Finite Group Databasebeta

← C59×#60032 #28472141

Subgroups — C59×#60032 #28472141

Order 15104.

2212 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#2736C211yesmaximal, characteristic, complemented
2C59×#2668C213yesmaximal, complemented
3C59×#2578C216yesmaximal, complemented
4C59×#2564C213yesmaximal, complemented
5C59×#2535C213yesmaximal, complemented
6C59×#2517C213yesmaximal, complemented
7C59×#2463C213yesmaximal, complemented
8C59×#2364C216yesmaximal, complemented
9C4×#120×C59C213yesmaximal, complemented
10C24×C4×C59C2211yescharacteristic
11C2×C22⋊Q8×C59C2213yescomplemented
12C2×#121×C59C2216yes—
13C2×#120×C59C2213yes—
14C2×C4×D4×C59C2213yes—
15C2×C4×D4×C59C2216yes—
16C2×C4×D4×C59C2213yescomplemented
17C59×#400C2213yescomplemented
18C59×#399C2213yes—
19C59×#397C2213yes—
20C59×#397C2216yes—
21C59×#397C2213yescomplemented
22C59×#395C2211yescharacteristic, complemented
23C59×#394C2216yes—
24C59×#393C2213yes—
25C59×#392C2213yes—
26C59×#392C2211yescharacteristic, complemented
27C59×#388C2216yes—
28C59×#388C2216yescomplemented
29C59×#387C2216yescomplemented
30C59×#387C2216yescomplemented
31C59×#387C2216yescomplemented
32C59×#386C2216yes—
33C59×#386C2213yes—
34C59×#386C2216yes—
35C59×#386C2216yes—
36C59×#386C2216yescomplemented
37C59×#385C2213yes—
38C59×#385C2216yes—
39C59×#383C2212yescomplemented
40C59×#382C2213yescomplemented
41C59×#380C2216yescomplemented
42C59×#379C2213yes—
43C4×C22⋊C4×C59C2216yes—
44C4×C22⋊C4×C59C2213yes—
45C4×C22⋊C4×C59C2216yescomplemented
46C2×#95×C59C2213yescomplemented
47C25×C59C2311yescharacteristic
48C22×Q8×C59C2311yescharacteristic
49C22×D4×C59C2316yes—
50C22×D4×C59C2313yes—
51C22×D4×C59C2313yes—
52C23×C4×C59—46no—
53C23×C4×C59C2313yes—
54C23×C4×C59C2316yes—
55C23×C4×C59C2313yes—
56C23×C4×C59C2313yes—
57C22⋊Q8×C59—46no—
58#121×C59—224no—
59#120×C59—212no—
60C4×D4×C59—46no—
61C4×D4×C59—46no—
62C4×D4×C59—412no—
63C2×C4⋊C4×C59C2316yes—
64C2×C4⋊C4×C59C2316yes—
65C2×C4⋊C4×C59C2313yes—
66C2×C4⋊C4×C59C2313yes—
67C2×C4⋊C4×C59C2313yes—
68C2×C22⋊C4×C59C2316yes—
69C2×C22⋊C4×C59C2316yes—
70C2×C22⋊C4×C59C2313yes—
71C2×C22⋊C4×C59C2316yes—
72C2×C22⋊C4×C59C2316yes—
73C2×C22⋊C4×C59C2313yes—
74C2×C22⋊C4×C59C2316yes—
75C2×C22⋊C4×C59C2313yes—
76C2×C22⋊C4×C59C2313yes—
77C2×C22⋊C4×C59C2316yes—
78C2×C42×C59C2313yes—
79C2×C42×C59C2316yes—
80C2×C42×C59C2312yes—
81#95×C59C2316yes—
82#95×C59C2313yes—
83#95×C59C2313yes—
84#95×C59C2316yes—
85#95×C59C2316yes—
86#95×C59C2316yes—
87#95×C59C2316yes—
88#95×C59C2311yescharacteristic
89#95×C59C2313yes—
90#95×C59C2316yes—
91C24×C59—26no—
92C24×C59—43no—
93C24×C59—41no—
94C24×C59C2413yes—
95C24×C59C2413yes—
96C2×Q8×C59—43no—
97C2×D4×C59—212no—
98C2×D4×C59—212no—
99C2×D4×C59—212no—
100C2×D4×C59—43no—
101C2×D4×C59—43no—
102C2×D4×C59—46no—
103C2×D4×C59—43no—
104C2×D4×C59#41112yes—
105C22×C4×C59—212no—
106C22×C4×C59—26no—
107C22×C4×C59—212no—
108C22×C4×C59—26no—
109C22×C4×C59—43no—
110C22×C4×C59—46no—
111C22×C4×C59—46no—
112C22×C4×C59—46no—
113C22×C4×C59—46no—
114C22×C4×C59—416no—
115C22×C4×C59C2416yes—
116C22×C4×C59C2416yes—
117C22×C4×C59C2413yes—
118C22×C4×C59C2411yescharacteristic
119C22×C4×C59C2413yes—
120C22×C4×C59C2413yes—
121C22×C4×C59C2413yes—
122C4⋊C4×C59—212no—
123C4⋊C4×C59—212no—
124C4⋊C4×C59—43no—
125C4⋊C4×C59—43no—
126C4⋊C4×C59—43no—
127C22⋊C4×C59—26no—
128C22⋊C4×C59—212no—
129C22⋊C4×C59—212no—
130C22⋊C4×C59—212no—
131C22⋊C4×C59—212no—
132C22⋊C4×C59—43no—
133C22⋊C4×C59—43no—
134C22⋊C4×C59—43no—
135C22⋊C4×C59—46no—
136C22⋊C4×C59—46no—
137C42×C59—26no—
138C42×C59—42no—
139C42×C59—46no—
140C23×C59—26no—
141C23×C59—26no—
142C23×C59—26no—
143C23×C59—23no—
144C23×C59—26no—
145C23×C59—23no—
146C23×C59—23no—
147C23×C59—23no—
148C23×C59—412no—
149C23×C59—412no—
150C23×C59—44no—
151C23×C59C2×#4116yes—
152C23×C59C2×#4116yes—
153C23×C59C2511yescharacteristic
154Q8×C59—82no—
155D4×C59—412no—
156D4×C59—412no—
157D4×C59—424no—
158C2×C4×C59—23no—
159C2×C4×C59—26no—
160C2×C4×C59—23no—
161C2×C4×C59—26no—
162C2×C4×C59—26no—
163C2×C4×C59—26no—
164C2×C4×C59—26no—
165C2×C4×C59—23no—
166C2×C4×C59—26no—
167C2×C4×C59—26no—
168C2×C4×C59—26no—
169C2×C4×C59—23no—
170C2×C4×C59—23no—
171C2×C4×C59—26no—
172C2×C4×C59—412no—
173C2×C4×C59—412no—
174C2×C4×C59—812no—
175C2×C4×C59—86no—
176C2×C4×C59C2×#4116yes—
177C2×C4×C59H(5,𝔽2)16yes—
178#60032C5911yesmaximal, characteristic, direct product factor, Sylow
179C22×C59—212no—
180C22×C59—212no—
181C22×C59—26no—
182C22×C59—26no—
183C22×C59—416no—
184C22×C59—43no—
185C22×C59—43no—
186C22×C59—46no—
187C22×C59—46no—
188C22×C59—43no—
189C22×C59—43no—
190C22×C59C22×#4113yes—
191C22×C59C2×H(5,𝔽2)13yes—
192C22×C59#58511yescharacteristic
193C4×C59—26no—
194C4×C59—26no—
195C4×C59—46no—
196C4×C59—43no—
197C4×C59—46no—
198C4×C59—41no—
199C4×C59—43no—
200#2736C2×C5911yescharacteristic, complemented
201#2668C2×C5913yescomplemented
202#2578C2×C5916yescomplemented
203#2564C2×C5913yescomplemented
204#2535C2×C5913yescomplemented
205#2517C2×C5913yescomplemented
206#2463C2×C5913yescomplemented
207#2364C2×C5916yescomplemented
208C4×#120C2×C5913yescomplemented
209C2×C59—46no—
210C2×C59—46no—
211C2×C59#348113yes—
212C2×C59#350513yes—
213C2×C59#353211yescharacteristic
214C24×C4C22×C5911yescharacteristic
215C2×C22⋊Q8C22×C5913yescomplemented
216C2×#121C22×C5916yes—
217C2×#120C22×C5913yes—
218C2×C4×D4C22×C5913yes—
219C2×C4×D4C22×C5916yes—
220C2×C4×D4C22×C5913yescomplemented
221#400C22×C5913yescomplemented
222#399C22×C5913yes—
223#397C22×C5916yes—
224#397C22×C5913yes—
225#397C22×C5913yescomplemented
226#395C22×C5911yescharacteristic, complemented
227#394C22×C5916yes—
228#393C22×C5913yes—
229#392C22×C5913yes—
230#392C22×C5911yescharacteristic, complemented
231#388C22×C5916yes—
232#388C22×C5916yescomplemented
233#387C22×C5916yescomplemented
234#387C22×C5916yescomplemented
235#387C22×C5916yescomplemented
236#386C22×C5916yes—
237#386C22×C5916yes—
238#386C22×C5916yes—
239#386C22×C5913yes—
240#386C22×C5916yescomplemented
241#385C22×C5916yes—
242#385C22×C5913yes—
243#383C22×C5912yescomplemented
244#382C22×C5913yescomplemented
245#380C22×C5916yescomplemented
246#379C22×C5913yes—
247C4×C22⋊C4C22×C5913yes—
248C4×C22⋊C4C22×C5916yes—
249C4×C22⋊C4C22×C5916yescomplemented
250C2×#95C22×C5913yescomplemented
251C59#6003211yescharacteristic, direct product factor, Sylow
252C25C23×C5911yescharacteristic
253C22×Q8C23×C5911yescharacteristic
254C22×D4C23×C5916yes—
255C22×D4C23×C5913yes—
256C22×D4C23×C5913yes—
257C23×C4—46no—
258C23×C4C23×C5913yes—
259C23×C4C23×C5913yes—
260C23×C4C23×C5913yes—
261C23×C4C23×C5916yes—
262C22⋊Q8—46no—
263#121—224no—
264#120—212no—
265C4×D4—46no—
266C4×D4—46no—
267C4×D4—412no—
268C2×C4⋊C4C23×C5916yes—
269C2×C4⋊C4C23×C5916yes—
270C2×C4⋊C4C23×C5913yes—
271C2×C4⋊C4C23×C5913yes—
272C2×C4⋊C4C23×C5913yes—
273C2×C22⋊C4C23×C5916yes—
274C2×C22⋊C4C23×C5916yes—
275C2×C22⋊C4C23×C5913yes—
276C2×C22⋊C4C23×C5916yes—
277C2×C22⋊C4C23×C5916yes—
278C2×C22⋊C4C23×C5916yes—
279C2×C22⋊C4C23×C5913yes—
280C2×C22⋊C4C23×C5913yes—
281C2×C22⋊C4C23×C5916yes—
282C2×C22⋊C4C23×C5913yes—
283C2×C42C23×C5913yes—
284C2×C42C23×C5916yes—
285C2×C42C23×C5912yes—
286#95C23×C5916yes—
287#95C23×C5913yes—
288#95C23×C5913yes—
289#95C23×C5916yes—
290#95C23×C5916yes—
291#95C23×C5916yes—
292#95C23×C5916yes—
293#95C23×C5911yescharacteristic
294#95C23×C5913yes—
295#95C23×C5916yes—
296C24—26no—
297C24—43no—
298C24—41no—
299C24C24×C5913yes—
300C24C24×C5913yes—
301C2×Q8—43no—
302C2×D4—212no—
303C2×D4—212no—
304C2×D4—212no—
305C2×D4—43no—
306C2×D4—43no—
307C2×D4—46no—
308C2×D4—43no—
309C2×D4#41×C59112yes—
310C22×C4—212no—
311C22×C4—26no—
312C22×C4—212no—
313C22×C4—26no—
314C22×C4—43no—
315C22×C4—46no—
316C22×C4—46no—
317C22×C4—46no—
318C22×C4—46no—
319C22×C4—416no—
320C22×C4C24×C5916yes—
321C22×C4C24×C5916yes—
322C22×C4C24×C5913yes—
323C22×C4C24×C5911yescharacteristic
324C22×C4C24×C5913yes—
325C22×C4C24×C5913yes—
326C22×C4C24×C5913yes—
327C4⋊C4—212no—
328C4⋊C4—212no—
329C4⋊C4—43no—
330C4⋊C4—43no—
331C4⋊C4—43no—
332C22⋊C4—26no—
333C22⋊C4—212no—
334C22⋊C4—212no—
335C22⋊C4—212no—
336C22⋊C4—212no—
337C22⋊C4—43no—
338C22⋊C4—43no—
339C22⋊C4—46no—
340C22⋊C4—46no—
341C22⋊C4—43no—
342C42—26no—
343C42—46no—
344C42—42no—
345C23—26no—
346C23—26no—
347C23—26no—
348C23—23no—
349C23—26no—
350C23—23no—
351C23—23no—
352C23—23no—
353C23—412no—
354C23—412no—
355C23—44no—
356C23C2×#41×C5916yes—
357C23C2×#41×C5916yes—
358C23C25×C5911yescharacteristic
359Q8—82no—
360D4—412no—
361D4—412no—
362D4—424no—
363C2×C4—23no—
364C2×C4—26no—
365C2×C4—23no—
366C2×C4—26no—
367C2×C4—26no—
368C2×C4—26no—
369C2×C4—26no—
370C2×C4—23no—
371C2×C4—26no—
372C2×C4—26no—
373C2×C4—26no—
374C2×C4—23no—
375C2×C4—23no—
376C2×C4—26no—
377C2×C4—412no—
378C2×C4—412no—
379C2×C4—86no—
380C2×C4—812no—
381C2×C4C2×#41×C5916yes—
382C2×C4H(5,𝔽2)×C5916yes—
383C22—212no—
384C22—212no—
385C22—26no—
386C22—26no—
387C22—416no—
388C22—43no—
389C22—43no—
390C22—43no—
391C22—43no—
392C22—46no—
393C22—46no—
394C22C22×#41×C5913yes—
395C22C2×H(5,𝔽2)×C5913yes—
396C22C59×#58511yescharacteristic
397C4—26no—
398C4—26no—
399C4—41no—
400C4—43no—
401C4—46no—
402C4—43no—
403C4—46no—
404C2—46no—
405C2—46no—
406C2C59×#348113yes—
407C2C59×#350513yes—
408C2C59×#353211yescharacteristic
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×#2736C2semidirect
2. C59×#2668C2semidirect
3. C59×#2578C2semidirect
4. C59×#2564C2semidirect
5. C59×#2535C2semidirect
6. C59×#2517C2semidirect
7. C59×#2463C2semidirect
8. C59×#2364C2semidirect
9. C4×#120×C59C2semidirect
11. C2×C22⋊Q8×C59C22semidirect
16. C2×C4×D4×C59C22semidirect
17. C59×#400C22semidirect
21. C59×#397C22semidirect
22. C59×#395C22semidirect
26. C59×#392C22semidirect
28. C59×#388C22semidirect
29. C59×#387C22semidirect
30. C59×#387C22semidirect
31. C59×#387C22semidirect
36. C59×#386C22semidirect
39. C59×#383C22semidirect
40. C59×#382C22semidirect
41. C59×#380C22semidirect
45. C4×C22⋊C4×C59C22semidirect
46. C2×#95×C59C22semidirect
178. #60032C59direct (N × H)
200. #2736C2×C59semidirect
201. #2668C2×C59semidirect
202. #2578C2×C59semidirect
203. #2564C2×C59semidirect
204. #2535C2×C59semidirect
205. #2517C2×C59semidirect
206. #2463C2×C59semidirect
207. #2364C2×C59semidirect
208. C4×#120C2×C59semidirect
215. C2×C22⋊Q8C22×C59semidirect
220. C2×C4×D4C22×C59semidirect
221. #400C22×C59semidirect
225. #397C22×C59semidirect
226. #395C22×C59semidirect
230. #392C22×C59semidirect
232. #388C22×C59semidirect
233. #387C22×C59semidirect
234. #387C22×C59semidirect
235. #387C22×C59semidirect
240. #386C22×C59semidirect
243. #383C22×C59semidirect
244. #382C22×C59semidirect
245. #380C22×C59semidirect
249. C4×C22⋊C4C22×C59semidirect
250. C2×#95C22×C59semidirect
251. C59#60032direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#27362
C59×#26682
C59×#25782
C59×#25642
C59×#25352
C59×#25172
C59×#24632
C59×#23642
C4×#120×C592
#6003259