318C2×C4⋊C4C23×C5913yes—
319C2×C4⋊C4C23×C5913yes—
320C2×C4⋊C4C23×C5913yes—
321C2×C4⋊C4C23×C5913yes—
322C2×C4⋊C4C23×C5913yes—
323C2×C4⋊C4C23×C5913yes—
324C2×C4⋊C4C23×C5913yes—
325C2×C4⋊C4C23×C5913yes—
326C2×C4⋊C4C23×C5913yes—
327C2×C4⋊C4C23×C5913yes—
328C2×C4⋊C4C23×C5913yes—
329C2×C22⋊C4—212no—
330C2×C22⋊C4C23×C5913yes—
331C2×C22⋊C4C23×C5913yes—
332C2×C22⋊C4C23×C5913yes—
333C2×C22⋊C4C23×C5913yes—
334C2×C22⋊C4C23×C5913yes—
335C2×C22⋊C4C23×C5913yes—
336C2×C22⋊C4C23×C5913yes—
337C2×C22⋊C4C23×C5913yes—
338C2×C22⋊C4C23×C5913yes—
339C2×C22⋊C4C23×C5913yes—
340C2×C22⋊C4C23×C5913yes—
341C2×C22⋊C4C23×C5913yes—
342C2×C42C23×C5913yes—
343C2×C42C23×C5913yes—
344C2×C42C23×C5913yes—
345C2×C42C23×C5913yes—
346C2×C42C23×C5911yescharacteristic
347C2×C42C23×C5913yes—
348C2×C42C23×C5913yes—
349C2×C42C23×C5911yescharacteristic
350#95C23×C5913yes—
351#95C23×C5913yes—
352#95C23×C5913yes—
353#95C23×C5913yes—
354#95C23×C5913yes—
355#95C23×C5913yes—
356#95C23×C5913yes—
357#95C23×C5913yes—
358#95C23×C5913yes—
359#95C23×C5913yes—
360#95C23×C5913yes—
361#95C23×C5913yes—
362#95C23×C5913yes—
363#95C23×C5913yes—
364#95C23×C5913yes—
365#95C23×C5913yes—
366#95C23×C5913yes—
367#95C23×C5913yes—
368#95C23×C5913yes—
369#95C23×C5911yescharacteristic
370C24—26no—
371C24—43no—
372C24—41no—
373C24C24×C5913yes—
374C2×Q8—43no—
375C22×C4—26no—
376C22×C4—26no—
377C22×C4—26no—
378C22×C4—43no—
379C22×C4—43no—
380C22×C4—43no—
381C22×C4C24×C5913yes—
382C22×C4C24×C5913yes—
383C22×C4C24×C5913yes—
384C22×C4C24×C5913yes—
385C22×C4C24×C5913yes—
386C22×C4C24×C5911yescharacteristic
387C22×C4C24×C5913yes—
388C22×C4C24×C5913yes—
389C22×C4C24×C5913yes—
390C22×C4C24×C5913yes—
391C4⋊C4—26no—
392C4⋊C4—26no—
393C4⋊C4—26no—
394C4⋊C4—26no—
395C4⋊C4—26no—
396C4⋊C4—43no—
397C4⋊C4—43no—
398C4⋊C4—43no—
399C4⋊C4—43no—
400C4⋊C4—43no—
401C4⋊C4—43no—
402C22⋊C4—26no—
403C22⋊C4—26no—
404C22⋊C4—26no—
405C22⋊C4—26no—
406C22⋊C4—26no—
407C22⋊C4—26no—
408C22⋊C4—43no—
409C22⋊C4—43no—
410C22⋊C4—43no—
411C22⋊C4—43no—
412C22⋊C4—43no—
413C22⋊C4#41×C59112yes—
414C42—26no—
415C42—26no—
416C42—26no—
417C42—43no—
418C42—43no—
419C42—43no—
420C42—41no—
421C42—41no—
422C23—23no—
423C23—23no—
424C23—23no—
425C23—23no—
426C23—23no—
427C23—23no—
428C23—412no—
429C23—86no—
430C23—82no—
431C23C2×#41×C5916yes—
432C23C25×C5911yescharacteristic
433Q8—82no—
434C2×C4—23no—
435C2×C4—23no—
436C2×C4—23no—
437C2×C4—23no—
438C2×C4—23no—
439C2×C4—23no—
440C2×C4—23no—
441C2×C4—23no—
442C2×C4—23no—
443C2×C4—23no—
444C2×C4—23no—
445C2×C4—23no—
446C2×C4—23no—
447C2×C4—23no—
448C2×C4—23no—
449C2×C4—23no—
450C2×C4—23no—
451C2×C4—23no—
452C2×C4—23no—
453C2×C4—23no—
454C2×C4—23no—
455C2×C4—23no—
456C2×C4—23no—
457C2×C4—23no—
458C2×C4—23no—
459C2×C4—23no—
460C2×C4—412no—
461C2×C4—86no—
462C2×C4C2×#41×C5916yes—
463C2×C4C2×#41×C5916yes—
464C22—26no—
465C22—26no—
466C22—26no—
467C22—43no—
468C22—43no—
469C22—43no—
470C22—43no—
471C22—88no—
472C22C22×#41×C5913yes—
473C22C59×#58511yescharacteristic
474C22C59×#58513yes—
475C4—26no—
476C4—26no—
477C4—43no—
478C4—43no—
479C4—43no—
480C4—43no—
481C4—41no—
482C4—43no—
483C4—43no—
484C4—43no—
485C2—46no—
486C2C59×#347513yes—
487C2C59×#352113yes—
488C2C59×#356811yescharacteristic
subgroupG/H
center, socleC23×C59C25
commutator, Frattini, cosocleC23C25×C59
prime radicalC25×C59C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C59 ◁ G

Complements

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

NH ≅ G/Ntype
1. C59×#2787C2semidirect
3. C59×#2574C2semidirect
4. C59×#2527C2semidirect
5. C59×#2515C2semidirect
6. C59×#2494C2semidirect
8. C59×#2478C2semidirect
9. C59×#2373C2semidirect
11. C59×#2298C2semidirect
15. C59×#401C22semidirect
16. C59×#401C22semidirect
17. C59×#400C22semidirect
18. C59×#398C22semidirect
19. C59×#398C22semidirect
25. C59×#395C22semidirect
27. C59×#391C22semidirect
28. C59×#389C22semidirect
29. C59×#389C22semidirect
39. C59×#387C22semidirect
40. C59×#387C22semidirect
41. C59×#387C22semidirect
42. C59×#387C22semidirect
43. C59×#387C22semidirect
44. C59×#387C22semidirect
45. C59×#387C22semidirect
46. C59×#387C22semidirect
51. C59×#383C22semidirect
52. C59×#382C22semidirect
58. C4×C4⋊C4×C59C22semidirect
59. C4×C4⋊C4×C59C22semidirect
60. C4×C4⋊C4×C59C22semidirect
65. C59×#376C22semidirect
66. C43×C59C22semidirect
219. #60027C59direct (N × H)
241. #2787C2×C59semidirect
243. #2574C2×C59semidirect
244. #2527C2×C59semidirect
245. #2515C2×C59semidirect
246. #2494C2×C59semidirect
248. #2478C2×C59semidirect
249. #2373C2×C59semidirect
251. #2298C2×C59semidirect
259. #401C22×C59semidirect
260. #401C22×C59semidirect
261. #400C22×C59semidirect
262. #398C22×C59semidirect
263. #398C22×C59semidirect
269. #395C22×C59semidirect
271. #391C22×C59semidirect
272. #389C22×C59semidirect
273. #389C22×C59semidirect
283. #387C22×C59semidirect
284. #387C22×C59semidirect
285. #387C22×C59semidirect
286. #387C22×C59semidirect
287. #387C22×C59semidirect
288. #387C22×C59semidirect
289. #387C22×C59semidirect
290. #387C22×C59semidirect
295. #383C22×C59semidirect
296. #382C22×C59semidirect
302. C4×C4⋊C4C22×C59semidirect
303. C4×C4⋊C4C22×C59semidirect
304. C4×C4⋊C4C22×C59semidirect
309. #376C22×C59semidirect
310. C43C22×C59semidirect
311. C59#60027direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#27872
C59×#27362
C59×#25742
C59×#25272
C59×#25152
C59×#24942
C59×#24802
C59×#24782
C59×#23732
C59×#23422
C59×#22982
#6002759