Finite Group Databasebeta

← C59×#10247 #28422356

Subgroups — C59×#10247 #28422356

Order 15104.

556 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3229C211yesmaximal, characteristic, complemented
2C59×#3077C211yesmaximal, characteristic
3C59×#2547C211yesmaximal, characteristic
4C59×#1546C211yesmaximal, characteristic, complemented
5C59×#1503C211yesmaximal, characteristic, complemented
6C59×#1478C211yesmaximal, characteristic
7C59×#1303C211yesmaximal, characteristic, complemented
8C59×#533C2211yescharacteristic
9C2×C4⋊Q8×C59C2211yescharacteristic
10C2×#124×C59—21no—
11C2×C4×D4×C59C2211yescharacteristic
12C59×#498—21no—
13C59×#487—21no—
14C59×#483—22no—
15C59×#478—22no—
16C59×#476—21no—
17C59×#475—22no—
18C59×#474—21no—
19C59×#431C2211yescharacteristic
20C59×#431C2211yescharacteristic
21C59×#428—21no—
22C59×#423C2211yescharacteristic
23C59×#418—21no—
24C59×#397—22no—
25C59×#391—21no—
26C59×#380—22no—
27C4×C4⋊C4×C59C2211yescharacteristic
28C59×#332—22no—
29C59×#328—22no—
30C59×D4⋊C8—22no—
31C22×Q8×C59—21no—
32C22×D4×C59D411yescharacteristic
33C23×C4×C59—21no—
34C2×M16×C59—21no—
35C4⋊Q8×C59—21no—
36C4⋊Q8×C59—21no—
37C4⋊Q8×C59—21no—
38C4⋊Q8×C59—21no—
39C4⋊Q8×C59D411yescharacteristic
40C4⋊Q8×C59D411yescharacteristic
41#125×C59—21no—
42#124×C59—42no—
43#124×C59—42no—
44C22⋊Q8×C59—21no—
45C22⋊Q8×C59—21no—
46C4×Q8×C59—21no—
47C4×Q8×C59—21no—
48C4×D4×C59—21no—
49C4×D4×C59—21no—
50C4×D4×C59—21no—
51C4×D4×C59—21no—
52#117×C59—21no—
53C2×C4⋊C4×C59—21no—
54C2×C4⋊C4×C59—21no—
55C2×C4⋊C4×C59D412yes—
56C2×C4⋊C4×C59D411yescharacteristic
57C2×C22⋊C4×C59—24no—
58C2×C22⋊C4×C59—21no—
59C2×C42×C59—21no—
60C2×C42×C59C2311yescharacteristic
61#107×C59—22no—
62#106×C59—22no—
63#106×C59—24no—
64C4⋊C8×C59—21no—
65C4⋊C8×C59—21no—
66C4⋊C8×C59D412yes—
67C4⋊C8×C59D412yes—
68#103×C59—24no—
69#102×C59—22no—
70#102×C59—22no—
71C22⋊C8×C59—21no—
72C22⋊C8×C59—21no—
73C4×C8×C59—21no—
74C4×C8×C59—21no—
75#95×C59—24no—
76#95×C59D412yes—
77C24×C59—21no—
78C2×Q8×C59—21no—
79C2×Q8×C59—21no—
80C2×Q8×C59—41no—
81C2×Q8×C59—41no—
82C2×Q8×C59—41no—
83C2×Q8×C59—41no—
84C2×Q8×C59—41no—
85C2×Q8×C59—41no—
86C2×D4×C59—21no—
87C2×D4×C59—21no—
88C2×D4×C59—21no—
89C2×D4×C59—21no—
90C2×D4×C59—21no—
91C2×D4×C59SD1612yes—
92C22×C4×C59—21no—
93C22×C4×C59—22no—
94C22×C4×C59—22no—
95C22×C4×C59—44no—
96C22×C4×C59—41no—
97C22×C4×C59—41no—
98C22×C4×C59C2×D411yescharacteristic
99C22×C4×C59C2×D411yescharacteristic
100C22×C4×C59C2×D411yescharacteristic
101M16×C59—41no—
102M16×C59—41no—
103C2×C8×C59—22no—
104C2×C8×C59—22no—
105C2×C8×C59—41no—
106C4⋊C4×C59—21no—
107C4⋊C4×C59—21no—
108C4⋊C4×C59—22no—
109C4⋊C4×C59—21no—
110C4⋊C4×C59—21no—
111C4⋊C4×C59—21no—
112C4⋊C4×C59—22no—
113C4⋊C4×C59—21no—
114C4⋊C4×C59—42no—
115C4⋊C4×C59—41no—
116C4⋊C4×C59—41no—
117C4⋊C4×C59—41no—
118C4⋊C4×C59—41no—
119C22⋊C4×C59—48no—
120C22⋊C4×C59—41no—
121C22⋊C4×C59—41no—
122C22⋊C4×C59—41no—
123C42×C59—41no—
124C42×C59—41no—
125C42×C59—41no—
126C42×C59C2×D411yescharacteristic
127C42×C59C2×D411yescharacteristic
128C42×C59C2×D411yescharacteristic
129C42×C59#4111yescharacteristic
130C23×C59—22no—
131C23×C59—42no—
132C23×C59—42no—
133C23×C59—41no—
134C23×C59—41no—
135C23×C59#12011yescharacteristic
136Q8×C59—42no—
137Q8×C59—81no—
138Q8×C59—81no—
139Q8×C59—81no—
140Q8×C59—81no—
141Q8×C59—81no—
142D4×C59—22no—
143D4×C59—22no—
144D4×C59—41no—
145D4×C59—41no—
146C2×C4×C59—22no—
147C2×C4×C59—41no—
148C2×C4×C59—42no—
149C2×C4×C59—42no—
150C2×C4×C59—42no—
151C2×C4×C59—41no—
152C2×C4×C59—41no—
153C2×C4×C59—41no—
154C2×C4×C59—42no—
155C2×C4×C59—42no—
156C2×C4×C59—42no—
157C2×C4×C59—42no—
158C2×C4×C59—82no—
159C2×C4×C59—82no—
160C2×C4×C59#12011yescharacteristic
161C2×C4×C59#12011yescharacteristic
162C2×C4×C59#12111yescharacteristic
163C2×C4×C59#12111yescharacteristic
164C2×C4×C59#12111yescharacteristic
165C2×C4×C59#12711yescharacteristic
166C2×C4×C59C2×SD1611yescharacteristic
167C2×C4×C59#13511yescharacteristic
168C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
169C2×C4×C59#13711yescharacteristic
170C8×C59—42no—
171C8×C59—42no—
172C8×C59—81no—
173#10247C5911yesmaximal, characteristic, direct product factor, Sylow
174C22×C59—21no—
175C22×C59—21no—
176C22×C59—44no—
177C22×C59—42no—
178C22×C59—82no—
179C22×C59—81no—
180C22×C59—81no—
181C22×C59#39211yescharacteristic
182C22×C59#45011yescharacteristic
183C22×C59#45211yescharacteristic
184C4×C59—21no—
185C4×C59—21no—
186C4×C59—21no—
187C4×C59—82no—
188C4×C59—82no—
189C4×C59—81no—
190C4×C59—81no—
191C4×C59—81no—
192C4×C59#44811yescharacteristic
193C4×C59#44911yescharacteristic
194C4×C59#45412yes—
195C4×C59#46511yescharacteristic
196C4×C59#46811yescharacteristic
197#3229C2×C5911yescharacteristic, complemented
198#3077C2×C5911yescharacteristic
199#2547C2×C5911yescharacteristic
200#1546C2×C5911yescharacteristic, complemented
201#1503C2×C5911yescharacteristic, complemented
202#1478C2×C5911yescharacteristic
203#1303C2×C5911yescharacteristic, complemented
204C2×C59—21no—
205C2×C59—21no—
206C2×C59—82no—
207C2×C59#200011yescharacteristic
208C2×C59#200311yescharacteristic
209C2×C59#200911yescharacteristic
210#533C22×C5911yescharacteristic
211C2×C4⋊Q8C22×C5911yescharacteristic
212C2×#124—21no—
213C2×C4×D4C22×C5911yescharacteristic
214#498—21no—
215#487—21no—
216#483—22no—
217#478—22no—
218#476—21no—
219#475—22no—
220#474—21no—
221#431C22×C5911yescharacteristic
222#431C22×C5911yescharacteristic
223#428—21no—
224#423C22×C5911yescharacteristic
225#418—21no—
226#397—22no—
227#391—21no—
228#380—22no—
229C4×C4⋊C4C22×C5911yescharacteristic
230#332—22no—
231#328—22no—
232D4⋊C8—22no—
233C59#1024711yescharacteristic, direct product factor, Sylow
234C22×Q8—21no—
235C22×D4D4×C5911yescharacteristic
236C23×C4—21no—
237C2×M16—21no—
238C4⋊Q8—21no—
239C4⋊Q8—21no—
240C4⋊Q8—21no—
241C4⋊Q8—21no—
242C4⋊Q8D4×C5911yescharacteristic
243C4⋊Q8D4×C5911yescharacteristic
244#125—21no—
245#124—42no—
246#124—42no—
247C22⋊Q8—21no—
248C22⋊Q8—21no—
249C4×Q8—21no—
250C4×Q8—21no—
251C4×D4—21no—
252C4×D4—21no—
253C4×D4—21no—
254C4×D4—21no—
255#117—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4D4×C5911yescharacteristic
259C2×C4⋊C4D4×C5912yes—
260C2×C22⋊C4—24no—
261C2×C22⋊C4—21no—
262C2×C42—21no—
263C2×C42C23×C5911yescharacteristic
264#107—22no—
265#106—22no—
266#106—24no—
267C4⋊C8—21no—
268C4⋊C8—21no—
269C4⋊C8D4×C5912yes—
270C4⋊C8D4×C5912yes—
271#103—24no—
272#102—22no—
273#102—22no—
274C22⋊C8—21no—
275C22⋊C8—21no—
276C4×C8—21no—
277C4×C8—21no—
278#95—24no—
279#95D4×C5912yes—
280C24—21no—
281C2×Q8—21no—
282C2×Q8—21no—
283C2×Q8—41no—
284C2×Q8—41no—
285C2×Q8—41no—
286C2×Q8—41no—
287C2×Q8—41no—
288C2×Q8—41no—
289C2×D4—21no—
290C2×D4—21no—
291C2×D4—21no—
292C2×D4—21no—
293C2×D4—21no—
294C2×D4SD16×C5912yes—
295C22×C4—21no—
296C22×C4—22no—
297C22×C4—22no—
298C22×C4—44no—
299C22×C4—41no—
300C22×C4—41no—
301C22×C4C2×D4×C5911yescharacteristic
302C22×C4C2×D4×C5911yescharacteristic
303C22×C4C2×D4×C5911yescharacteristic
304M16—41no—
305M16—41no—
306C2×C8—22no—
307C2×C8—22no—
308C2×C8—41no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—22no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—22no—
316C4⋊C4—21no—
317C4⋊C4—42no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C22⋊C4—48no—
323C22⋊C4—41no—
324C22⋊C4—41no—
325C22⋊C4—41no—
326C42—41no—
327C42—41no—
328C42—41no—
329C42C2×D4×C5911yescharacteristic
330C42C2×D4×C5911yescharacteristic
331C42C2×D4×C5911yescharacteristic
332C42#41×C5911yescharacteristic
333C23—22no—
334C23—42no—
335C23—42no—
336C23—41no—
337C23—41no—
338C23#120×C5911yescharacteristic
339Q8—42no—
340Q8—81no—
341Q8—81no—
342Q8—81no—
343Q8—81no—
344Q8—81no—
345D4—22no—
346D4—22no—
347D4—41no—
348D4—41no—
349C2×C4—22no—
350C2×C4—41no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—82no—
362C2×C4—82no—
363C2×C4#120×C5911yescharacteristic
364C2×C4#120×C5911yescharacteristic
365C2×C4#121×C5911yescharacteristic
366C2×C4#121×C5911yescharacteristic
367C2×C4#121×C5911yescharacteristic
368C2×C4#127×C5911yescharacteristic
369C2×C4C2×SD16×C5911yescharacteristic
370C2×C4#135×C5911yescharacteristic
371C2×C4AGL(1,ℤ/8)×C5911yescharacteristic
372C2×C4#137×C5911yescharacteristic
373C8—42no—
374C8—42no—
375C8—81no—
376C22—21no—
377C22—21no—
378C22—44no—
379C22—42no—
380C22—82no—
381C22—81no—
382C22—81no—
383C22C59×#39211yescharacteristic
384C22C59×#45011yescharacteristic
385C22C59×#45211yescharacteristic
386C4—21no—
387C4—21no—
388C4—21no—
389C4—82no—
390C4—82no—
391C4—81no—
392C4—81no—
393C4—81no—
394C4C59×#44811yescharacteristic
395C4C59×#44911yescharacteristic
396C4C59×#45412yes—
397C4C59×#46511yescharacteristic
398C4C59×#46811yescharacteristic
399C2—21no—
400C2—21no—
401C2—82no—
402C2C59×#200011yescharacteristic
403C2C59×#200311yescharacteristic
404C2C59×#200911yescharacteristic
subgroupG/H
center, socleC22×C59#392
commutator, Frattini, cosocleC2×C42C23×C59
prime radicalC22×D4×C59D4
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C59 ◁ C2×C42×C59 ◁ G

Complements

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

NH ≅ G/Ntype
1. C59×#3229C2semidirect
4. C59×#1546C2semidirect
5. C59×#1503C2semidirect
7. C59×#1303C2semidirect
173. #10247C59direct (N × H)
197. #3229C2×C59semidirect
200. #1546C2×C59semidirect
201. #1503C2×C59semidirect
203. #1303C2×C59semidirect
233. C59#10247direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#32292
C59×#30772
C59×#25472
C59×#15462
C59×#15032
C59×#14782
C59×#13032
#1024759