Finite Group Databasebeta

← C59×#10050 #28422159

Subgroups — C59×#10050 #28422159

Order 15104.

702 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×#486C211yesmaximal, characteristic, complemented
2C2×C59×#459C211yesmaximal, characteristic
3C59×#2547C211yesmaximal, characteristic, complemented
4C59×#1982C211yesmaximal, characteristic, complemented
5C2×C59×#332C211yesmaximal, characteristic, complemented
6C2×C59×D4⋊C8C211yesmaximal, characteristic, complemented
7C59×#1279C211yesmaximal, characteristic, complemented
8C22×D8×C59—21no—
9C2×C4⋊Q8×C59C2211yescharacteristic
10C2×#127×C59C2211yescharacteristic
11C2×#124×C59—21no—
12C2×C4×D4×C59C2211yescharacteristic
13C59×#486—22no—
14C59×#486—22no—
15C59×#459—22no—
16C59×#459—22no—
17C2×C4⋊C8×C59C2211yescharacteristic
18C2×C4⋊C8×C59C2211yescharacteristic
19C2×#102×C59—21no—
20C2×#102×C59—22no—
21C2×#102×C59—22no—
22C2×C4×C8×C59C2211yescharacteristic
23C59×#397—22no—
24C59×#391—21no—
25C59×#380—22no—
26C4×C4⋊C4×C59C2211yescharacteristic
27C59×#332—22no—
28C59×D4⋊C8—22no—
29C22×Q8×C59—21no—
30C22×D4×C59—21no—
31C22×D4×C59—21no—
32C22×D4×C59—21no—
33C22×D4×C59D411yescharacteristic
34C23×C4×C59—21no—
35C2×D8×C59—24no—
36C2×D8×C59—42no—
37C2×D8×C59—42no—
38C22×C8×C59—21no—
39C22×C8×C59—21no—
40C22×C8×C59—21no—
41C4⋊Q8×C59—21no—
42C4⋊Q8×C59—21no—
43C4⋊Q8×C59—21no—
44C4⋊Q8×C59—21no—
45#127×C59—21no—
46#127×C59—21no—
47#127×C59—21no—
48#127×C59D412yes—
49#124×C59—42no—
50#124×C59—42no—
51C4×D4×C59—21no—
52C4×D4×C59—21no—
53C4×D4×C59—21no—
54C4×D4×C59—21no—
55C2×C4⋊C4×C59—21no—
56C2×C4⋊C4×C59D412yes—
57C2×C4⋊C4×C59D411yescharacteristic
58C2×C4⋊C4×C59D412yes—
59C2×C22⋊C4×C59—24no—
60C2×C22⋊C4×C59—21no—
61C2×C42×C59—21no—
62C2×C42×C59C2311yescharacteristic
63C4⋊C8×C59—21no—
64C4⋊C8×C59—21no—
65C4⋊C8×C59—21no—
66C4⋊C8×C59D412yes—
67#102×C59—24no—
68#102×C59—28no—
69#102×C59—44no—
70C4×C8×C59—21no—
71C4×C8×C59D412yes—
72#95×C59—24no—
73#95×C59—21no—
74C24×C59—21no—
75C24×C59—41no—
76C2×Q8×C59—41no—
77C2×Q8×C59—41no—
78C2×Q8×C59—41no—
79C2×Q8×C59—41no—
80C2×Q8×C59—41no—
81C2×Q8×C59—41no—
82C2×D4×C59—21no—
83C2×D4×C59—22no—
84C2×D4×C59—22no—
85C2×D4×C59—21no—
86C2×D4×C59—22no—
87C2×D4×C59—21no—
88C2×D4×C59—21no—
89C2×D4×C59—21no—
90C2×D4×C59—44no—
91C2×D4×C59—41no—
92C2×D4×C59—41no—
93C2×D4×C59—41no—
94C2×D4×C59—41no—
95C2×D4×C59—41no—
96C2×D4×C59—42no—
97C2×D4×C59—42no—
98C2×D4×C59—41no—
99C2×D4×C59—41no—
100C2×D4×C59D812yes—
101C22×C4×C59—21no—
102C22×C4×C59—22no—
103C22×C4×C59—22no—
104C22×C4×C59—41no—
105C22×C4×C59—41no—
106C22×C4×C59—42no—
107C22×C4×C59—42no—
108C22×C4×C59C2×D411yescharacteristic
109C22×C4×C59C2×D411yescharacteristic
110C22×C4×C59C2×D411yescharacteristic
111D8×C59—48no—
112C2×C8×C59—22no—
113C2×C8×C59—22no—
114C2×C8×C59—42no—
115C2×C8×C59—41no—
116C2×C8×C59—41no—
117C2×C8×C59—41no—
118C2×C8×C59—42no—
119C4⋊C4×C59—21no—
120C4⋊C4×C59—22no—
121C4⋊C4×C59—21no—
122C4⋊C4×C59—22no—
123C4⋊C4×C59—22no—
124C4⋊C4×C59—22no—
125C4⋊C4×C59—41no—
126C4⋊C4×C59—41no—
127C22⋊C4×C59—48no—
128C22⋊C4×C59—41no—
129C22⋊C4×C59—41no—
130C42×C59—41no—
131C42×C59—41no—
132C42×C59C2×D411yescharacteristic
133C42×C59C2×D411yescharacteristic
134C42×C59C2×D411yescharacteristic
135C42×C59#4111yescharacteristic
136C23×C59—22no—
137C23×C59—41no—
138C23×C59—42no—
139C23×C59—41no—
140C23×C59—42no—
141C23×C59—42no—
142C23×C59—81no—
143C23×C59—81no—
144C23×C59—82no—
145C23×C59—82no—
146C23×C59#12011yescharacteristic
147Q8×C59—81no—
148Q8×C59—81no—
149Q8×C59—81no—
150Q8×C59—81no—
151D4×C59—22no—
152D4×C59—22no—
153D4×C59—44no—
154D4×C59—42no—
155D4×C59—41no—
156D4×C59—42no—
157D4×C59—44no—
158D4×C59—41no—
159D4×C59—82no—
160D4×C59—81no—
161D4×C59—81no—
162D4×C59—81no—
163D4×C59—81no—
164C2×C4×C59—22no—
165C2×C4×C59—41no—
166C2×C4×C59—42no—
167C2×C4×C59—42no—
168C2×C4×C59—42no—
169C2×C4×C59—42no—
170C2×C4×C59—42no—
171C2×C4×C59—42no—
172C2×C4×C59—42no—
173C2×C4×C59—82no—
174C2×C4×C59—81no—
175C2×C4×C59—81no—
176C2×C4×C59#12011yescharacteristic
177C2×C4×C59#12011yescharacteristic
178C2×C4×C59#12111yescharacteristic
179C2×C4×C59#12111yescharacteristic
180C2×C4×C59#12111yescharacteristic
181C2×C4×C59#12711yescharacteristic
182C2×C4×C59C2×D811yescharacteristic
183C2×C4×C59#13511yescharacteristic
184C2×C4×C59#13512yes—
185C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
186C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
187C2×C4×C59AGL(1,ℤ/8)12yes—
188C8×C59—42no—
189C8×C59—42no—
190C8×C59—81no—
191#10050C5911yesmaximal, characteristic, direct product factor, Sylow
192C22×C59—44no—
193C22×C59—42no—
194C22×C59—82no—
195C22×C59—81no—
196C22×C59—81no—
197C22×C59—82no—
198C22×C59—82no—
199C22×C59—82no—
200C22×C59—162no—
201C22×C59—162no—
202C22×C59#39211yescharacteristic
203C22×C59#44711yescharacteristic
204C22×C59#44912yes—
205C22×C59#44911yescharacteristic
206C22×C59#45412yes—
207C4×C59—21no—
208C4×C59—21no—
209C4×C59—82no—
210C4×C59—82no—
211C4×C59—81no—
212C4×C59#44711yescharacteristic
213C4×C59#44911yescharacteristic
214C4×C59#46312yes—
215C4×C59#46611yescharacteristic
216C4×C59#46911yescharacteristic
217C4×C59#49511yescharacteristic
218C4×C59#49611yescharacteristic
219C2×#486C2×C5911yescharacteristic, complemented
220C2×#459C2×C5911yescharacteristic
221#2547C2×C5911yescharacteristic, complemented
222#1982C2×C5911yescharacteristic, complemented
223C2×#332C2×C5911yescharacteristic, complemented
224C2×D4⋊C8C2×C5911yescharacteristic, complemented
225#1279C2×C5911yescharacteristic, complemented
226C2×C59—82no—
227C2×C59—162no—
228C2×C59#162512yes—
229C2×C59#162812yes—
230C2×C59#199911yescharacteristic
231C2×C59#200311yescharacteristic
232C2×C59#201211yescharacteristic
233C22×D8—21no—
234C2×C4⋊Q8C22×C5911yescharacteristic
235C2×#127C22×C5911yescharacteristic
236C2×#124—21no—
237C2×C4×D4C22×C5911yescharacteristic
238#486—22no—
239#486—22no—
240#459—22no—
241#459—22no—
242C2×C4⋊C8C22×C5911yescharacteristic
243C2×C4⋊C8C22×C5911yescharacteristic
244C2×#102—22no—
245C2×#102—21no—
246C2×#102—22no—
247C2×C4×C8C22×C5911yescharacteristic
248#397—22no—
249#391—21no—
250#380—22no—
251C4×C4⋊C4C22×C5911yescharacteristic
252#332—22no—
253D4⋊C8—22no—
254C59#1005011yescharacteristic, direct product factor, Sylow
255C22×Q8—21no—
256C22×D4—21no—
257C22×D4—21no—
258C22×D4—21no—
259C22×D4D4×C5911yescharacteristic
260C23×C4—21no—
261C2×D8—24no—
262C2×D8—42no—
263C2×D8—42no—
264C22×C8—21no—
265C22×C8—21no—
266C22×C8—21no—
267C4⋊Q8—21no—
268C4⋊Q8—21no—
269C4⋊Q8—21no—
270C4⋊Q8—21no—
271#127—21no—
272#127—21no—
273#127—21no—
274#127D4×C5912yes—
275#124—42no—
276#124—42no—
277C4×D4—21no—
278C4×D4—21no—
279C4×D4—21no—
280C4×D4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4D4×C5911yescharacteristic
283C2×C4⋊C4D4×C5912yes—
284C2×C4⋊C4D4×C5912yes—
285C2×C22⋊C4—24no—
286C2×C22⋊C4—21no—
287C2×C42—21no—
288C2×C42C23×C5911yescharacteristic
289C4⋊C8—21no—
290C4⋊C8—21no—
291C4⋊C8—21no—
292C4⋊C8D4×C5912yes—
293#102—24no—
294#102—28no—
295#102—44no—
296C4×C8—21no—
297C4×C8D4×C5912yes—
298#95—24no—
299#95—21no—
300C24—21no—
301C24—41no—
302C2×Q8—41no—
303C2×Q8—41no—
304C2×Q8—41no—
305C2×Q8—41no—
306C2×Q8—41no—
307C2×Q8—41no—
308C2×D4—21no—
309C2×D4—22no—
310C2×D4—22no—
311C2×D4—21no—
312C2×D4—22no—
313C2×D4—21no—
314C2×D4—21no—
315C2×D4—21no—
316C2×D4—44no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—41no—
322C2×D4—42no—
323C2×D4—42no—
324C2×D4—41no—
325C2×D4—41no—
326C2×D4D8×C5912yes—
327C22×C4—21no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—42no—
333C22×C4—42no—
334C22×C4C2×D4×C5911yescharacteristic
335C22×C4C2×D4×C5911yescharacteristic
336C22×C4C2×D4×C5911yescharacteristic
337D8—48no—
338C2×C8—22no—
339C2×C8—22no—
340C2×C8—42no—
341C2×C8—41no—
342C2×C8—41no—
343C2×C8—41no—
344C2×C8—42no—
345C4⋊C4—21no—
346C4⋊C4—22no—
347C4⋊C4—21no—
348C4⋊C4—22no—
349C4⋊C4—22no—
350C4⋊C4—22no—
351C4⋊C4—41no—
352C4⋊C4—41no—
353C22⋊C4—48no—
354C22⋊C4—41no—
355C22⋊C4—41no—
356C42—41no—
357C42—41no—
358C42C2×D4×C5911yescharacteristic
359C42C2×D4×C5911yescharacteristic
360C42C2×D4×C5911yescharacteristic
361C42#41×C5911yescharacteristic
362C23—22no—
363C23—41no—
364C23—42no—
365C23—41no—
366C23—42no—
367C23—42no—
368C23—81no—
369C23—81no—
370C23—82no—
371C23—82no—
372C23#120×C5911yescharacteristic
373Q8—81no—
374Q8—81no—
375Q8—81no—
376Q8—81no—
377D4—22no—
378D4—22no—
379D4—44no—
380D4—42no—
381D4—41no—
382D4—42no—
383D4—44no—
384D4—41no—
385D4—82no—
386D4—81no—
387D4—81no—
388D4—81no—
389D4—81no—
390C2×C4—22no—
391C2×C4—41no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—82no—
400C2×C4—81no—
401C2×C4—81no—
402C2×C4#120×C5911yescharacteristic
403C2×C4#120×C5911yescharacteristic
404C2×C4#121×C5911yescharacteristic
405C2×C4#121×C5911yescharacteristic
406C2×C4#121×C5911yescharacteristic
407C2×C4#127×C5911yescharacteristic
408C2×C4C2×D8×C5911yescharacteristic
409C2×C4#135×C5911yescharacteristic
410C2×C4#135×C5912yes—
411C2×C4AGL(1,ℤ/8)×C5911yescharacteristic
412C2×C4AGL(1,ℤ/8)×C5911yescharacteristic
413C2×C4AGL(1,ℤ/8)×C5912yes—
414C8—42no—
415C8—42no—
416C8—81no—
417C22—42no—
418C22—44no—
419C22—81no—
420C22—81no—
421C22—82no—
422C22—82no—
423C22—82no—
424C22—82no—
425C22—162no—
426C22—162no—
427C22C59×#39211yescharacteristic
428C22C59×#44711yescharacteristic
429C22C59×#44911yescharacteristic
430C22C59×#44912yes—
431C22C59×#45412yes—
432C4—21no—
433C4—21no—
434C4—82no—
435C4—81no—
436C4—82no—
437C4C59×#44711yescharacteristic
438C4C59×#44911yescharacteristic
439C4C59×#46312yes—
440C4C59×#46611yescharacteristic
441C4C59×#46911yescharacteristic
442C4C59×#49511yescharacteristic
443C4C59×#49611yescharacteristic
444C2—82no—
445C2—162no—
446C2C59×#162512yes—
447C2C59×#162812yes—
448C2C59×#199911yescharacteristic
449C2C59×#200311yescharacteristic
450C2C59×#201211yescharacteristic
subgroupG/H
center, socleC23×C59#120
commutator, Frattini, cosocleC2×C42C23×C59
prime radicalC2×C59×#459C2
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×#486C2semidirect
3. C59×#2547C2semidirect
4. C59×#1982C2semidirect
5. C2×C59×#332C2semidirect
6. C2×C59×D4⋊C8C2semidirect
7. C59×#1279C2semidirect
191. #10050C59direct (N × H)
219. C2×#486C2×C59semidirect
221. #2547C2×C59semidirect
222. #1982C2×C59semidirect
223. C2×#332C2×C59semidirect
224. C2×D4⋊C8C2×C59semidirect
225. #1279C2×C59semidirect
254. C59#10050direct (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×#4592
C59×#25472
C59×#19822
C2×C59×#3322
C2×C59×D4⋊C82
C59×#12792
#1005059