Finite Group Databasebeta

← C59×#10248 #28422357

Subgroups — C59×#10248 #28422357

Order 15104.

604 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3209C211yesmaximal, characteristic, complemented
2C59×#3077C211yesmaximal, characteristic
3C59×#2542C211yesmaximal, characteristic
4C59×#1548C211yesmaximal, characteristic, complemented
5C59×#1503C211yesmaximal, characteristic, complemented
6C59×#1478C211yesmaximal, characteristic
7C59×#1303C211yesmaximal, characteristic, complemented
8C59×#533C2211yescharacteristic
9C2×C4⋊Q8×C59C2211yescharacteristic
10C2×C22⋊Q8×C59—22no—
11C2×C4×D4×C59C2211yescharacteristic
12C59×#494—21no—
13C59×#487—21no—
14C59×#478—22no—
15C59×#476—21no—
16C59×#474—21no—
17C59×#462—22no—
18C59×#451—22no—
19C59×#431C2211yescharacteristic
20C59×#431C2211yescharacteristic
21C59×#428—21no—
22C59×#423C2211yescharacteristic
23C59×#418—21no—
24C59×#399—22no—
25C59×#390—21no—
26C59×#384—21no—
27C4×C4⋊C4×C59C2211yescharacteristic
28C59×#333—22no—
29C59×#328—22no—
30C59×D4⋊C8—22no—
31C22×Q8×C59D412yes—
32C22×D4×C59D411yescharacteristic
33C23×C4×C59—21no—
34C2×Q16×C59—24no—
35C2×M16×C59—21no—
36C4⋊Q8×C59—21no—
37C4⋊Q8×C59—21no—
38C4⋊Q8×C59—21no—
39C4⋊Q8×C59—21no—
40C4⋊Q8×C59D411yescharacteristic
41C4⋊Q8×C59D411yescharacteristic
42#125×C59—21no—
43C22⋊Q8×C59—21no—
44C22⋊Q8×C59—21no—
45C22⋊Q8×C59—48no—
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—24no—
55C2×C4⋊C4×C59—21no—
56C2×C4⋊C4×C59—21no—
57C2×C4⋊C4×C59D411yescharacteristic
58C2×C22⋊C4×C59—24no—
59C2×C22⋊C4×C59—21no—
60C2×C42×C59—21no—
61C2×C42×C59C2311yescharacteristic
62#107×C59—22no—
63#106×C59—22no—
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×C59D412yes—
76C24×C59—21no—
77C2×Q8×C59—22no—
78C2×Q8×C59—21no—
79C2×Q8×C59—21no—
80C2×Q8×C59—22no—
81C2×Q8×C59—44no—
82C2×D4×C59—21no—
83C2×D4×C59—21no—
84C2×D4×C59—21no—
85C2×D4×C59—21no—
86C2×D4×C59—21no—
87C2×D4×C59Q1612yescomplemented
88C22×C4×C59—22no—
89C22×C4×C59—22no—
90C22×C4×C59—21no—
91C22×C4×C59—44no—
92C22×C4×C59—41no—
93C22×C4×C59—41no—
94C22×C4×C59C2×D411yescharacteristic
95C22×C4×C59C2×D411yescharacteristic
96C22×C4×C59C2×D411yescharacteristic
97Q16×C59—84no—
98M16×C59—41no—
99M16×C59—41no—
100C2×C8×C59—22no—
101C2×C8×C59—22no—
102C2×C8×C59—41no—
103C4⋊C4×C59—24no—
104C4⋊C4×C59—21no—
105C4⋊C4×C59—21no—
106C4⋊C4×C59—21no—
107C4⋊C4×C59—21no—
108C4⋊C4×C59—21no—
109C4⋊C4×C59—21no—
110C4⋊C4×C59—48no—
111C4⋊C4×C59—41no—
112C4⋊C4×C59—41no—
113C4⋊C4×C59—41no—
114C4⋊C4×C59—41no—
115C4⋊C4×C59—41no—
116C4⋊C4×C59—41no—
117C22⋊C4×C59—48no—
118C22⋊C4×C59—41no—
119C22⋊C4×C59—41no—
120C22⋊C4×C59—41no—
121C42×C59—41no—
122C42×C59—41no—
123C42×C59—41no—
124C42×C59C2×D411yescharacteristic
125C42×C59C2×D411yescharacteristic
126C42×C59C2×D411yescharacteristic
127C42×C59#4111yescharacteristic
128C23×C59—22no—
129C23×C59—42no—
130C23×C59—42no—
131C23×C59—41no—
132C23×C59—41no—
133C23×C59#12011yescharacteristic
134Q8×C59—42no—
135Q8×C59—44no—
136Q8×C59—81no—
137Q8×C59—82no—
138D4×C59—22no—
139D4×C59—22no—
140D4×C59—41no—
141D4×C59—41no—
142C2×C4×C59—22no—
143C2×C4×C59—24no—
144C2×C4×C59—41no—
145C2×C4×C59—42no—
146C2×C4×C59—42no—
147C2×C4×C59—44no—
148C2×C4×C59—42no—
149C2×C4×C59—41no—
150C2×C4×C59—41no—
151C2×C4×C59—41no—
152C2×C4×C59—42no—
153C2×C4×C59—82no—
154C2×C4×C59—82no—
155C2×C4×C59#12011yescharacteristic
156C2×C4×C59#12011yescharacteristic
157C2×C4×C59#12111yescharacteristic
158C2×C4×C59#12111yescharacteristic
159C2×C4×C59#12111yescharacteristic
160C2×C4×C59#12711yescharacteristic
161C2×C4×C59C2×Q1611yescharacteristic
162C2×C4×C59#13511yescharacteristic
163C2×C4×C59#13711yescharacteristic
164C2×C4×C59#13711yescharacteristic
165C8×C59—42no—
166C8×C59—42no—
167C8×C59—81no—
168#10248C5911yesmaximal, characteristic, direct product factor, Sylow
169C22×C59—21no—
170C22×C59—21no—
171C22×C59—44no—
172C22×C59—42no—
173C22×C59—82no—
174C22×C59—81no—
175C22×C59—81no—
176C22×C59#39211yescharacteristic
177C22×C59#45111yescharacteristic
178C22×C59#45211yescharacteristic
179C4×C59—21no—
180C4×C59—21no—
181C4×C59—21no—
182C4×C59—44no—
183C4×C59—81no—
184C4×C59—82no—
185C4×C59—81no—
186C4×C59—81no—
187C4×C59#45111yescharacteristic
188C4×C59#45211yescharacteristic
189C4×C59#45312yes—
190C4×C59#46711yescharacteristic
191C4×C59#47011yescharacteristic
192#3209C2×C5911yescharacteristic, complemented
193#3077C2×C5911yescharacteristic
194#2542C2×C5911yescharacteristic
195#1548C2×C5911yescharacteristic, complemented
196#1503C2×C5911yescharacteristic, complemented
197#1478C2×C5911yescharacteristic
198#1303C2×C5911yescharacteristic, complemented
199C2×C59—21no—
200C2×C59—21no—
201C2×C59—82no—
202C2×C59#200111yescharacteristic
203C2×C59#200211yescharacteristic
204C2×C59#200911yescharacteristic
205#533C22×C5911yescharacteristic
206C2×C4⋊Q8C22×C5911yescharacteristic
207C2×C22⋊Q8—22no—
208C2×C4×D4C22×C5911yescharacteristic
209#494—21no—
210#487—21no—
211#478—22no—
212#476—21no—
213#474—21no—
214#462—22no—
215#451—22no—
216#431C22×C5911yescharacteristic
217#431C22×C5911yescharacteristic
218#428—21no—
219#423C22×C5911yescharacteristic
220#418—21no—
221#399—22no—
222#390—21no—
223#384—21no—
224C4×C4⋊C4C22×C5911yescharacteristic
225#333—22no—
226#328—22no—
227D4⋊C8—22no—
228C59#1024811yescharacteristic, direct product factor, Sylow
229C22×Q8D4×C5912yes—
230C22×D4D4×C5911yescharacteristic
231C23×C4—21no—
232C2×Q16—24no—
233C2×M16—21no—
234C4⋊Q8—21no—
235C4⋊Q8—21no—
236C4⋊Q8—21no—
237C4⋊Q8—21no—
238C4⋊Q8D4×C5911yescharacteristic
239C4⋊Q8D4×C5911yescharacteristic
240#125—21no—
241C22⋊Q8—21no—
242C22⋊Q8—21no—
243C22⋊Q8—48no—
244C4×Q8—21no—
245C4×Q8—21no—
246C4×D4—21no—
247C4×D4—21no—
248C4×D4—21no—
249C4×D4—21no—
250#117—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—24no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4D4×C5911yescharacteristic
256C2×C22⋊C4—24no—
257C2×C22⋊C4—21no—
258C2×C42—21no—
259C2×C42C23×C5911yescharacteristic
260#107—22no—
261#106—22no—
262C4⋊C8—21no—
263C4⋊C8—21no—
264C4⋊C8D4×C5912yes—
265C4⋊C8D4×C5912yes—
266#103—24no—
267#102—22no—
268#102—22no—
269C22⋊C8—21no—
270C22⋊C8—21no—
271C4×C8—21no—
272C4×C8—21no—
273#95D4×C5912yes—
274C24—21no—
275C2×Q8—22no—
276C2×Q8—21no—
277C2×Q8—21no—
278C2×Q8—22no—
279C2×Q8—44no—
280C2×D4—21no—
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—21no—
284C2×D4—21no—
285C2×D4Q16×C5912yescomplemented
286C22×C4—22no—
287C22×C4—22no—
288C22×C4—21no—
289C22×C4—44no—
290C22×C4—41no—
291C22×C4—41no—
292C22×C4C2×D4×C5911yescharacteristic
293C22×C4C2×D4×C5911yescharacteristic
294C22×C4C2×D4×C5911yescharacteristic
295Q16—84no—
296M16—41no—
297M16—41no—
298C2×C8—22no—
299C2×C8—22no—
300C2×C8—41no—
301C4⋊C4—24no—
302C4⋊C4—21no—
303C4⋊C4—21no—
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—48no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C22⋊C4—48no—
316C22⋊C4—41no—
317C22⋊C4—41no—
318C22⋊C4—41no—
319C42—41no—
320C42—41no—
321C42—41no—
322C42C2×D4×C5911yescharacteristic
323C42C2×D4×C5911yescharacteristic
324C42C2×D4×C5911yescharacteristic
325C42#41×C5911yescharacteristic
326C23—22no—
327C23—42no—
328C23—42no—
329C23—41no—
330C23—41no—
331C23#120×C5911yescharacteristic
332Q8—42no—
333Q8—44no—
334Q8—81no—
335Q8—82no—
336D4—22no—
337D4—22no—
338D4—41no—
339D4—41no—
340C2×C4—22no—
341C2×C4—24no—
342C2×C4—41no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—44no—
346C2×C4—42no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—42no—
351C2×C4—82no—
352C2×C4—82no—
353C2×C4#120×C5911yescharacteristic
354C2×C4#120×C5911yescharacteristic
355C2×C4#121×C5911yescharacteristic
356C2×C4#121×C5911yescharacteristic
357C2×C4#121×C5911yescharacteristic
358C2×C4#127×C5911yescharacteristic
359C2×C4C2×Q16×C5911yescharacteristic
360C2×C4#135×C5911yescharacteristic
361C2×C4#137×C5911yescharacteristic
362C2×C4#137×C5911yescharacteristic
363C8—42no—
364C8—42no—
365C8—81no—
366C22—21no—
367C22—21no—
368C22—44no—
369C22—42no—
370C22—82no—
371C22—81no—
372C22—81no—
373C22C59×#39211yescharacteristic
374C22C59×#45111yescharacteristic
375C22C59×#45211yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—44no—
380C4—81no—
381C4—82no—
382C4—81no—
383C4—81no—
384C4C59×#45111yescharacteristic
385C4C59×#45211yescharacteristic
386C4C59×#45312yes—
387C4C59×#46711yescharacteristic
388C4C59×#47011yescharacteristic
389C2—21no—
390C2—21no—
391C2—82no—
392C2C59×#200111yescharacteristic
393C2C59×#200211yescharacteristic
394C2C59×#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×#3209C2semidirect
4. C59×#1548C2semidirect
5. C59×#1503C2semidirect
7. C59×#1303C2semidirect
87. C2×D4×C59Q16semidirect
168. #10248C59direct (N × H)
192. #3209C2×C59semidirect
195. #1548C2×C59semidirect
196. #1503C2×C59semidirect
198. #1303C2×C59semidirect
228. C59#10248direct (N × H)
285. C2×D4Q16×C59semidirect

Maximal subgroups

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

subgroupindex
C59×#32092
C59×#30772
C59×#25422
C59×#15482
C59×#15032
C59×#14782
C59×#13032
#1024859