Finite Group Databasebeta

← C59×#9311 #28421420

Subgroups — C59×#9311 #28421420

Order 15104.

514 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3115C211yesmaximal, characteristic
2C59×#2875C211yesmaximal, characteristic, complemented
3C59×#1530C211yesmaximal, characteristic, complemented
4C59×#1488C211yesmaximal, characteristic, complemented
5C59×#1484C211yesmaximal, characteristic, complemented
6C59×#1302C211yesmaximal, characteristic, complemented
7C59×#1291C211yesmaximal, characteristic, complemented
8C2×#131×C59—21no—
9C59×#532C2211yescharacteristic
10C4×#41×C59C2211yescharacteristic
11C59×#482—21no—
12C59×#475C411yescharacteristic
13C59×#474C411yescharacteristic
14C59×#460C411yescharacteristic
15C59×#459C411yescharacteristic
16C59×#449—21no—
17C59×#442—21no—
18C59×#440—21no—
19C59×#432C2211yescharacteristic
20C59×#432C2211yescharacteristic
21C59×#431C2211yescharacteristic
22C59×#405—21no—
23C59×#405—22no—
24C4×M16×C59—21no—
25C4×M16×C59C2211yescharacteristic
26C2×#97×C59—21no—
27C2×#97×C59C2211yescharacteristic
28C59×#329—21no—
29C59×#329—21no—
30C59×Q8⋊C8—21no—
31C59×D4⋊C8—21no—
32C59×D4⋊C8—22no—
33C2×#41×C59—21no—
34C2×#41×C59D411yescharacteristic
35C2×SD16×C59—21no—
36C2×D8×C59—21no—
37#131×C59—24no—
38#131×C59—24no—
39C2×M16×C59—22no—
40C2×M16×C59—21no—
41C22×C8×C59—22no—
42C22×C8×C59—21no—
43C4⋊Q8×C59C2×C411yescharacteristic
44#127×C59C2×C411yescharacteristic
45#124×C59—21no—
46#121×C59—21no—
47#121×C59—21no—
48C4×Q8×C59C2×C411yescharacteristic
49C4×Q8×C59D411yescharacteristic
50C4×D4×C59—21no—
51C4×D4×C59—21no—
52C4×D4×C59—21no—
53C4×D4×C59—21no—
54C4×D4×C59C2×C411yescharacteristic
55C4×D4×C59D411yescharacteristic
56#117×C59—21no—
57#117×C59D411yescharacteristic
58C2×C42×C59—21no—
59C2×C42×C59C2311yescharacteristic
60#107×C59—21no—
61#106×C59—21no—
62C4⋊C8×C59—21no—
63C4⋊C8×C59—21no—
64C4⋊C8×C59C2×C411yescharacteristic
65C4⋊C8×C59C2×C411yescharacteristic
66#103×C59—21no—
67#102×C59—21no—
68#102×C59—21no—
69#102×C59—21no—
70C22⋊C8×C59—21no—
71C22⋊C8×C59—21no—
72C22⋊C8×C59—21no—
73#97×C59—22no—
74#97×C59—21no—
75#97×C59—21no—
76#97×C59—21no—
77#97×C59—21no—
78#97×C59D411yescharacteristic
79#97×C59D411yescharacteristic
80C4×C8×C59—22no—
81C4×C8×C59—21no—
82C4×C8×C59D412yes—
83#41×C59—22no—
84#41×C59—22no—
85#41×C59—82no—
86C2×Q8×C59—21no—
87C2×Q8×C59C22⋊C411yescharacteristic
88C2×D4×C59—21no—
89C2×D4×C59—21no—
90C2×D4×C59—21no—
91C2×D4×C59—21no—
92C2×D4×C59—41no—
93C2×D4×C59C22⋊C411yescharacteristic
94C22×C4×C59—21no—
95C22×C4×C59—21no—
96C22×C4×C59—21no—
97C22×C4×C59—41no—
98C22×C4×C59C2×D411yescharacteristic
99C22×C4×C59#4111yescharacteristic
100C22×C4×C59#4111yescharacteristic
101SD16×C59—42no—
102D8×C59—42no—
103M16×C59—28no—
104M16×C59—22no—
105M16×C59—22no—
106C2×C8×C59—28no—
107C2×C8×C59—22no—
108C2×C8×C59—22no—
109C2×C8×C59—21no—
110C2×C8×C59—22no—
111C2×C8×C59—21no—
112C2×C8×C59—21no—
113C2×C8×C59—21no—
114C2×C8×C59—41no—
115C2×C8×C59—41no—
116C4⋊C4×C59—21no—
117C4⋊C4×C59—21no—
118C4⋊C4×C59—21no—
119C4⋊C4×C59—21no—
120C4⋊C4×C59C22⋊C411yescharacteristic
121C4⋊C4×C59C22⋊C411yescharacteristic
122C22⋊C4×C59—21no—
123C22⋊C4×C59—21no—
124C22⋊C4×C59—21no—
125C22⋊C4×C59—41no—
126C22⋊C4×C59—41no—
127C42×C59—21no—
128C42×C59—21no—
129C42×C59—21no—
130C42×C59C22×C411yescharacteristic
131C42×C59C2×D411yescharacteristic
132C42×C59C2×D411yescharacteristic
133C42×C59C2×D411yescharacteristic
134C23×C59—21no—
135C23×C59—41no—
136C23×C59#12311yescharacteristic
137Q8×C59—21no—
138Q8×C59—81no—
139Q8×C59#10412yes—
140D4×C59—24no—
141D4×C59—21no—
142D4×C59—42no—
143D4×C59—41no—
144D4×C59—41no—
145D4×C59—81no—
146D4×C59—82no—
147D4×C59#10412yes—
148C2×C4×C59—24no—
149C2×C4×C59—21no—
150C2×C4×C59—21no—
151C2×C4×C59—21no—
152C2×C4×C59—21no—
153C2×C4×C59—21no—
154C2×C4×C59—41no—
155C2×C4×C59—41no—
156C2×C4×C59—41no—
157C2×C4×C59—81no—
158C2×C4×C59—81no—
159C2×C4×C59—82no—
160C2×C4×C59C2×C22⋊C411yescharacteristic
161C2×C4×C59C4×D411yescharacteristic
162C2×C4×C59C4×D411yescharacteristic
163C2×C4×C59#12011yescharacteristic
164C2×C4×C59#12111yescharacteristic
165C2×C4×C59#12111yescharacteristic
166C8×C59—22no—
167C8×C59—22no—
168C8×C59—24no—
169C8×C59—41no—
170C8×C59—41no—
171C8×C59—81no—
172C8×C59—81no—
173#9311C5911yesmaximal, characteristic, direct product factor, Sylow
174C22×C59—21no—
175C22×C59—21no—
176C22×C59—22no—
177C22×C59—21no—
178C22×C59—41no—
179C22×C59—41no—
180C22×C59—81no—
181C22×C59—81no—
182C22×C59—81no—
183C22×C59#38611yescharacteristic
184C4×C59—21no—
185C4×C59—21no—
186C4×C59—21no—
187C4×C59—22no—
188C4×C59—21no—
189C4×C59—21no—
190C4×C59—41no—
191C4×C59—41no—
192C4×C59—81no—
193C4×C59C2×#10411yescharacteristic
194C4×C59C2×#10411yescharacteristic
195#3115C2×C5911yescharacteristic
196#2875C2×C5911yescharacteristic, complemented
197#1530C2×C5911yescharacteristic, complemented
198#1488C2×C5911yescharacteristic, complemented
199#1484C2×C5911yescharacteristic, complemented
200#1302C2×C5911yescharacteristic, complemented
201#1291C2×C5911yescharacteristic, complemented
202C2×C59—41no—
203C2×C59—42no—
204C2×C59—161no—
205C2×C59#188111yescharacteristic
206C2×C59#189611yescharacteristic
207C2×C59#190311yescharacteristic
208C2×#131—21no—
209#532C22×C5911yescharacteristic
210C4×#41C22×C5911yescharacteristic
211#482—21no—
212#475C4×C5911yescharacteristic
213#474C4×C5911yescharacteristic
214#460C4×C5911yescharacteristic
215#459C4×C5911yescharacteristic
216#449—21no—
217#442—21no—
218#440—21no—
219#432C22×C5911yescharacteristic
220#432C22×C5911yescharacteristic
221#431C22×C5911yescharacteristic
222#405—21no—
223#405—22no—
224C4×M16—21no—
225C4×M16C22×C5911yescharacteristic
226C2×#97—21no—
227C2×#97C22×C5911yescharacteristic
228#329—21no—
229#329—21no—
230Q8⋊C8—21no—
231D4⋊C8—21no—
232D4⋊C8—22no—
233C59#931111yescharacteristic, direct product factor, Sylow
234C2×#41—21no—
235C2×#41D4×C5911yescharacteristic
236C2×SD16—21no—
237C2×D8—21no—
238#131—24no—
239#131—24no—
240C2×M16—22no—
241C2×M16—21no—
242C22×C8—22no—
243C22×C8—21no—
244C4⋊Q8C2×C4×C5911yescharacteristic
245#127C2×C4×C5911yescharacteristic
246#124—21no—
247#121—21no—
248#121—21no—
249C4×Q8C2×C4×C5911yescharacteristic
250C4×Q8D4×C5911yescharacteristic
251C4×D4—21no—
252C4×D4—21no—
253C4×D4—21no—
254C4×D4—21no—
255C4×D4C2×C4×C5911yescharacteristic
256C4×D4D4×C5911yescharacteristic
257#117—21no—
258#117D4×C5911yescharacteristic
259C2×C42—21no—
260C2×C42C23×C5911yescharacteristic
261#107—21no—
262#106—21no—
263C4⋊C8—21no—
264C4⋊C8—21no—
265C4⋊C8C2×C4×C5911yescharacteristic
266C4⋊C8C2×C4×C5911yescharacteristic
267#103—21no—
268#102—21no—
269#102—21no—
270#102—21no—
271C22⋊C8—21no—
272C22⋊C8—21no—
273C22⋊C8—21no—
274#97—22no—
275#97—21no—
276#97—21no—
277#97—21no—
278#97—21no—
279#97D4×C5911yescharacteristic
280#97D4×C5911yescharacteristic
281C4×C8—22no—
282C4×C8—21no—
283C4×C8D4×C5912yes—
284#41—22no—
285#41—22no—
286#41—82no—
287C2×Q8—21no—
288C2×Q8C22⋊C4×C5911yescharacteristic
289C2×D4—21no—
290C2×D4—21no—
291C2×D4—21no—
292C2×D4—21no—
293C2×D4—41no—
294C2×D4C22⋊C4×C5911yescharacteristic
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—41no—
299C22×C4C2×D4×C5911yescharacteristic
300C22×C4#41×C5911yescharacteristic
301C22×C4#41×C5911yescharacteristic
302SD16—42no—
303D8—42no—
304M16—28no—
305M16—22no—
306M16—22no—
307C2×C8—28no—
308C2×C8—22no—
309C2×C8—22no—
310C2×C8—21no—
311C2×C8—22no—
312C2×C8—21no—
313C2×C8—21no—
314C2×C8—21no—
315C2×C8—41no—
316C2×C8—41no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4C22⋊C4×C5911yescharacteristic
322C4⋊C4C22⋊C4×C5911yescharacteristic
323C22⋊C4—21no—
324C22⋊C4—21no—
325C22⋊C4—21no—
326C22⋊C4—41no—
327C22⋊C4—41no—
328C42—21no—
329C42—21no—
330C42—21no—
331C42C22×C4×C5911yescharacteristic
332C42C2×D4×C5911yescharacteristic
333C42C2×D4×C5911yescharacteristic
334C42C2×D4×C5911yescharacteristic
335C23—21no—
336C23—41no—
337C23#123×C5911yescharacteristic
338Q8—21no—
339Q8—81no—
340Q8#104×C5912yes—
341D4—24no—
342D4—21no—
343D4—42no—
344D4—41no—
345D4—41no—
346D4—81no—
347D4—82no—
348D4#104×C5912yes—
349C2×C4—24no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—81no—
359C2×C4—81no—
360C2×C4—82no—
361C2×C4C2×C22⋊C4×C5911yescharacteristic
362C2×C4C4×D4×C5911yescharacteristic
363C2×C4C4×D4×C5911yescharacteristic
364C2×C4#120×C5911yescharacteristic
365C2×C4#121×C5911yescharacteristic
366C2×C4#121×C5911yescharacteristic
367C8—22no—
368C8—22no—
369C8—24no—
370C8—41no—
371C8—41no—
372C8—81no—
373C8—81no—
374C22—21no—
375C22—21no—
376C22—22no—
377C22—21no—
378C22—41no—
379C22—41no—
380C22—81no—
381C22—81no—
382C22—81no—
383C22C59×#38611yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—22no—
388C4—21no—
389C4—21no—
390C4—41no—
391C4—41no—
392C4—81no—
393C4C2×#104×C5911yescharacteristic
394C4C2×#104×C5911yescharacteristic
395C2—41no—
396C2—42no—
397C2—161no—
398C2C59×#188111yescharacteristic
399C2C59×#189611yescharacteristic
400C2C59×#190311yescharacteristic
subgroupG/H
center, socleC22×C59#386
commutatorC42C22×C4×C59
Frattini, cosocleC2×C42C23×C59
prime radicalC59×#3115C2
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
2. C59×#2875C2semidirect
3. C59×#1530C2semidirect
4. C59×#1488C2semidirect
5. C59×#1484C2semidirect
6. C59×#1302C2semidirect
7. C59×#1291C2semidirect
173. #9311C59direct (N × H)
196. #2875C2×C59semidirect
197. #1530C2×C59semidirect
198. #1488C2×C59semidirect
199. #1484C2×C59semidirect
200. #1302C2×C59semidirect
201. #1291C2×C59semidirect
233. C59#9311direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#31152
C59×#28752
C59×#15302
C59×#14882
C59×#14842
C59×#13022
C59×#12912
#931159