Finite Group Databasebeta

← C59×#35438 #28447547

Subgroups — C59×#35438 #28447547

Order 15104.

2392 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#2607C213yesmaximal, complemented
2C59×#2557C216yesmaximal, complemented
3C59×#2539C213yesmaximal, complemented
4C59×#2471C216yesmaximal, complemented
5C59×#2431C213yesmaximal, complemented
6C59×#2404C213yesmaximal, complemented
7C59×#2333C213yesmaximal, complemented
8C59×#2297C213yesmaximal, complemented
9C59×#2273C211yesmaximal, characteristic, complemented
10C22×#41×C59C2213yes—
11C2×#127×C59C2211yescharacteristic, complemented
12C2×#124×C59C2213yescomplemented
13C2×#123×C59C2216yes—
14C2×#121×C59C2213yes—
15C2×#120×C59C2213yes—
16C2×#120×C59C2211yescharacteristic
17C2×#117×C59C2213yescomplemented
18C22×C22⋊C4×C59C2213yes—
19C22×C42×C59C2211yescharacteristic, complemented
20C59×#399C2216yes—
21C59×#397C2216yescomplemented
22C59×#396C2212yescomplemented
23C59×#393C2216yes—
24C59×#392C2216yes—
25C59×#392C2216yes—
26C59×#391C2216yescomplemented
27C59×#391C2213yescomplemented
28C59×#390C2216yes—
29C59×#390C2216yes—
30C59×#390C2213yescomplemented
31C59×#388C2216yescomplemented
32C59×#387C2216yescomplemented
33C59×#387C2216yescomplemented
34C59×#386C2216yes—
35C59×#386C2213yes—
36C59×#386C2216yes—
37C59×#386C2213yes—
38C59×#386C2216yescomplemented
39C59×#386C2216yescomplemented
40C59×#381C2213yes—
41C4×C22⋊C4×C59C2213yes—
42C4×C22⋊C4×C59C2216yes—
43C4×C22⋊C4×C59C2213yes—
44C4×C22⋊C4×C59C2213yes—
45C4×C22⋊C4×C59C2213yescomplemented
46C4×C22⋊C4×C59C2213yescomplemented
47C25×C59C2311yescharacteristic
48C2×#41×C59—212no—
49C2×#41×C59—46no—
50C2×#41×C59—46no—
51C22×Q8×C59C2313yes—
52C22×D4×C59C2313yes—
53C22×D4×C59C2313yes—
54C22×D4×C59C2313yes—
55C22×D4×C59C2316yes—
56C22×D4×C59C2313yes—
57C23×C4×C59C2313yes—
58C23×C4×C59C2313yes—
59C23×C4×C59C2313yes—
60C23×C4×C59C2313yes—
61#127×C59—42no—
62#124×C59—46no—
63#123×C59—412no—
64#121×C59—212no—
65#120×C59—46no—
66#120×C59—42no—
67#117×C59—46no—
68C2×C4⋊C4×C59C2313yes—
69C2×C4⋊C4×C59C2316yes—
70C2×C4⋊C4×C59C2316yes—
71C2×C22⋊C4×C59—212no—
72C2×C22⋊C4×C59C2316yes—
73C2×C22⋊C4×C59C2316yes—
74C2×C22⋊C4×C59C2316yes—
75C2×C22⋊C4×C59C2316yes—
76C2×C22⋊C4×C59C2316yes—
77C2×C22⋊C4×C59C2313yes—
78C2×C22⋊C4×C59C2313yes—
79C2×C22⋊C4×C59C2316yes—
80C2×C22⋊C4×C59C2316yes—
81C2×C22⋊C4×C59C2316yes—
82C2×C42×C59—42no—
83C2×C42×C59C2311yescharacteristic
84C2×C42×C59C2313yes—
85C2×C42×C59C2313yes—
86C2×C42×C59C2311yescharacteristic
87C2×C42×C59C2313yes—
88C2×C42×C59C2313yes—
89#95×C59C2316yes—
90#95×C59C2312yes—
91#95×C59C2316yes—
92#95×C59C2316yes—
93#95×C59C2316yes—
94#95×C59C2316yes—
95#95×C59C2316yes—
96C24×C59—26no—
97C24×C59—43no—
98C24×C59—41no—
99C24×C59C2413yes—
100C24×C59C2413yes—
101C24×C59C2411yescharacteristic
102#41×C59—448no—
103C2×Q8×C59—26no—
104C2×Q8×C59—26no—
105C2×Q8×C59—43no—
106C2×D4×C59—26no—
107C2×D4×C59—26no—
108C2×D4×C59—26no—
109C2×D4×C59—26no—
110C2×D4×C59—212no—
111C2×D4×C59—26no—
112C2×D4×C59—26no—
113C2×D4×C59—26no—
114C2×D4×C59—43no—
115C2×D4×C59—43no—
116C2×D4×C59—43no—
117C2×D4×C59—46no—
118C2×D4×C59—46no—
119C2×D4×C59—43no—
120C2×D4×C59—43no—
121C22×C4×C59—26no—
122C22×C4×C59—26no—
123C22×C4×C59—26no—
124C22×C4×C59—26no—
125C22×C4×C59—26no—
126C22×C4×C59—43no—
127C22×C4×C59—43no—
128C22×C4×C59—43no—
129C22×C4×C59—43no—
130C22×C4×C59—46no—
131C22×C4×C59#41112yescomplemented
132C22×C4×C59C2413yes—
133C22×C4×C59C2416yes—
134C22×C4×C59C2416yes—
135C22×C4×C59C2413yes—
136C22×C4×C59C2413yes—
137C22×C4×C59C2413yes—
138C4⋊C4×C59—26no—
139C4⋊C4×C59—212no—
140C4⋊C4×C59—46no—
141C22⋊C4×C59—212no—
142C22⋊C4×C59—212no—
143C22⋊C4×C59—212no—
144C22⋊C4×C59—212no—
145C22⋊C4×C59—212no—
146C22⋊C4×C59—46no—
147C22⋊C4×C59—43no—
148C22⋊C4×C59—43no—
149C22⋊C4×C59—46no—
150C22⋊C4×C59—46no—
151C42×C59—41no—
152C42×C59—43no—
153C42×C59—43no—
154C42×C59—43no—
155C42×C59—43no—
156C42×C59—41no—
157C23×C59—28no—
158C23×C59—26no—
159C23×C59—23no—
160C23×C59—26no—
161C23×C59—23no—
162C23×C59—23no—
163C23×C59—23no—
164C23×C59—26no—
165C23×C59—23no—
166C23×C59—26no—
167C23×C59—23no—
168C23×C59—23no—
169C23×C59—86no—
170C23×C59—86no—
171C23×C59C2×#4116yes—
172C23×C59H(5,𝔽2)12yes—
173C23×C59C2511yescharacteristic
174Q8×C59—412no—
175D4×C59—412no—
176D4×C59—412no—
177D4×C59—412no—
178D4×C59—86no—
179D4×C59—812no—
180C2×C4×C59—224no—
181C2×C4×C59—23no—
182C2×C4×C59—23no—
183C2×C4×C59—23no—
184C2×C4×C59—23no—
185C2×C4×C59—23no—
186C2×C4×C59—23no—
187C2×C4×C59—26no—
188C2×C4×C59—26no—
189C2×C4×C59—23no—
190C2×C4×C59—26no—
191C2×C4×C59—26no—
192C2×C4×C59—26no—
193C2×C4×C59—26no—
194C2×C4×C59—23no—
195C2×C4×C59—23no—
196C2×C4×C59—412no—
197C2×C4×C59—412no—
198C2×C4×C59—86no—
199C2×C4×C59C2×#4116yes—
200C2×C4×C59C2×#4116yes—
201C2×C4×C59H(5,𝔽2)16yes—
202#35438C5911yesmaximal, characteristic, direct product factor, Sylow
203C22×C59—26no—
204C22×C59—26no—
205C22×C59—26no—
206C22×C59—26no—
207C22×C59—41no—
208C22×C59—46no—
209C22×C59—43no—
210C22×C59—46no—
211C22×C59—43no—
212C22×C59—43no—
213C22×C59—46no—
214C22×C59—46no—
215C22×C59—43no—
216C22×C59—88no—
217C22×C59C22×#4113yes—
218C22×C59C2×H(5,𝔽2)11yescharacteristic
219C22×C59C2×H(5,𝔽2)13yes—
220C4×C59—26no—
221C4×C59—26no—
222C4×C59—26no—
223C4×C59—43no—
224C4×C59—46no—
225C4×C59—46no—
226#2607C2×C5913yescomplemented
227#2557C2×C5916yescomplemented
228#2539C2×C5913yescomplemented
229#2471C2×C5916yescomplemented
230#2431C2×C5913yescomplemented
231#2404C2×C5913yescomplemented
232#2333C2×C5913yescomplemented
233#2297C2×C5913yescomplemented
234#2273C2×C5911yescharacteristic, complemented
235C2×C59—42no—
236C2×C59—46no—
237C2×C59—83no—
238C2×C59#344411yescharacteristic
239C2×C59#349013yes—
240C2×C59#350813yes—
241C22×#41C22×C5913yes—
242C2×#127C22×C5911yescharacteristic, complemented
243C2×#124C22×C5913yescomplemented
244C2×#123C22×C5916yes—
245C2×#121C22×C5913yes—
246C2×#120C22×C5911yescharacteristic
247C2×#120C22×C5913yes—
248C2×#117C22×C5913yescomplemented
249C22×C22⋊C4C22×C5913yes—
250C22×C42C22×C5911yescharacteristic, complemented
251#399C22×C5916yes—
252#397C22×C5916yescomplemented
253#396C22×C5912yescomplemented
254#393C22×C5916yes—
255#392C22×C5916yes—
256#392C22×C5916yes—
257#391C22×C5913yescomplemented
258#391C22×C5916yescomplemented
259#390C22×C5916yes—
260#390C22×C5916yes—
261#390C22×C5913yescomplemented
262#388C22×C5916yescomplemented
263#387C22×C5916yescomplemented
264#387C22×C5916yescomplemented
265#386C22×C5916yes—
266#386C22×C5913yes—
267#386C22×C5916yes—
268#386C22×C5913yes—
269#386C22×C5916yescomplemented
270#386C22×C5916yescomplemented
271#381C22×C5913yes—
272C4×C22⋊C4C22×C5913yes—
273C4×C22⋊C4C22×C5913yes—
274C4×C22⋊C4C22×C5913yes—
275C4×C22⋊C4C22×C5916yes—
276C4×C22⋊C4C22×C5913yescomplemented
277C4×C22⋊C4C22×C5913yescomplemented
278C59#3543811yescharacteristic, direct product factor, Sylow
279C25C23×C5911yescharacteristic
280C2×#41—212no—
281C2×#41—46no—
282C2×#41—46no—
283C22×Q8C23×C5913yes—
284C22×D4C23×C5913yes—
285C22×D4C23×C5913yes—
286C22×D4C23×C5913yes—
287C22×D4C23×C5916yes—
288C22×D4C23×C5913yes—
289C23×C4C23×C5913yes—
290C23×C4C23×C5913yes—
291C23×C4C23×C5913yes—
292C23×C4C23×C5913yes—
293#127—42no—
294#124—46no—
295#123—412no—
296#121—212no—
297#120—46no—
298#120—42no—
299#117—46no—
300C2×C4⋊C4C23×C5916yes—
301C2×C4⋊C4C23×C5913yes—
302C2×C4⋊C4C23×C5916yes—
303C2×C22⋊C4—212no—
304C2×C22⋊C4C23×C5916yes—
305C2×C22⋊C4C23×C5916yes—
306C2×C22⋊C4C23×C5916yes—
307C2×C22⋊C4C23×C5916yes—
308C2×C22⋊C4C23×C5916yes—
309C2×C22⋊C4C23×C5916yes—
310C2×C22⋊C4C23×C5913yes—
311C2×C22⋊C4C23×C5913yes—
312C2×C22⋊C4C23×C5916yes—
313C2×C22⋊C4C23×C5916yes—
314C2×C42—42no—
315C2×C42C23×C5913yes—
316C2×C42C23×C5913yes—
317C2×C42C23×C5913yes—
318C2×C42C23×C5911yescharacteristic
319C2×C42C23×C5911yescharacteristic
320C2×C42C23×C5913yes—
321#95C23×C5916yes—
322#95C23×C5912yes—
323#95C23×C5916yes—
324#95C23×C5916yes—
325#95C23×C5916yes—
326#95C23×C5916yes—
327#95C23×C5916yes—
328C24—26no—
329C24—43no—
330C24—41no—
331C24C24×C5913yes—
332C24C24×C5913yes—
333C24C24×C5911yescharacteristic
334#41—448no—
335C2×Q8—26no—
336C2×Q8—26no—
337C2×Q8—43no—
338C2×D4—26no—
339C2×D4—26no—
340C2×D4—26no—
341C2×D4—26no—
342C2×D4—212no—
343C2×D4—26no—
344C2×D4—26no—
345C2×D4—26no—
346C2×D4—43no—
347C2×D4—43no—
348C2×D4—43no—
349C2×D4—46no—
350C2×D4—46no—
351C2×D4—43no—
352C2×D4—43no—
353C22×C4—26no—
354C22×C4—26no—
355C22×C4—26no—
356C22×C4—26no—
357C22×C4—26no—
358C22×C4—43no—
359C22×C4—43no—
360C22×C4—43no—
361C22×C4—43no—
362C22×C4—46no—
363C22×C4#41×C59112yescomplemented
364C22×C4C24×C5913yes—
365C22×C4C24×C5916yes—
366C22×C4C24×C5916yes—
367C22×C4C24×C5913yes—
368C22×C4C24×C5913yes—
369C22×C4C24×C5913yes—
370C4⋊C4—26no—
371C4⋊C4—212no—
372C4⋊C4—46no—
373C22⋊C4—212no—
374C22⋊C4—212no—
375C22⋊C4—212no—
376C22⋊C4—212no—
377C22⋊C4—212no—
378C22⋊C4—46no—
379C22⋊C4—43no—
380C22⋊C4—43no—
381C22⋊C4—46no—
382C22⋊C4—46no—
383C42—41no—
384C42—43no—
385C42—43no—
386C42—43no—
387C42—43no—
388C42—41no—
389C23—28no—
390C23—26no—
391C23—23no—
392C23—26no—
393C23—23no—
394C23—23no—
395C23—23no—
396C23—26no—
397C23—23no—
398C23—26no—
399C23—23no—
400C23—23no—
401C23—86no—
402C23—86no—
403C23C2×#41×C5916yes—
404C23H(5,𝔽2)×C5912yes—
405C23C25×C5911yescharacteristic
406Q8—412no—
407D4—412no—
408D4—412no—
409D4—412no—
410D4—86no—
411D4—812no—
412C2×C4—224no—
413C2×C4—23no—
414C2×C4—23no—
415C2×C4—23no—
416C2×C4—23no—
417C2×C4—23no—
418C2×C4—23no—
419C2×C4—26no—
420C2×C4—26no—
421C2×C4—23no—
422C2×C4—26no—
423C2×C4—26no—
424C2×C4—26no—
425C2×C4—26no—
426C2×C4—23no—
427C2×C4—23no—
428C2×C4—412no—
429C2×C4—412no—
430C2×C4—86no—
431C2×C4C2×#41×C5916yes—
432C2×C4C2×#41×C5916yes—
433C2×C4H(5,𝔽2)×C5916yes—
434C22—26no—
435C22—26no—
436C22—26no—
437C22—26no—
438C22—46no—
439C22—43no—
440C22—41no—
441C22—46no—
442C22—46no—
443C22—43no—
444C22—43no—
445C22—43no—
446C22—46no—
447C22—88no—
448C22C22×#41×C5913yes—
449C22C2×H(5,𝔽2)×C5913yes—
450C22C2×H(5,𝔽2)×C5911yescharacteristic
451C4—26no—
452C4—26no—
453C4—26no—
454C4—46no—
455C4—46no—
456C4—43no—
457C2—46no—
458C2—42no—
459C2—83no—
460C2C59×#344411yescharacteristic
461C2C59×#349013yes—
462C2C59×#350813yes—
subgroupG/H
center, socleC23×C59C25
commutator, Frattini, cosocleC23C25×C59
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C59 ◁ G

Complements

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

NH ≅ G/Ntype
1. C59×#2607C2semidirect
2. C59×#2557C2semidirect
3. C59×#2539C2semidirect
4. C59×#2471C2semidirect
5. C59×#2431C2semidirect
6. C59×#2404C2semidirect
7. C59×#2333C2semidirect
8. C59×#2297C2semidirect
9. C59×#2273C2semidirect
11. C2×#127×C59C22semidirect
12. C2×#124×C59C22semidirect
17. C2×#117×C59C22semidirect
19. C22×C42×C59C22semidirect
21. C59×#397C22semidirect
22. C59×#396C22semidirect
26. C59×#391C22semidirect
27. C59×#391C22semidirect
30. C59×#390C22semidirect
31. C59×#388C22semidirect
32. C59×#387C22semidirect
33. C59×#387C22semidirect
38. C59×#386C22semidirect
39. C59×#386C22semidirect
45. C4×C22⋊C4×C59C22semidirect
46. C4×C22⋊C4×C59C22semidirect
131. C22×C4×C59#41semidirect
202. #35438C59direct (N × H)
226. #2607C2×C59semidirect
227. #2557C2×C59semidirect
228. #2539C2×C59semidirect
229. #2471C2×C59semidirect
230. #2431C2×C59semidirect
231. #2404C2×C59semidirect
232. #2333C2×C59semidirect
233. #2297C2×C59semidirect
234. #2273C2×C59semidirect
242. C2×#127C22×C59semidirect
243. C2×#124C22×C59semidirect
248. C2×#117C22×C59semidirect
250. C22×C42C22×C59semidirect
252. #397C22×C59semidirect
253. #396C22×C59semidirect
257. #391C22×C59semidirect
258. #391C22×C59semidirect
261. #390C22×C59semidirect
262. #388C22×C59semidirect
263. #387C22×C59semidirect
264. #387C22×C59semidirect
269. #386C22×C59semidirect
270. #386C22×C59semidirect
276. C4×C22⋊C4C22×C59semidirect
277. C4×C22⋊C4C22×C59semidirect
278. C59#35438direct (N × H)
363. C22×C4#41×C59semidirect

Maximal subgroups

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

subgroupindex
C59×#26072
C59×#25572
C59×#25392
C59×#24712
C59×#24312
C59×#24042
C59×#23332
C59×#22972
C59×#22732
#3543859