Finite Group Databasebeta

← C59×#10035 #28422144

Subgroups — C59×#10035 #28422144

Order 15104.

498 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3135C211yesmaximal, characteristic
2C59×#3104C211yesmaximal, characteristic, complemented
3C59×#3103C211yesmaximal, characteristic
4C59×#1985C211yesmaximal, characteristic, complemented
5C59×#1481C211yesmaximal, characteristic, complemented
6C59×#1480C211yesmaximal, characteristic
7C59×#1275C211yesmaximal, characteristic, complemented
8C59×#533C2211yescharacteristic
9C59×#532C2211yescharacteristic
10C2×C4×Q8×C59C2211yescharacteristic
11C59×#491—21no—
12C59×#490—21no—
13C59×#489—21no—
14C59×#489—21no—
15C59×#484—21no—
16C59×#481—21no—
17C59×#477—21no—
18C59×#475—21no—
19C59×#462—21no—
20C59×#460—21no—
21C59×#451—21no—
22C59×#448—21no—
23C4×Q16×C59—22no—
24C4×SD16×C59—22no—
25C59×#431C2211yescharacteristic
26C59×#431C2211yescharacteristic
27C2×C4⋊C8×C59C2211yescharacteristic
28C59×#416—22no—
29C2×#97×C59C2211yescharacteristic
30C59×#336—22no—
31C59×Q8⋊C8—22no—
32C59×D4⋊C8—22no—
33C2×#41×C59—21no—
34C22×Q8×C59D411yescharacteristic
35C2×Q16×C59—22no—
36C2×SD16×C59—22no—
37C22×C8×C59—21no—
38C22×C8×C59D412yes—
39C4⋊Q8×C59D411yescharacteristic
40C4⋊Q8×C59D411yescharacteristic
41C4⋊Q8×C59D411yescharacteristic
42#127×C59D411yescharacteristic
43#125×C59—21no—
44#124×C59—21no—
45C22⋊Q8×C59—21no—
46C22⋊Q8×C59—21no—
47#121×C59—21no—
48#121×C59—21no—
49C4×Q8×C59—21no—
50C4×Q8×C59—21no—
51C4×Q8×C59—21no—
52C4×Q8×C59—21no—
53C4×Q8×C59—21no—
54C4×Q8×C59—21no—
55C4×D4×C59—21no—
56C4×D4×C59—21no—
57#117×C59—21no—
58C2×C4⋊C4×C59—21no—
59C2×C4⋊C4×C59D411yescharacteristic
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×C59—21no—
67C4⋊C8×C59—21no—
68#103×C59—22no—
69#103×C59—22no—
70#103×C59—22no—
71#103×C59—22no—
72#103×C59—22no—
73#102×C59—22no—
74#102×C59—22no—
75#102×C59—22no—
76C22⋊C8×C59—21no—
77C22⋊C8×C59—21no—
78#97×C59—21no—
79#97×C59—21no—
80C4×C8×C59D412yes—
81C4×C8×C59D412yes—
82#41×C59—42no—
83#41×C59—42no—
84C2×Q8×C59—21no—
85C2×Q8×C59—21no—
86C2×Q8×C59—21no—
87C2×Q8×C59—21no—
88C2×Q8×C59—21no—
89C2×Q8×C59—42no—
90C2×D4×C59—21no—
91C2×D4×C59—21no—
92C2×D4×C59—21no—
93C2×D4×C59—41no—
94C22×C4×C59—21no—
95C22×C4×C59—21no—
96C22×C4×C59—41no—
97C22×C4×C59C2×D411yescharacteristic
98C22×C4×C59C2×D411yescharacteristic
99C22×C4×C59#4111yescharacteristic
100Q16×C59—44no—
101SD16×C59—44no—
102C2×C8×C59—22no—
103C2×C8×C59—22no—
104C2×C8×C59—22no—
105C2×C8×C59—22no—
106C2×C8×C59—22no—
107C2×C8×C59—41no—
108C2×C8×C59—42no—
109C4⋊C4×C59—21no—
110C4⋊C4×C59—21no—
111C4⋊C4×C59—21no—
112C4⋊C4×C59—21no—
113C4⋊C4×C59—21no—
114C4⋊C4×C59—21no—
115C4⋊C4×C59—21no—
116C4⋊C4×C59—21no—
117C4⋊C4×C59—41no—
118C4⋊C4×C59—41no—
119C4⋊C4×C59—41no—
120C4⋊C4×C59—41no—
121C22⋊C4×C59—41no—
122C22⋊C4×C59—41no—
123C22⋊C4×C59—41no—
124C42×C59—41no—
125C42×C59—41no—
126C42×C59—41no—
127C42×C59C2×D411yescharacteristic
128C42×C59C2×D411yescharacteristic
129C42×C59C2×D411yescharacteristic
130C42×C59C2×D411yescharacteristic
131C23×C59—41no—
132C23×C59#12111yescharacteristic
133Q8×C59—22no—
134Q8×C59—22no—
135Q8×C59—41no—
136Q8×C59—41no—
137Q8×C59—42no—
138Q8×C59—42no—
139Q8×C59—42no—
140D4×C59—42no—
141D4×C59—42no—
142D4×C59—42no—
143D4×C59—82no—
144C2×C4×C59—22no—
145C2×C4×C59—41no—
146C2×C4×C59—41no—
147C2×C4×C59—41no—
148C2×C4×C59—41no—
149C2×C4×C59—42no—
150C2×C4×C59—41no—
151C2×C4×C59—41no—
152C2×C4×C59—41no—
153C2×C4×C59—41no—
154C2×C4×C59—81no—
155C2×C4×C59—81no—
156C2×C4×C59#12011yescharacteristic
157C2×C4×C59#12011yescharacteristic
158C2×C4×C59#12011yescharacteristic
159C2×C4×C59#12111yescharacteristic
160C2×C4×C59#12111yescharacteristic
161C2×C4×C59#12711yescharacteristic
162C2×C4×C59#13512yes—
163C2×C4×C59#13712yes—
164C8×C59—42no—
165C8×C59—42no—
166C8×C59—42no—
167C8×C59—81no—
168#10035C5911yesmaximal, characteristic, direct product factor, Sylow
169C22×C59—21no—
170C22×C59—21no—
171C22×C59—81no—
172C22×C59—81no—
173C22×C59—81no—
174C22×C59#39211yescharacteristic
175C22×C59#46412yes—
176C4×C59—21no—
177C4×C59—21no—
178C4×C59—21no—
179C4×C59—21no—
180C4×C59—42no—
181C4×C59—81no—
182C4×C59—81no—
183C4×C59—81no—
184C4×C59—81no—
185C4×C59#45212yes—
186C4×C59#49511yescharacteristic
187C4×C59#49711yescharacteristic
188#3135C2×C5911yescharacteristic
189#3104C2×C5911yescharacteristic, complemented
190#3103C2×C5911yescharacteristic
191#1985C2×C5911yescharacteristic, complemented
192#1481C2×C5911yescharacteristic, complemented
193#1480C2×C5911yescharacteristic
194#1275C2×C5911yescharacteristic, complemented
195C2×C59—22no—
196C2×C59—161no—
197C2×C59#201011yescharacteristic
198C2×C59#201511yescharacteristic
199C2×C59#201711yescharacteristic
200#533C22×C5911yescharacteristic
201#532C22×C5911yescharacteristic
202C2×C4×Q8C22×C5911yescharacteristic
203#491—21no—
204#490—21no—
205#489—21no—
206#489—21no—
207#484—21no—
208#481—21no—
209#477—21no—
210#475—21no—
211#462—21no—
212#460—21no—
213#451—21no—
214#448—21no—
215C4×Q16—22no—
216C4×SD16—22no—
217#431C22×C5911yescharacteristic
218#431C22×C5911yescharacteristic
219C2×C4⋊C8C22×C5911yescharacteristic
220#416—22no—
221C2×#97C22×C5911yescharacteristic
222#336—22no—
223Q8⋊C8—22no—
224D4⋊C8—22no—
225C59#1003511yescharacteristic, direct product factor, Sylow
226C2×#41—21no—
227C22×Q8D4×C5911yescharacteristic
228C2×Q16—22no—
229C2×SD16—22no—
230C22×C8—21no—
231C22×C8D4×C5912yes—
232C4⋊Q8D4×C5911yescharacteristic
233C4⋊Q8D4×C5911yescharacteristic
234C4⋊Q8D4×C5911yescharacteristic
235#127D4×C5911yescharacteristic
236#125—21no—
237#124—21no—
238C22⋊Q8—21no—
239C22⋊Q8—21no—
240#121—21no—
241#121—21no—
242C4×Q8—21no—
243C4×Q8—21no—
244C4×Q8—21no—
245C4×Q8—21no—
246C4×Q8—21no—
247C4×Q8—21no—
248C4×D4—21no—
249C4×D4—21no—
250#117—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4D4×C5911yescharacteristic
253C2×C42—21no—
254C2×C42C23×C5911yescharacteristic
255#107—22no—
256#106—22no—
257C4⋊C8—21no—
258C4⋊C8—21no—
259C4⋊C8—21no—
260C4⋊C8—21no—
261#103—22no—
262#103—22no—
263#103—22no—
264#103—22no—
265#103—22no—
266#102—22no—
267#102—22no—
268#102—22no—
269C22⋊C8—21no—
270C22⋊C8—21no—
271#97—21no—
272#97—21no—
273C4×C8D4×C5912yes—
274C4×C8D4×C5912yes—
275#41—42no—
276#41—42no—
277C2×Q8—21no—
278C2×Q8—21no—
279C2×Q8—21no—
280C2×Q8—21no—
281C2×Q8—21no—
282C2×Q8—42no—
283C2×D4—21no—
284C2×D4—21no—
285C2×D4—21no—
286C2×D4—41no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—41no—
290C22×C4C2×D4×C5911yescharacteristic
291C22×C4C2×D4×C5911yescharacteristic
292C22×C4#41×C5911yescharacteristic
293Q16—44no—
294SD16—44no—
295C2×C8—22no—
296C2×C8—22no—
297C2×C8—22no—
298C2×C8—22no—
299C2×C8—22no—
300C2×C8—41no—
301C2×C8—42no—
302C4⋊C4—21no—
303C4⋊C4—21no—
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C22⋊C4—41no—
315C22⋊C4—41no—
316C22⋊C4—41no—
317C42—41no—
318C42—41no—
319C42—41no—
320C42C2×D4×C5911yescharacteristic
321C42C2×D4×C5911yescharacteristic
322C42C2×D4×C5911yescharacteristic
323C42C2×D4×C5911yescharacteristic
324C23—41no—
325C23#121×C5911yescharacteristic
326Q8—22no—
327Q8—22no—
328Q8—41no—
329Q8—41no—
330Q8—42no—
331Q8—42no—
332Q8—42no—
333D4—42no—
334D4—42no—
335D4—42no—
336D4—82no—
337C2×C4—22no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—42no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—81no—
348C2×C4—81no—
349C2×C4#120×C5911yescharacteristic
350C2×C4#120×C5911yescharacteristic
351C2×C4#120×C5911yescharacteristic
352C2×C4#121×C5911yescharacteristic
353C2×C4#121×C5911yescharacteristic
354C2×C4#127×C5911yescharacteristic
355C2×C4#135×C5912yes—
356C2×C4#137×C5912yes—
357C8—42no—
358C8—42no—
359C8—42no—
360C8—81no—
361C22—21no—
362C22—21no—
363C22—81no—
364C22—81no—
365C22—81no—
366C22C59×#39211yescharacteristic
367C22C59×#46412yes—
368C4—21no—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—42no—
373C4—81no—
374C4—81no—
375C4—81no—
376C4—81no—
377C4C59×#45212yes—
378C4C59×#49511yescharacteristic
379C4C59×#49711yescharacteristic
380C2—22no—
381C2—161no—
382C2C59×#201011yescharacteristic
383C2C59×#201511yescharacteristic
384C2C59×#201711yescharacteristic
subgroupG/H
centerC2×C4×C59#127
commutator, Frattini, cosocleC2×C42C23×C59
socleC22×C59#392
prime radicalC59×#532C22
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C59 ◁ C2×C42×C59 ◁ G

Complements

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

NH ≅ G/Ntype
2. C59×#3104C2semidirect
4. C59×#1985C2semidirect
5. C59×#1481C2semidirect
7. C59×#1275C2semidirect
168. #10035C59direct (N × H)
189. #3104C2×C59semidirect
191. #1985C2×C59semidirect
192. #1481C2×C59semidirect
194. #1275C2×C59semidirect
225. C59#10035direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#31352
C59×#31042
C59×#31032
C59×#19852
C59×#14812
C59×#14802
C59×#12752
#1003559