Finite Group Databasebeta

← C59×#10071 #28422180

Subgroups — C59×#10071 #28422180

Order 15104.

654 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×#486C211yesmaximal, characteristic
2C2×C59×#475C211yesmaximal, characteristic, complemented
3C59×#2548C211yesmaximal, characteristic
4C59×#1981C211yesmaximal, characteristic, complemented
5C2×C59×#331C211yesmaximal, characteristic
6C2×C59×Q8⋊C8C211yesmaximal, characteristic, complemented
7C59×#1279C211yesmaximal, characteristic, complemented
8C2×C4⋊Q8×C59C2211yescharacteristic
9C2×#127×C59C2211yescharacteristic
10C2×#124×C59—21no—
11C2×C4×Q8×C59C2211yescharacteristic
12C59×#486—22no—
13C59×#486—22no—
14C59×#475—22no—
15C59×#475—22no—
16C2×#106×C59—21no—
17C2×C4⋊C8×C59C2211yescharacteristic
18C2×C4⋊C8×C59C2211yescharacteristic
19C2×#103×C59—21no—
20C2×#103×C59—22no—
21C2×#102×C59—22no—
22C2×C4×C8×C59C2211yescharacteristic
23C59×#394—22no—
24C59×#390—21no—
25C59×#390—22no—
26C4×C4⋊C4×C59C2211yescharacteristic
27C59×#331—22no—
28C59×Q8⋊C8—22no—
29C22×Q8×C59—21no—
30C22×Q8×C59D411yescharacteristic
31C22×D4×C59—21no—
32C22×D4×C59—21no—
33C22×D4×C59D412yes—
34C22×C8×C59—21no—
35C22×C8×C59—21no—
36C22×C8×C59—21no—
37C4⋊Q8×C59—21no—
38C4⋊Q8×C59—21no—
39C4⋊Q8×C59—21no—
40C4⋊Q8×C59D412yes—
41#127×C59—21no—
42#127×C59—21no—
43#127×C59—21no—
44#127×C59—21no—
45#124×C59—42no—
46#124×C59—42no—
47C4×Q8×C59—21no—
48C4×Q8×C59—21no—
49C4×Q8×C59—21no—
50C4×Q8×C59—21no—
51C2×C4⋊C4×C59—21no—
52C2×C4⋊C4×C59—21no—
53C2×C4⋊C4×C59—21no—
54C2×C4⋊C4×C59D412yes—
55C2×C4⋊C4×C59D411yescharacteristic
56C2×C22⋊C4×C59—24no—
57C2×C22⋊C4×C59—24no—
58C2×C42×C59—21no—
59C2×C42×C59—21no—
60C2×C42×C59C2311yescharacteristic
61#106×C59—24no—
62C4⋊C8×C59—21no—
63C4⋊C8×C59—21no—
64C4⋊C8×C59—21no—
65C4⋊C8×C59D412yes—
66#103×C59—24no—
67#103×C59—44no—
68#102×C59—28no—
69C4×C8×C59—21no—
70C4×C8×C59D412yes—
71#95×C59—21no—
72C24×C59—22no—
73C2×Q8×C59—21no—
74C2×Q8×C59—21no—
75C2×Q8×C59—21no—
76C2×Q8×C59—22no—
77C2×Q8×C59—21no—
78C2×Q8×C59—21no—
79C2×Q8×C59—41no—
80C2×Q8×C59—42no—
81C2×Q8×C59—42no—
82C2×Q8×C59SD1612yes—
83C2×D4×C59—22no—
84C2×D4×C59—22no—
85C2×D4×C59—44no—
86C2×D4×C59—41no—
87C2×D4×C59—41no—
88C2×D4×C59—41no—
89C2×D4×C59—41no—
90C2×D4×C59—41no—
91C2×D4×C59—41no—
92C2×D4×C59—42no—
93C2×D4×C59—41no—
94C2×D4×C59—42no—
95C2×D4×C59—41no—
96C22×C4×C59—21no—
97C22×C4×C59—22no—
98C22×C4×C59—21no—
99C22×C4×C59—41no—
100C22×C4×C59C2×D411yescharacteristic
101C22×C4×C59C2×D411yescharacteristic
102C22×C4×C59C2×D411yescharacteristic
103C2×C8×C59—22no—
104C2×C8×C59—22no—
105C2×C8×C59—42no—
106C2×C8×C59—41no—
107C2×C8×C59—41no—
108C2×C8×C59—41no—
109C2×C8×C59—42no—
110C4⋊C4×C59—22no—
111C4⋊C4×C59—22no—
112C4⋊C4×C59—21no—
113C4⋊C4×C59—21no—
114C4⋊C4×C59—22no—
115C4⋊C4×C59—22no—
116C4⋊C4×C59—41no—
117C4⋊C4×C59—41no—
118C4⋊C4×C59—41no—
119C4⋊C4×C59—41no—
120C22⋊C4×C59—48no—
121C22⋊C4×C59—84no—
122C42×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—42no—
131C23×C59—44no—
132C23×C59—42no—
133C23×C59—42no—
134C23×C59—44no—
135C23×C59#12011yescharacteristic
136Q8×C59—22no—
137Q8×C59—22no—
138Q8×C59—41no—
139Q8×C59—41no—
140Q8×C59—44no—
141Q8×C59—81no—
142Q8×C59—81no—
143D4×C59—44no—
144D4×C59—82no—
145D4×C59—81no—
146D4×C59—81no—
147D4×C59—82no—
148D4×C59—81no—
149D4×C59—81no—
150D4×C59—81no—
151D4×C59—81no—
152C2×C4×C59—22no—
153C2×C4×C59—22no—
154C2×C4×C59—41no—
155C2×C4×C59—41no—
156C2×C4×C59—41no—
157C2×C4×C59—42no—
158C2×C4×C59—42no—
159C2×C4×C59—42no—
160C2×C4×C59—42no—
161C2×C4×C59—42no—
162C2×C4×C59—82no—
163C2×C4×C59#12011yescharacteristic
164C2×C4×C59#12011yescharacteristic
165C2×C4×C59#12111yescharacteristic
166C2×C4×C59#12111yescharacteristic
167C2×C4×C59#12111yescharacteristic
168C2×C4×C59#12711yescharacteristic
169C2×C4×C59C2×SD1611yescharacteristic
170C2×C4×C59#13511yescharacteristic
171C2×C4×C59#13512yes—
172C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
173C2×C4×C59AGL(1,ℤ/8)12yes—
174C2×C4×C59#13711yescharacteristic
175C8×C59—42no—
176C8×C59—42no—
177C8×C59—81no—
178#10071C5911yesmaximal, characteristic, direct product factor, Sylow
179C22×C59—84no—
180C22×C59—84no—
181C22×C59—82no—
182C22×C59—82no—
183C22×C59—82no—
184C22×C59#39211yescharacteristic
185C22×C59#44912yes—
186C22×C59#45011yescharacteristic
187C22×C59#45211yescharacteristic
188C22×C59#45512yes—
189C4×C59—21no—
190C4×C59—21no—
191C4×C59—42no—
192C4×C59—82no—
193C4×C59—81no—
194C4×C59—82no—
195C4×C59#44811yescharacteristic
196C4×C59#44911yescharacteristic
197C4×C59#46312yes—
198C4×C59#46511yescharacteristic
199C4×C59#46811yescharacteristic
200C4×C59#49511yescharacteristic
201C4×C59#49611yescharacteristic
202C2×#486C2×C5911yescharacteristic
203C2×#475C2×C5911yescharacteristic, complemented
204#2548C2×C5911yescharacteristic
205#1981C2×C5911yescharacteristic, complemented
206C2×#331C2×C5911yescharacteristic
207C2×Q8⋊C8C2×C5911yescharacteristic, complemented
208#1279C2×C5911yescharacteristic, complemented
209C2×C59—162no—
210C2×C59#164012yes—
211C2×C59#164212yes—
212C2×C59#200011yescharacteristic
213C2×C59#200411yescharacteristic
214C2×C59#201211yescharacteristic
215C2×C4⋊Q8C22×C5911yescharacteristic
216C2×#127C22×C5911yescharacteristic
217C2×#124—21no—
218C2×C4×Q8C22×C5911yescharacteristic
219#486—22no—
220#486—22no—
221#475—22no—
222#475—22no—
223C2×#106—21no—
224C2×C4⋊C8C22×C5911yescharacteristic
225C2×C4⋊C8C22×C5911yescharacteristic
226C2×#103—21no—
227C2×#103—22no—
228C2×#102—22no—
229C2×C4×C8C22×C5911yescharacteristic
230#394—22no—
231#390—22no—
232#390—21no—
233C4×C4⋊C4C22×C5911yescharacteristic
234#331—22no—
235Q8⋊C8—22no—
236C59#1007111yescharacteristic, direct product factor, Sylow
237C22×Q8—21no—
238C22×Q8D4×C5911yescharacteristic
239C22×D4—21no—
240C22×D4—21no—
241C22×D4D4×C5912yes—
242C22×C8—21no—
243C22×C8—21no—
244C22×C8—21no—
245C4⋊Q8—21no—
246C4⋊Q8—21no—
247C4⋊Q8—21no—
248C4⋊Q8D4×C5912yes—
249#127—21no—
250#127—21no—
251#127—21no—
252#127—21no—
253#124—42no—
254#124—42no—
255C4×Q8—21no—
256C4×Q8—21no—
257C4×Q8—21no—
258C4×Q8—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4D4×C5911yescharacteristic
263C2×C4⋊C4D4×C5912yes—
264C2×C22⋊C4—24no—
265C2×C22⋊C4—24no—
266C2×C42—21no—
267C2×C42—21no—
268C2×C42C23×C5911yescharacteristic
269#106—24no—
270C4⋊C8—21no—
271C4⋊C8—21no—
272C4⋊C8—21no—
273C4⋊C8D4×C5912yes—
274#103—24no—
275#103—44no—
276#102—28no—
277C4×C8—21no—
278C4×C8D4×C5912yes—
279#95—21no—
280C24—22no—
281C2×Q8—21no—
282C2×Q8—21no—
283C2×Q8—21no—
284C2×Q8—22no—
285C2×Q8—21no—
286C2×Q8—21no—
287C2×Q8—41no—
288C2×Q8—42no—
289C2×Q8—42no—
290C2×Q8SD16×C5912yes—
291C2×D4—22no—
292C2×D4—22no—
293C2×D4—44no—
294C2×D4—41no—
295C2×D4—41no—
296C2×D4—41no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—41no—
300C2×D4—42no—
301C2×D4—41no—
302C2×D4—42no—
303C2×D4—41no—
304C22×C4—21no—
305C22×C4—22no—
306C22×C4—21no—
307C22×C4—41no—
308C22×C4C2×D4×C5911yescharacteristic
309C22×C4C2×D4×C5911yescharacteristic
310C22×C4C2×D4×C5911yescharacteristic
311C2×C8—22no—
312C2×C8—22no—
313C2×C8—42no—
314C2×C8—41no—
315C2×C8—41no—
316C2×C8—41no—
317C2×C8—42no—
318C4⋊C4—22no—
319C4⋊C4—22no—
320C4⋊C4—21no—
321C4⋊C4—21no—
322C4⋊C4—22no—
323C4⋊C4—22no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C22⋊C4—48no—
329C22⋊C4—84no—
330C42—41no—
331C42—41no—
332C42—41no—
333C42—41no—
334C42C2×D4×C5911yescharacteristic
335C42C2×D4×C5911yescharacteristic
336C42C2×D4×C5911yescharacteristic
337C42#41×C5911yescharacteristic
338C23—42no—
339C23—44no—
340C23—42no—
341C23—42no—
342C23—44no—
343C23#120×C5911yescharacteristic
344Q8—22no—
345Q8—22no—
346Q8—41no—
347Q8—41no—
348Q8—44no—
349Q8—81no—
350Q8—81no—
351D4—44no—
352D4—82no—
353D4—81no—
354D4—81no—
355D4—82no—
356D4—81no—
357D4—81no—
358D4—81no—
359D4—81no—
360C2×C4—22no—
361C2×C4—22no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—82no—
371C2×C4#120×C5911yescharacteristic
372C2×C4#120×C5911yescharacteristic
373C2×C4#121×C5911yescharacteristic
374C2×C4#121×C5911yescharacteristic
375C2×C4#121×C5911yescharacteristic
376C2×C4#127×C5911yescharacteristic
377C2×C4C2×SD16×C5911yescharacteristic
378C2×C4#135×C5911yescharacteristic
379C2×C4#135×C5912yes—
380C2×C4AGL(1,ℤ/8)×C5911yescharacteristic
381C2×C4AGL(1,ℤ/8)×C5912yes—
382C2×C4#137×C5911yescharacteristic
383C8—42no—
384C8—42no—
385C8—81no—
386C22—82no—
387C22—82no—
388C22—82no—
389C22—84no—
390C22—84no—
391C22C59×#39211yescharacteristic
392C22C59×#44912yes—
393C22C59×#45011yescharacteristic
394C22C59×#45211yescharacteristic
395C22C59×#45512yes—
396C4—21no—
397C4—21no—
398C4—42no—
399C4—81no—
400C4—82no—
401C4—82no—
402C4C59×#44811yescharacteristic
403C4C59×#44911yescharacteristic
404C4C59×#46312yes—
405C4C59×#46511yescharacteristic
406C4C59×#46811yescharacteristic
407C4C59×#49511yescharacteristic
408C4C59×#49611yescharacteristic
409C2—162no—
410C2C59×#164012yes—
411C2C59×#164212yes—
412C2C59×#200011yescharacteristic
413C2C59×#200411yescharacteristic
414C2C59×#201211yescharacteristic
subgroupG/H
center, socleC23×C59#120
commutator, Frattini, cosocleC2×C42C23×C59
prime radicalC2×#127×C59C22
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C59 ◁ C2×C42×C59 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C59×#475C2semidirect
4. C59×#1981C2semidirect
6. C2×C59×Q8⋊C8C2semidirect
7. C59×#1279C2semidirect
178. #10071C59direct (N × H)
203. C2×#475C2×C59semidirect
205. #1981C2×C59semidirect
207. C2×Q8⋊C8C2×C59semidirect
208. #1279C2×C59semidirect
236. C59#10071direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C59×#4862
C2×C59×#4752
C59×#25482
C59×#19812
C2×C59×#3312
C2×C59×Q8⋊C82
C59×#12792
#1007159