Finite Group Databasebeta

← C59×#9160 #28421269

Subgroups — C59×#9160 #28421269

Order 15104.

450 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3116C211yesmaximal, characteristic
2C59×#2971C211yesmaximal, characteristic
3C59×#1759C211yesmaximal, characteristic
4C59×#1526C211yesmaximal, characteristic, complemented
5C59×#1506C211yesmaximal, characteristic, complemented
6C59×#1300C211yesmaximal, characteristic, complemented
7C59×#1291C211yesmaximal, characteristic, complemented
8C59×#533C2211yescharacteristic
9C4×#41×C59C2211yescharacteristic
10C59×#485—21no—
11C59×#477C411yescharacteristic, complemented
12C59×#476C411yescharacteristic, complemented
13C59×#462C411yescharacteristic, complemented
14C59×#461C411yescharacteristic, complemented
15C59×#452—21no—
16C8×Q8×C59—21no—
17C59×#441—21no—
18C59×#440—21no—
19C59×#436—21no—
20C59×#436—22no—
21C59×#432—21no—
22C59×#432C2211yescharacteristic
23C59×#432C2211yescharacteristic
24C2×#104×C59—21no—
25C4×M16×C59—21no—
26C4×M16×C59C2211yescharacteristic
27C4×M16×C59C2211yescharacteristic
28C59×#376C2211yescharacteristic
29C59×#339—21no—
30C59×#330—21no—
31C59×#330—21no—
32C59×#328—22no—
33C2×#41×C59D411yescharacteristic
34C2×Q16×C59—21no—
35C2×SD16×C59—21no—
36C2×M16×C59—22no—
37C2×M16×C59—21no—
38C2×M16×C59—21no—
39C4⋊Q8×C59C2×C411yescharacteristic
40C4⋊Q8×C59C2×C411yescharacteristic
41#125×C59—21no—
42C22⋊Q8×C59—21no—
43C22⋊Q8×C59—21no—
44C4×Q8×C59—21no—
45C4×Q8×C59—21no—
46C4×Q8×C59C2×C411yescharacteristic
47C4×Q8×C59D411yescharacteristic
48C4×D4×C59—21no—
49C4×D4×C59—21no—
50C4×D4×C59C2×C411yescharacteristic
51C4×D4×C59D411yescharacteristic
52#117×C59—21no—
53#117×C59—21no—
54#117×C59D411yescharacteristic
55C2×C42×C59—21no—
56C2×C42×C59—21no—
57C2×C42×C59C2311yescharacteristic
58#107×C59—21no—
59#106×C59—21no—
60C4⋊C8×C59—22no—
61C4⋊C8×C59—21no—
62C4⋊C8×C59C2×C411yescharacteristic
63C4⋊C8×C59C2×C411yescharacteristic
64#104×C59—24no—
65#103×C59—21no—
66#103×C59—21no—
67#103×C59—21no—
68#102×C59—21no—
69C22⋊C8×C59—22no—
70C22⋊C8×C59—21no—
71C22⋊C8×C59D412yes—
72#97×C59—21no—
73#97×C59—21no—
74#97×C59—21no—
75#97×C59D411yescharacteristic
76#97×C59D411yescharacteristic
77C4×C8×C59—22no—
78C4×C8×C59—21no—
79C4×C8×C59—21no—
80#95×C59—21no—
81#95×C59—21no—
82#41×C59—22no—
83#41×C59—41no—
84C2×Q8×C59—21no—
85C2×Q8×C59—21no—
86C2×Q8×C59C22⋊C411yescharacteristic
87C2×D4×C59—21no—
88C2×D4×C59C22⋊C411yescharacteristic
89C22×C4×C59—21no—
90C22×C4×C59—21no—
91C22×C4×C59—21no—
92C22×C4×C59—41no—
93C22×C4×C59C2×D411yescharacteristic
94C22×C4×C59C2×D411yescharacteristic
95C22×C4×C59#4111yescharacteristic
96Q16×C59—42no—
97SD16×C59—42no—
98M16×C59—22no—
99M16×C59—42no—
100M16×C59—44no—
101M16×C59—41no—
102C2×C8×C59—21no—
103C2×C8×C59—21no—
104C2×C8×C59—21no—
105C2×C8×C59—22no—
106C2×C8×C59—21no—
107C2×C8×C59—41no—
108C4⋊C4×C59—21no—
109C4⋊C4×C59—21no—
110C4⋊C4×C59—21no—
111C4⋊C4×C59—21no—
112C4⋊C4×C59—21no—
113C4⋊C4×C59—21no—
114C4⋊C4×C59—41no—
115C4⋊C4×C59—41no—
116C4⋊C4×C59C22⋊C411yescharacteristic
117C4⋊C4×C59C22⋊C411yescharacteristic
118C22⋊C4×C59—21no—
119C22⋊C4×C59—21no—
120C22⋊C4×C59—21no—
121C22⋊C4×C59—41no—
122C42×C59—21no—
123C42×C59—21no—
124C42×C59—21no—
125C42×C59—22no—
126C42×C59—41no—
127C42×C59—41no—
128C42×C59C22×C411yescharacteristic
129C42×C59C2×D411yescharacteristic
130C42×C59C2×D411yescharacteristic
131C42×C59#4111yescharacteristic
132C23×C59—21no—
133C23×C59#12111yescharacteristic
134Q8×C59—21no—
135Q8×C59—41no—
136Q8×C59—41no—
137Q8×C59—81no—
138Q8×C59#10412yes—
139D4×C59—21no—
140D4×C59—21no—
141D4×C59—42no—
142C2×C4×C59—21no—
143C2×C4×C59—21no—
144C2×C4×C59—21no—
145C2×C4×C59—21no—
146C2×C4×C59—21no—
147C2×C4×C59—41no—
148C2×C4×C59—41no—
149C2×C4×C59—42no—
150C2×C4×C59—42no—
151C2×C4×C59—42no—
152C2×C4×C59—41no—
153C2×C4×C59—41no—
154C2×C4×C59—81no—
155C2×C4×C59—81no—
156C2×C4×C59—81no—
157C2×C4×C59C2×C22⋊C411yescharacteristic
158C2×C4×C59C4×D411yescharacteristic
159C2×C4×C59C4×D411yescharacteristic
160C2×C4×C59#12011yescharacteristic
161C2×C4×C59#12111yescharacteristic
162C2×C4×C59#12311yescharacteristic
163C8×C59—22no—
164C8×C59—42no—
165C8×C59—41no—
166C8×C59—42no—
167C8×C59—41no—
168C8×C59—41no—
169#9160C5911yesmaximal, characteristic, direct product factor, Sylow
170C22×C59—21no—
171C22×C59—21no—
172C22×C59—21no—
173C22×C59—41no—
174C22×C59—41no—
175C22×C59—41no—
176C22×C59#38611yescharacteristic
177C4×C59—21no—
178C4×C59—22no—
179C4×C59—21no—
180C4×C59—21no—
181C4×C59—21no—
182C4×C59—21no—
183C4×C59—41no—
184C4×C59—41no—
185C4×C59—82no—
186C4×C59—81no—
187C4×C59—81no—
188C4×C59C2×#10411yescharacteristic
189C4×C59#42111yescharacteristic
190#3116C2×C5911yescharacteristic
191#2971C2×C5911yescharacteristic
192#1759C2×C5911yescharacteristic
193#1526C2×C5911yescharacteristic, complemented
194#1506C2×C5911yescharacteristic, complemented
195#1300C2×C5911yescharacteristic, complemented
196#1291C2×C5911yescharacteristic, complemented
197C2×C59—41no—
198C2×C59—81no—
199C2×C59#187111yescharacteristic
200C2×C59#190211yescharacteristic
201C2×C59#190611yescharacteristic
202#533C22×C5911yescharacteristic
203C4×#41C22×C5911yescharacteristic
204#485—21no—
205#477C4×C5911yescharacteristic, complemented
206#476C4×C5911yescharacteristic, complemented
207#462C4×C5911yescharacteristic, complemented
208#461C4×C5911yescharacteristic, complemented
209#452—21no—
210C8×Q8—21no—
211#441—21no—
212#440—21no—
213#436—21no—
214#436—22no—
215#432—21no—
216#432C22×C5911yescharacteristic
217#432C22×C5911yescharacteristic
218C2×#104—21no—
219C4×M16—21no—
220C4×M16C22×C5911yescharacteristic
221C4×M16C22×C5911yescharacteristic
222#376C22×C5911yescharacteristic
223#339—21no—
224#330—21no—
225#330—21no—
226#328—22no—
227C59#916011yescharacteristic, direct product factor, Sylow
228C2×#41D4×C5911yescharacteristic
229C2×Q16—21no—
230C2×SD16—21no—
231C2×M16—22no—
232C2×M16—21no—
233C2×M16—21no—
234C4⋊Q8C2×C4×C5911yescharacteristic
235C4⋊Q8C2×C4×C5911yescharacteristic
236#125—21no—
237C22⋊Q8—21no—
238C22⋊Q8—21no—
239C4×Q8—21no—
240C4×Q8—21no—
241C4×Q8C2×C4×C5911yescharacteristic
242C4×Q8D4×C5911yescharacteristic
243C4×D4—21no—
244C4×D4—21no—
245C4×D4C2×C4×C5911yescharacteristic
246C4×D4D4×C5911yescharacteristic
247#117—21no—
248#117—21no—
249#117D4×C5911yescharacteristic
250C2×C42—21no—
251C2×C42—21no—
252C2×C42C23×C5911yescharacteristic
253#107—21no—
254#106—21no—
255C4⋊C8—22no—
256C4⋊C8—21no—
257C4⋊C8C2×C4×C5911yescharacteristic
258C4⋊C8C2×C4×C5911yescharacteristic
259#104—24no—
260#103—21no—
261#103—21no—
262#103—21no—
263#102—21no—
264C22⋊C8—22no—
265C22⋊C8—21no—
266C22⋊C8D4×C5912yes—
267#97—21no—
268#97—21no—
269#97—21no—
270#97D4×C5911yescharacteristic
271#97D4×C5911yescharacteristic
272C4×C8—22no—
273C4×C8—21no—
274C4×C8—21no—
275#95—21no—
276#95—21no—
277#41—22no—
278#41—41no—
279C2×Q8—21no—
280C2×Q8—21no—
281C2×Q8C22⋊C4×C5911yescharacteristic
282C2×D4—21no—
283C2×D4C22⋊C4×C5911yescharacteristic
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—41no—
288C22×C4C2×D4×C5911yescharacteristic
289C22×C4C2×D4×C5911yescharacteristic
290C22×C4#41×C5911yescharacteristic
291Q16—42no—
292SD16—42no—
293M16—22no—
294M16—42no—
295M16—44no—
296M16—41no—
297C2×C8—21no—
298C2×C8—21no—
299C2×C8—21no—
300C2×C8—22no—
301C2×C8—21no—
302C2×C8—41no—
303C4⋊C4—21no—
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—21no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4C22⋊C4×C5911yescharacteristic
312C4⋊C4C22⋊C4×C5911yescharacteristic
313C22⋊C4—21no—
314C22⋊C4—21no—
315C22⋊C4—21no—
316C22⋊C4—41no—
317C42—21no—
318C42—21no—
319C42—21no—
320C42—22no—
321C42—41no—
322C42—41no—
323C42C22×C4×C5911yescharacteristic
324C42C2×D4×C5911yescharacteristic
325C42C2×D4×C5911yescharacteristic
326C42#41×C5911yescharacteristic
327C23—21no—
328C23#121×C5911yescharacteristic
329Q8—21no—
330Q8—41no—
331Q8—41no—
332Q8—81no—
333Q8#104×C5912yes—
334D4—21no—
335D4—21no—
336D4—42no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—81no—
350C2×C4—81no—
351C2×C4—81no—
352C2×C4C2×C22⋊C4×C5911yescharacteristic
353C2×C4C4×D4×C5911yescharacteristic
354C2×C4C4×D4×C5911yescharacteristic
355C2×C4#120×C5911yescharacteristic
356C2×C4#121×C5911yescharacteristic
357C2×C4#123×C5911yescharacteristic
358C8—22no—
359C8—42no—
360C8—41no—
361C8—42no—
362C8—41no—
363C8—41no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22C59×#38611yescharacteristic
371C4—21no—
372C4—22no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—21no—
377C4—41no—
378C4—41no—
379C4—82no—
380C4—81no—
381C4—81no—
382C4C2×#104×C5911yescharacteristic
383C4C59×#42111yescharacteristic
384C2—41no—
385C2—81no—
386C2C59×#187111yescharacteristic
387C2C59×#190211yescharacteristic
388C2C59×#190611yescharacteristic
subgroupG/H
center, socleC22×C59#386
commutatorC42C22×C4×C59
Frattini, cosocleC2×C42C23×C59
prime radicalC2×#41×C59D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C59 ◁ C2×C42×C59 ◁ G

Complements

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

NH ≅ G/Ntype
4. C59×#1526C2semidirect
5. C59×#1506C2semidirect
6. C59×#1300C2semidirect
7. C59×#1291C2semidirect
11. C59×#477C4semidirect
12. C59×#476C4semidirect
13. C59×#462C4semidirect
14. C59×#461C4semidirect
169. #9160C59direct (N × H)
193. #1526C2×C59semidirect
194. #1506C2×C59semidirect
195. #1300C2×C59semidirect
196. #1291C2×C59semidirect
205. #477C4×C59semidirect
206. #476C4×C59semidirect
207. #462C4×C59semidirect
208. #461C4×C59semidirect
227. C59#9160direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#31162
C59×#29712
C59×#17592
C59×#15262
C59×#15062
C59×#13002
C59×#12912
#916059