Finite Group Databasebeta

← C59×#36676 #28448785

Subgroups — C59×#36676 #28448785

Order 15104.

2006 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#2842C211yesmaximal, characteristic, complemented
2C59×#2834C211yesmaximal, characteristic, complemented
3C59×#2827C216yesmaximal, complemented
4C59×#2826C213yesmaximal, complemented
5C59×#2825C212yesmaximal, complemented
6C59×#2812C213yesmaximal, complemented
7C59×#2401C212yesmaximal, complemented
8C59×#2397C211yesmaximal, characteristic, complemented
9C59×#2395C213yesmaximal, complemented
10C59×#2392C216yesmaximal, complemented
11C4×#120×C59C213yesmaximal, complemented
12C24×C4×C59C2211yescharacteristic
13C2×#120×C59C2213yes—
14C2×C4×D4×C59C2216yes—
15C2×C4×D4×C59C2213yes—
16C2×C4×D4×C59C2213yescomplemented
17C2×#117×C59C2213yescomplemented
18C59×#401C2212yescomplemented
19C59×#400C2216yescomplemented
20C59×#400C2213yescomplemented
21C59×#399C2213yes—
22C59×#399C2211yescharacteristic
23C59×#399C2213yescomplemented
24C59×#398C2213yescomplemented
25C59×#398C2216yescomplemented
26C59×#397C2216yes—
27C59×#397C2213yes—
28C59×#397C2216yescomplemented
29C59×#397C2216yescomplemented
30C59×#396C2212yes—
31C59×#396C2216yes—
32C59×#396C2216yescomplemented
33C59×#394C2216yes—
34C59×#394C2216yes—
35C59×#394C2216yes—
36C59×#394C2216yescomplemented
37C59×#392C2216yes—
38C59×#392C2213yes—
39C59×#392C2211yescharacteristic, complemented
40C59×#386C2216yes—
41C59×#386C2213yes—
42C59×#385C2213yes—
43C59×#385C2216yes—
44C59×#379C2213yes—
45C4×C4⋊C4×C59C2216yescomplemented
46C4×C22⋊C4×C59C2216yes—
47C4×C22⋊C4×C59C2213yes—
48C4×C22⋊C4×C59C2213yescomplemented
49C59×#376C2211yescharacteristic, complemented
50C25×C59C2311yescharacteristic
51C22×D4×C59C2316yes—
52C22×D4×C59C2313yes—
53C22×D4×C59C2313yes—
54C23×C4×C59—46no—
55C23×C4×C59C2312yes—
56C23×C4×C59C2311yescharacteristic
57C23×C4×C59C2313yes—
58C23×C4×C59C2311yescharacteristic
59C23×C4×C59C2312yes—
60#120×C59—212no—
61C4×D4×C59—412no—
62C4×D4×C59—46no—
63C4×D4×C59—46no—
64#117×C59—46no—
65C2×C4⋊C4×C59C2316yes—
66C2×C4⋊C4×C59C2316yes—
67C2×C4⋊C4×C59C2316yes—
68C2×C4⋊C4×C59C2313yes—
69C2×C4⋊C4×C59C2313yes—
70C2×C4⋊C4×C59C2313yes—
71C2×C4⋊C4×C59C2313yes—
72C2×C22⋊C4×C59C2316yes—
73C2×C22⋊C4×C59C2313yes—
74C2×C22⋊C4×C59C2316yes—
75C2×C22⋊C4×C59C2313yes—
76C2×C22⋊C4×C59C2316yes—
77C2×C22⋊C4×C59C2313yes—
78C2×C22⋊C4×C59C2316yes—
79C2×C22⋊C4×C59C2313yes—
80C2×C22⋊C4×C59C2316yes—
81C2×C22⋊C4×C59C2316yes—
82C2×C22⋊C4×C59C2316yes—
83C2×C42×C59C2313yes—
84C2×C42×C59C2316yes—
85#95×C59C2313yes—
86#95×C59C2311yescharacteristic
87#95×C59C2316yes—
88#95×C59C2316yes—
89#95×C59C2316yes—
90#95×C59C2313yes—
91#95×C59C2313yes—
92#95×C59C2316yes—
93#95×C59C2316yes—
94C24×C59—43no—
95C24×C59—43no—
96C24×C59#4114yes—
97C24×C59C2413yes—
98C24×C59C2412yes—
99C24×C59C2411yescharacteristic
100C2×D4×C59—212no—
101C2×D4×C59—26no—
102C2×D4×C59—43no—
103C2×D4×C59—43no—
104C2×D4×C59—46no—
105C2×D4×C59—46no—
106C2×D4×C59—46no—
107C2×D4×C59—43no—
108C22×C4×C59—26no—
109C22×C4×C59—212no—
110C22×C4×C59—212no—
111C22×C4×C59—26no—
112C22×C4×C59—43no—
113C22×C4×C59—46no—
114C22×C4×C59—416no—
115C22×C4×C59C2413yes—
116C22×C4×C59C2416yes—
117C22×C4×C59C2413yes—
118C22×C4×C59C2412yes—
119C22×C4×C59C2411yescharacteristic
120C22×C4×C59C2416yes—
121C22×C4×C59C2413yes—
122C22×C4×C59C2411yescharacteristic
123C4⋊C4×C59—46no—
124C4⋊C4×C59—46no—
125C4⋊C4×C59—43no—
126C4⋊C4×C59—43no—
127C4⋊C4×C59—43no—
128C4⋊C4×C59—43no—
129C4⋊C4×C59—46no—
130C22⋊C4×C59—212no—
131C22⋊C4×C59—26no—
132C22⋊C4×C59—43no—
133C22⋊C4×C59—46no—
134C22⋊C4×C59—46no—
135C22⋊C4×C59—46no—
136C22⋊C4×C59—46no—
137C22⋊C4×C59—46no—
138C22⋊C4×C59—46no—
139C22⋊C4×C59—43no—
140C22⋊C4×C59—43no—
141C42×C59—212no—
142C42×C59—26no—
143C23×C59—26no—
144C23×C59—23no—
145C23×C59—23no—
146C23×C59—26no—
147C23×C59—23no—
148C23×C59—23no—
149C23×C59—26no—
150C23×C59—26no—
151C23×C59—23no—
152C23×C59—412no—
153C23×C59—44no—
154C23×C59—412no—
155C23×C59C2×#4114yes—
156C23×C59C2×#4112yes—
157C23×C59C2511yescharacteristic
158D4×C59—412no—
159D4×C59—424no—
160D4×C59—412no—
161C2×C4×C59—23no—
162C2×C4×C59—26no—
163C2×C4×C59—26no—
164C2×C4×C59—23no—
165C2×C4×C59—23no—
166C2×C4×C59—26no—
167C2×C4×C59—26no—
168C2×C4×C59—23no—
169C2×C4×C59—26no—
170C2×C4×C59—23no—
171C2×C4×C59—26no—
172C2×C4×C59—26no—
173C2×C4×C59—26no—
174C2×C4×C59—26no—
175C2×C4×C59—23no—
176C2×C4×C59—44no—
177C2×C4×C59—48no—
178C2×C4×C59—412no—
179C2×C4×C59—48no—
180C2×C4×C59—44no—
181C2×C4×C59H(5,𝔽2)16yes—
182#36676C5911yesmaximal, characteristic, direct product factor, Sylow
183C22×C59—26no—
184C22×C59—212no—
185C22×C59—416no—
186C22×C59—42no—
187C22×C59—41no—
188C22×C59—46no—
189C22×C59—43no—
190C22×C59—43no—
191C22×C59—46no—
192C22×C59—43no—
193C22×C59—46no—
194C22×C59—43no—
195C22×C59C22×#4111yescharacteristic
196C22×C59C2×H(5,𝔽2)13yes—
197C22×C59#58513yes—
198C4×C59—43no—
199C4×C59—46no—
200C4×C59—43no—
201C4×C59—42no—
202C4×C59—41no—
203C4×C59—46no—
204C4×C59—43no—
205C4×C59#56014yes—
206#2842C2×C5911yescharacteristic, complemented
207#2834C2×C5911yescharacteristic, complemented
208#2827C2×C5916yescomplemented
209#2826C2×C5913yescomplemented
210#2825C2×C5912yescomplemented
211#2812C2×C5913yescomplemented
212#2401C2×C5912yescomplemented
213#2397C2×C5911yescharacteristic, complemented
214#2395C2×C5913yescomplemented
215#2392C2×C5916yescomplemented
216C4×#120C2×C5913yescomplemented
217C2×C59—42no—
218C2×C59—44no—
219C2×C59—83no—
220C2×C59#345913yes—
221C2×C59C2×#56011yescharacteristic
222C2×C59#352913yes—
223C24×C4C22×C5911yescharacteristic
224C2×#120C22×C5913yes—
225C2×C4×D4C22×C5916yes—
226C2×C4×D4C22×C5913yes—
227C2×C4×D4C22×C5913yescomplemented
228C2×#117C22×C5913yescomplemented
229#401C22×C5912yescomplemented
230#400C22×C5916yescomplemented
231#400C22×C5913yescomplemented
232#399C22×C5913yes—
233#399C22×C5911yescharacteristic
234#399C22×C5913yescomplemented
235#398C22×C5913yescomplemented
236#398C22×C5916yescomplemented
237#397C22×C5916yes—
238#397C22×C5913yes—
239#397C22×C5916yescomplemented
240#397C22×C5916yescomplemented
241#396C22×C5912yes—
242#396C22×C5916yes—
243#396C22×C5916yescomplemented
244#394C22×C5916yes—
245#394C22×C5916yes—
246#394C22×C5916yes—
247#394C22×C5916yescomplemented
248#392C22×C5916yes—
249#392C22×C5913yes—
250#392C22×C5911yescharacteristic, complemented
251#386C22×C5916yes—
252#386C22×C5913yes—
253#385C22×C5913yes—
254#385C22×C5916yes—
255#379C22×C5913yes—
256C4×C4⋊C4C22×C5916yescomplemented
257C4×C22⋊C4C22×C5916yes—
258C4×C22⋊C4C22×C5913yes—
259C4×C22⋊C4C22×C5913yescomplemented
260#376C22×C5911yescharacteristic, complemented
261C59#3667611yescharacteristic, direct product factor, Sylow
262C25C23×C5911yescharacteristic
263C22×D4C23×C5916yes—
264C22×D4C23×C5913yes—
265C22×D4C23×C5913yes—
266C23×C4—46no—
267C23×C4C23×C5913yes—
268C23×C4C23×C5912yes—
269C23×C4C23×C5911yescharacteristic
270C23×C4C23×C5911yescharacteristic
271C23×C4C23×C5912yes—
272#120—212no—
273C4×D4—412no—
274C4×D4—46no—
275C4×D4—46no—
276#117—46no—
277C2×C4⋊C4C23×C5913yes—
278C2×C4⋊C4C23×C5913yes—
279C2×C4⋊C4C23×C5916yes—
280C2×C4⋊C4C23×C5913yes—
281C2×C4⋊C4C23×C5913yes—
282C2×C4⋊C4C23×C5916yes—
283C2×C4⋊C4C23×C5916yes—
284C2×C22⋊C4C23×C5916yes—
285C2×C22⋊C4C23×C5913yes—
286C2×C22⋊C4C23×C5916yes—
287C2×C22⋊C4C23×C5913yes—
288C2×C22⋊C4C23×C5916yes—
289C2×C22⋊C4C23×C5913yes—
290C2×C22⋊C4C23×C5916yes—
291C2×C22⋊C4C23×C5916yes—
292C2×C22⋊C4C23×C5916yes—
293C2×C22⋊C4C23×C5913yes—
294C2×C22⋊C4C23×C5916yes—
295C2×C42C23×C5916yes—
296C2×C42C23×C5913yes—
297#95C23×C5913yes—
298#95C23×C5911yescharacteristic
299#95C23×C5916yes—
300#95C23×C5916yes—
301#95C23×C5916yes—
302#95C23×C5913yes—
303#95C23×C5913yes—
304#95C23×C5916yes—
305#95C23×C5916yes—
306C24—43no—
307C24—43no—
308C24#41×C5914yes—
309C24C24×C5913yes—
310C24C24×C5911yescharacteristic
311C24C24×C5912yes—
312C2×D4—212no—
313C2×D4—26no—
314C2×D4—43no—
315C2×D4—43no—
316C2×D4—46no—
317C2×D4—46no—
318C2×D4—46no—
319C2×D4—43no—
320C22×C4—26no—
321C22×C4—212no—
322C22×C4—212no—
323C22×C4—26no—
324C22×C4—43no—
325C22×C4—46no—
326C22×C4—416no—
327C22×C4C24×C5913yes—
328C22×C4C24×C5916yes—
329C22×C4C24×C5913yes—
330C22×C4C24×C5912yes—
331C22×C4C24×C5911yescharacteristic
332C22×C4C24×C5916yes—
333C22×C4C24×C5913yes—
334C22×C4C24×C5911yescharacteristic
335C4⋊C4—43no—
336C4⋊C4—43no—
337C4⋊C4—43no—
338C4⋊C4—43no—
339C4⋊C4—46no—
340C4⋊C4—46no—
341C4⋊C4—46no—
342C22⋊C4—212no—
343C22⋊C4—26no—
344C22⋊C4—46no—
345C22⋊C4—46no—
346C22⋊C4—46no—
347C22⋊C4—46no—
348C22⋊C4—43no—
349C22⋊C4—43no—
350C22⋊C4—43no—
351C22⋊C4—46no—
352C22⋊C4—46no—
353C42—212no—
354C42—26no—
355C23—26no—
356C23—23no—
357C23—23no—
358C23—26no—
359C23—23no—
360C23—23no—
361C23—26no—
362C23—26no—
363C23—23no—
364C23—412no—
365C23—44no—
366C23—412no—
367C23C2×#41×C5912yes—
368C23C2×#41×C5914yes—
369C23C25×C5911yescharacteristic
370D4—412no—
371D4—424no—
372D4—412no—
373C2×C4—23no—
374C2×C4—26no—
375C2×C4—26no—
376C2×C4—23no—
377C2×C4—23no—
378C2×C4—26no—
379C2×C4—26no—
380C2×C4—23no—
381C2×C4—26no—
382C2×C4—23no—
383C2×C4—26no—
384C2×C4—26no—
385C2×C4—26no—
386C2×C4—26no—
387C2×C4—23no—
388C2×C4—44no—
389C2×C4—48no—
390C2×C4—412no—
391C2×C4—48no—
392C2×C4—44no—
393C2×C4H(5,𝔽2)×C5916yes—
394C22—26no—
395C22—212no—
396C22—416no—
397C22—42no—
398C22—41no—
399C22—46no—
400C22—43no—
401C22—43no—
402C22—46no—
403C22—43no—
404C22—43no—
405C22—46no—
406C22C22×#41×C5911yescharacteristic
407C22C2×H(5,𝔽2)×C5913yes—
408C22C59×#58513yes—
409C4—42no—
410C4—41no—
411C4—43no—
412C4—43no—
413C4—46no—
414C4—43no—
415C4—46no—
416C4C59×#56014yes—
417C2—42no—
418C2—44no—
419C2—83no—
420C2C59×#345913yes—
421C2C2×C59×#56011yescharacteristic
422C2C59×#352913yes—
subgroupG/H
centerC22×C4×C59C24
commutator, Frattini, cosocleC23C25×C59
socleC23×C59C25
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C59 ◁ G

Complements

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

NH ≅ G/Ntype
1. C59×#2842C2semidirect
2. C59×#2834C2semidirect
3. C59×#2827C2semidirect
4. C59×#2826C2semidirect
5. C59×#2825C2semidirect
6. C59×#2812C2semidirect
7. C59×#2401C2semidirect
8. C59×#2397C2semidirect
9. C59×#2395C2semidirect
10. C59×#2392C2semidirect
11. C4×#120×C59C2semidirect
16. C2×C4×D4×C59C22semidirect
17. C2×#117×C59C22semidirect
18. C59×#401C22semidirect
19. C59×#400C22semidirect
20. C59×#400C22semidirect
23. C59×#399C22semidirect
24. C59×#398C22semidirect
25. C59×#398C22semidirect
28. C59×#397C22semidirect
29. C59×#397C22semidirect
32. C59×#396C22semidirect
36. C59×#394C22semidirect
39. C59×#392C22semidirect
45. C4×C4⋊C4×C59C22semidirect
48. C4×C22⋊C4×C59C22semidirect
49. C59×#376C22semidirect
182. #36676C59direct (N × H)
206. #2842C2×C59semidirect
207. #2834C2×C59semidirect
208. #2827C2×C59semidirect
209. #2826C2×C59semidirect
210. #2825C2×C59semidirect
211. #2812C2×C59semidirect
212. #2401C2×C59semidirect
213. #2397C2×C59semidirect
214. #2395C2×C59semidirect
215. #2392C2×C59semidirect
216. C4×#120C2×C59semidirect
227. C2×C4×D4C22×C59semidirect
228. C2×#117C22×C59semidirect
229. #401C22×C59semidirect
230. #400C22×C59semidirect
231. #400C22×C59semidirect
234. #399C22×C59semidirect
235. #398C22×C59semidirect
236. #398C22×C59semidirect
239. #397C22×C59semidirect
240. #397C22×C59semidirect
243. #396C22×C59semidirect
247. #394C22×C59semidirect
250. #392C22×C59semidirect
256. C4×C4⋊C4C22×C59semidirect
259. C4×C22⋊C4C22×C59semidirect
260. #376C22×C59semidirect
261. C59#36676direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#28422
C59×#28342
C59×#28272
C59×#28262
C59×#28252
C59×#28122
C59×#24012
C59×#23972
C59×#23952
C59×#23922
C4×#120×C592
#3667659