Finite Group Databasebeta

← C59×#10064 #28422173

Subgroups — C59×#10064 #28422173

Order 15104.

614 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×#487C211yesmaximal, characteristic, complemented
2C2×C59×#461C211yesmaximal, characteristic
3C59×#2563C211yesmaximal, characteristic
4C59×#1988C211yesmaximal, characteristic, complemented
5C2×C59×#333C211yesmaximal, characteristic, complemented
6C2×C59×D4⋊C8C211yesmaximal, characteristic
7C59×#1279C211yesmaximal, characteristic, complemented
8C22×SD16×C59—21no—
9C2×C4⋊Q8×C59C2211yescharacteristic
10C2×C4⋊Q8×C59C2211yescharacteristic
11C2×C4×D4×C59C2211yescharacteristic
12C59×#487—22no—
13C59×#487—22no—
14C59×#461—22no—
15C59×#461—22no—
16C2×C4⋊C8×C59C2211yescharacteristic
17C2×C4⋊C8×C59C2211yescharacteristic
18C2×#103×C59—22no—
19C2×#103×C59—21no—
20C2×C4×C8×C59C2211yescharacteristic
21C59×#393—22no—
22C59×#390—21no—
23C59×#382—21no—
24C59×#380—22no—
25C4×C4⋊C4×C59C2211yescharacteristic
26C59×#340—22no—
27C59×#333—22no—
28C59×D4⋊C8—22no—
29C22×Q8×C59—21no—
30C22×Q8×C59D412yes—
31C22×D4×C59D411yescharacteristic
32C23×C4×C59—21no—
33C2×SD16×C59—24no—
34C2×SD16×C59—42no—
35C2×SD16×C59—42no—
36C22×C8×C59—21no—
37C22×C8×C59—21no—
38C22×C8×C59—21no—
39C4⋊Q8×C59—21no—
40C4⋊Q8×C59—21no—
41C4⋊Q8×C59—21no—
42C4⋊Q8×C59—21no—
43C4⋊Q8×C59—21no—
44C4⋊Q8×C59—21no—
45C4⋊Q8×C59—21no—
46C4⋊Q8×C59D412yes—
47C4×D4×C59—21no—
48C4×D4×C59—21no—
49C4×D4×C59—21no—
50C4×D4×C59—21no—
51C2×C4⋊C4×C59—21no—
52C2×C4⋊C4×C59—21no—
53C2×C4⋊C4×C59—21no—
54C2×C4⋊C4×C59—21no—
55C2×C4⋊C4×C59D412yes—
56C2×C4⋊C4×C59D411yescharacteristic
57C2×C22⋊C4×C59—21no—
58C2×C22⋊C4×C59—24no—
59C2×C42×C59—21no—
60C2×C42×C59C2311yescharacteristic
61C4⋊C8×C59—21no—
62C4⋊C8×C59—21no—
63C4⋊C8×C59—21no—
64C4⋊C8×C59D412yes—
65#103×C59—24no—
66#103×C59—28no—
67C4×C8×C59—21no—
68C4×C8×C59D412yes—
69#95×C59—24no—
70#95×C59—21no—
71C24×C59—21no—
72C2×Q8×C59—22no—
73C2×Q8×C59—22no—
74C2×Q8×C59—22no—
75C2×Q8×C59—44no—
76C2×Q8×C59—41no—
77C2×Q8×C59—41no—
78C2×Q8×C59—41no—
79C2×Q8×C59—41no—
80C2×Q8×C59—41no—
81C2×D4×C59—21no—
82C2×D4×C59—21no—
83C2×D4×C59—21no—
84C2×D4×C59—21no—
85C2×D4×C59—21no—
86C2×D4×C59SD1612yes—
87C22×C4×C59—21no—
88C22×C4×C59—22no—
89C22×C4×C59—22no—
90C22×C4×C59—41no—
91C22×C4×C59—41no—
92C22×C4×C59—41no—
93C22×C4×C59—42no—
94C22×C4×C59—42no—
95C22×C4×C59C2×D411yescharacteristic
96C22×C4×C59C2×D411yescharacteristic
97C22×C4×C59C2×D411yescharacteristic
98SD16×C59—48no—
99C2×C8×C59—22no—
100C2×C8×C59—22no—
101C2×C8×C59—42no—
102C2×C8×C59—41no—
103C2×C8×C59—41no—
104C2×C8×C59—41no—
105C2×C8×C59—42no—
106C4⋊C4×C59—22no—
107C4⋊C4×C59—21no—
108C4⋊C4×C59—22no—
109C4⋊C4×C59—21no—
110C4⋊C4×C59—22no—
111C4⋊C4×C59—22no—
112C4⋊C4×C59—41no—
113C4⋊C4×C59—41no—
114C4⋊C4×C59—41no—
115C4⋊C4×C59—41no—
116C4⋊C4×C59—41no—
117C4⋊C4×C59—41no—
118C22⋊C4×C59—41no—
119C22⋊C4×C59—41no—
120C22⋊C4×C59—84no—
121C42×C59—41no—
122C42×C59—41no—
123C42×C59C2×D411yescharacteristic
124C42×C59C2×D411yescharacteristic
125C42×C59C2×D411yescharacteristic
126C42×C59#4111yescharacteristic
127C23×C59—22no—
128C23×C59—41no—
129C23×C59—41no—
130C23×C59—42no—
131C23×C59—42no—
132C23×C59#12011yescharacteristic
133Q8×C59—44no—
134Q8×C59—42no—
135Q8×C59—42no—
136Q8×C59—82no—
137Q8×C59—81no—
138Q8×C59—81no—
139D4×C59—22no—
140D4×C59—22no—
141D4×C59—41no—
142D4×C59—41no—
143C2×C4×C59—22no—
144C2×C4×C59—41no—
145C2×C4×C59—42no—
146C2×C4×C59—42no—
147C2×C4×C59—42no—
148C2×C4×C59—42no—
149C2×C4×C59—42no—
150C2×C4×C59—42no—
151C2×C4×C59—44no—
152C2×C4×C59—81no—
153C2×C4×C59—81no—
154C2×C4×C59—82no—
155C2×C4×C59—81no—
156C2×C4×C59—81no—
157C2×C4×C59#12011yescharacteristic
158C2×C4×C59#12011yescharacteristic
159C2×C4×C59#12111yescharacteristic
160C2×C4×C59#12111yescharacteristic
161C2×C4×C59#12111yescharacteristic
162C2×C4×C59#12711yescharacteristic
163C2×C4×C59C2×SD1611yescharacteristic
164C2×C4×C59#13511yescharacteristic
165C2×C4×C59#13512yes—
166C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
167C2×C4×C59#13711yescharacteristic
168C2×C4×C59#13712yes—
169C8×C59—42no—
170C8×C59—42no—
171C8×C59—81no—
172#10064C5911yesmaximal, characteristic, direct product factor, Sylow
173C22×C59—44no—
174C22×C59—42no—
175C22×C59—82no—
176C22×C59—81no—
177C22×C59—81no—
178C22×C59#39211yescharacteristic
179C22×C59#44811yescharacteristic
180C22×C59#44911yescharacteristic
181C22×C59#45212yes—
182C22×C59#45512yes—
183C4×C59—21no—
184C4×C59—21no—
185C4×C59—82no—
186C4×C59—82no—
187C4×C59—82no—
188C4×C59—81no—
189C4×C59#45011yescharacteristic
190C4×C59#45211yescharacteristic
191C4×C59#46412yes—
192C4×C59#46511yescharacteristic
193C4×C59#46811yescharacteristic
194C4×C59#49511yescharacteristic
195C4×C59#49711yescharacteristic
196C2×#487C2×C5911yescharacteristic, complemented
197C2×#461C2×C5911yescharacteristic
198#2563C2×C5911yescharacteristic
199#1988C2×C5911yescharacteristic, complemented
200C2×#333C2×C5911yescharacteristic, complemented
201C2×D4⋊C8C2×C5911yescharacteristic
202#1279C2×C5911yescharacteristic, complemented
203C2×C59—82no—
204C2×C59#164312yes—
205C2×C59#164612yes—
206C2×C59#200011yescharacteristic
207C2×C59#200411yescharacteristic
208C2×C59#201511yescharacteristic
209C22×SD16—21no—
210C2×C4⋊Q8C22×C5911yescharacteristic
211C2×C4⋊Q8C22×C5911yescharacteristic
212C2×C4×D4C22×C5911yescharacteristic
213#487—22no—
214#487—22no—
215#461—22no—
216#461—22no—
217C2×C4⋊C8C22×C5911yescharacteristic
218C2×C4⋊C8C22×C5911yescharacteristic
219C2×#103—22no—
220C2×#103—21no—
221C2×C4×C8C22×C5911yescharacteristic
222#393—22no—
223#390—21no—
224#382—21no—
225#380—22no—
226C4×C4⋊C4C22×C5911yescharacteristic
227#340—22no—
228#333—22no—
229D4⋊C8—22no—
230C59#1006411yescharacteristic, direct product factor, Sylow
231C22×Q8—21no—
232C22×Q8D4×C5912yes—
233C22×D4D4×C5911yescharacteristic
234C23×C4—21no—
235C2×SD16—24no—
236C2×SD16—42no—
237C2×SD16—42no—
238C22×C8—21no—
239C22×C8—21no—
240C22×C8—21no—
241C4⋊Q8—21no—
242C4⋊Q8—21no—
243C4⋊Q8—21no—
244C4⋊Q8—21no—
245C4⋊Q8—21no—
246C4⋊Q8—21no—
247C4⋊Q8—21no—
248C4⋊Q8D4×C5912yes—
249C4×D4—21no—
250C4×D4—21no—
251C4×D4—21no—
252C4×D4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4D4×C5911yescharacteristic
258C2×C4⋊C4D4×C5912yes—
259C2×C22⋊C4—21no—
260C2×C22⋊C4—24no—
261C2×C42—21no—
262C2×C42C23×C5911yescharacteristic
263C4⋊C8—21no—
264C4⋊C8—21no—
265C4⋊C8—21no—
266C4⋊C8D4×C5912yes—
267#103—24no—
268#103—28no—
269C4×C8—21no—
270C4×C8D4×C5912yes—
271#95—24no—
272#95—21no—
273C24—21no—
274C2×Q8—22no—
275C2×Q8—22no—
276C2×Q8—22no—
277C2×Q8—44no—
278C2×Q8—41no—
279C2×Q8—41no—
280C2×Q8—41no—
281C2×Q8—41no—
282C2×Q8—41no—
283C2×D4—21no—
284C2×D4—21no—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4SD16×C5912yes—
289C22×C4—21no—
290C22×C4—22no—
291C22×C4—22no—
292C22×C4—41no—
293C22×C4—41no—
294C22×C4—41no—
295C22×C4—42no—
296C22×C4—42no—
297C22×C4C2×D4×C5911yescharacteristic
298C22×C4C2×D4×C5911yescharacteristic
299C22×C4C2×D4×C5911yescharacteristic
300SD16—48no—
301C2×C8—22no—
302C2×C8—22no—
303C2×C8—42no—
304C2×C8—41no—
305C2×C8—41no—
306C2×C8—41no—
307C2×C8—42no—
308C4⋊C4—22no—
309C4⋊C4—21no—
310C4⋊C4—22no—
311C4⋊C4—21no—
312C4⋊C4—22no—
313C4⋊C4—22no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C22⋊C4—41no—
321C22⋊C4—41no—
322C22⋊C4—84no—
323C42—41no—
324C42—41no—
325C42C2×D4×C5911yescharacteristic
326C42C2×D4×C5911yescharacteristic
327C42C2×D4×C5911yescharacteristic
328C42#41×C5911yescharacteristic
329C23—22no—
330C23—41no—
331C23—41no—
332C23—42no—
333C23—42no—
334C23#120×C5911yescharacteristic
335Q8—44no—
336Q8—42no—
337Q8—42no—
338Q8—82no—
339Q8—81no—
340Q8—81no—
341D4—22no—
342D4—22no—
343D4—41no—
344D4—41no—
345C2×C4—22no—
346C2×C4—41no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—44no—
354C2×C4—81no—
355C2×C4—81no—
356C2×C4—82no—
357C2×C4—81no—
358C2×C4—81no—
359C2×C4#120×C5911yescharacteristic
360C2×C4#120×C5911yescharacteristic
361C2×C4#121×C5911yescharacteristic
362C2×C4#121×C5911yescharacteristic
363C2×C4#121×C5911yescharacteristic
364C2×C4#127×C5911yescharacteristic
365C2×C4C2×SD16×C5911yescharacteristic
366C2×C4#135×C5911yescharacteristic
367C2×C4#135×C5912yes—
368C2×C4AGL(1,ℤ/8)×C5911yescharacteristic
369C2×C4#137×C5911yescharacteristic
370C2×C4#137×C5912yes—
371C8—42no—
372C8—42no—
373C8—81no—
374C22—42no—
375C22—44no—
376C22—81no—
377C22—81no—
378C22—82no—
379C22C59×#39211yescharacteristic
380C22C59×#44811yescharacteristic
381C22C59×#44911yescharacteristic
382C22C59×#45212yes—
383C22C59×#45512yes—
384C4—21no—
385C4—21no—
386C4—82no—
387C4—82no—
388C4—81no—
389C4—82no—
390C4C59×#45011yescharacteristic
391C4C59×#45211yescharacteristic
392C4C59×#46412yes—
393C4C59×#46511yescharacteristic
394C4C59×#46811yescharacteristic
395C4C59×#49511yescharacteristic
396C4C59×#49711yescharacteristic
397C2—82no—
398C2C59×#164312yes—
399C2C59×#164612yes—
400C2C59×#200011yescharacteristic
401C2C59×#200411yescharacteristic
402C2C59×#201511yescharacteristic
subgroupG/H
center, socleC23×C59#120
commutator, Frattini, cosocleC2×C42C23×C59
prime radicalC22×D4×C59D4
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
1. C2×C59×#487C2semidirect
4. C59×#1988C2semidirect
5. C2×C59×#333C2semidirect
7. C59×#1279C2semidirect
172. #10064C59direct (N × H)
196. C2×#487C2×C59semidirect
199. #1988C2×C59semidirect
200. C2×#333C2×C59semidirect
202. #1279C2×C59semidirect
230. C59#10064direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C59×#4872
C2×C59×#4612
C59×#25632
C59×#19882
C2×C59×#3332
C2×C59×D4⋊C82
C59×#12792
#1006459