Finite Group Databasebeta

← C59×#10236 #28422345

Subgroups — C59×#10236 #28422345

Order 15104.

628 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×#477C211yesmaximal, characteristic, complemented
2C2×C59×#476C211yesmaximal, characteristic
3C59×#2538C211yesmaximal, characteristic
4C59×#1956C211yesmaximal, characteristic, complemented
5C2×C59×Q8⋊C8C211yesmaximal, characteristic, complemented
6C2×C59×D4⋊C8C211yesmaximal, characteristic
7C59×#1296C211yesmaximal, characteristic, complemented
8C2×C4⋊Q8×C59C2211yescharacteristic
9C2×C22⋊Q8×C59—21no—
10C2×C4×Q8×C59C2211yescharacteristic
11C2×C4×D4×C59C2211yescharacteristic
12C59×#477—22no—
13C59×#477—22no—
14C59×#476—22no—
15C59×#476—22no—
16C2×#107×C59—21no—
17C2×#106×C59—21no—
18C2×C4⋊C8×C59C2211yescharacteristic
19C2×C4⋊C8×C59C2211yescharacteristic
20C2×#103×C59—21no—
21C2×#103×C59—22no—
22C2×#102×C59—21no—
23C2×C4×C8×C59C2211yescharacteristic
24C59×#396—22no—
25C59×#390—21no—
26C59×#389—21no—
27C59×#384C2211yescharacteristic
28C59×#380—21no—
29C59×Q8⋊C8—22no—
30C59×D4⋊C8—22no—
31C22×Q8×C59—21no—
32C22×Q8×C59D411yescharacteristic
33C22×D4×C59D411yescharacteristic
34C23×C4×C59—21no—
35C22×C8×C59—21no—
36C22×C8×C59—21no—
37C22×C8×C59—21no—
38C4⋊Q8×C59—21no—
39C4⋊Q8×C59—21no—
40C4⋊Q8×C59—21no—
41C4⋊Q8×C59D412yes—
42C22⋊Q8×C59—42no—
43C22⋊Q8×C59—42no—
44C4×Q8×C59—21no—
45C4×Q8×C59—21no—
46C4×Q8×C59—21no—
47C4×Q8×C59—21no—
48C4×D4×C59—21no—
49C4×D4×C59—21no—
50C4×D4×C59—21no—
51C4×D4×C59—21no—
52C2×C4⋊C4×C59—21no—
53C2×C4⋊C4×C59—21no—
54C2×C4⋊C4×C59—22no—
55C2×C4⋊C4×C59—21no—
56C2×C4⋊C4×C59—21no—
57C2×C4⋊C4×C59—21no—
58C2×C4⋊C4×C59D411yescharacteristic
59C2×C4⋊C4×C59D411yescharacteristic
60C2×C4⋊C4×C59D412yes—
61C2×C22⋊C4×C59—22no—
62C2×C22⋊C4×C59—21no—
63C2×C22⋊C4×C59—22no—
64C2×C42×C59—21no—
65C2×C42×C59C2311yescharacteristic
66#107×C59—24no—
67#106×C59—24no—
68C4⋊C8×C59—21no—
69C4⋊C8×C59—21no—
70C4⋊C8×C59D412yes—
71C4⋊C8×C59D412yes—
72#103×C59—24no—
73#103×C59—44no—
74#102×C59—24no—
75C4×C8×C59—21no—
76C4×C8×C59—21no—
77#95×C59—22no—
78C24×C59—21no—
79C2×Q8×C59—21no—
80C2×Q8×C59—21no—
81C2×Q8×C59—21no—
82C2×Q8×C59—22no—
83C2×Q8×C59—21no—
84C2×Q8×C59—21no—
85C2×Q8×C59—42no—
86C2×Q8×C59—42no—
87C2×Q8×C59—41no—
88C2×Q8×C59SD1612yes—
89C2×D4×C59—21no—
90C2×D4×C59—21no—
91C2×D4×C59—21no—
92C2×D4×C59—21no—
93C2×D4×C59—21no—
94C2×D4×C59Q1612yes—
95C22×C4×C59—21no—
96C22×C4×C59—21no—
97C22×C4×C59—21no—
98C22×C4×C59—22no—
99C22×C4×C59—41no—
100C22×C4×C59—41no—
101C22×C4×C59—41no—
102C22×C4×C59—41no—
103C22×C4×C59—41no—
104C22×C4×C59—41no—
105C22×C4×C59—41no—
106C22×C4×C59C2×D411yescharacteristic
107C22×C4×C59C2×D411yescharacteristic
108C22×C4×C59C2×D411yescharacteristic
109C2×C8×C59—22no—
110C2×C8×C59—22no—
111C2×C8×C59—22no—
112C2×C8×C59—41no—
113C2×C8×C59—41no—
114C2×C8×C59—41no—
115C2×C8×C59—41no—
116C2×C8×C59—41no—
117C2×C8×C59—41no—
118C4⋊C4×C59—22no—
119C4⋊C4×C59—22no—
120C4⋊C4×C59—21no—
121C4⋊C4×C59—21no—
122C4⋊C4×C59—21no—
123C4⋊C4×C59—21no—
124C4⋊C4×C59—44no—
125C4⋊C4×C59—42no—
126C4⋊C4×C59—41no—
127C4⋊C4×C59—41no—
128C4⋊C4×C59—41no—
129C4⋊C4×C59—41no—
130C4⋊C4×C59—41no—
131C4⋊C4×C59—41no—
132C4⋊C4×C59—41no—
133C4⋊C4×C59—41no—
134C22⋊C4×C59—44no—
135C22⋊C4×C59—41no—
136C22⋊C4×C59—41no—
137C22⋊C4×C59—82no—
138C42×C59—41no—
139C42×C59—41no—
140C42×C59C2×D411yescharacteristic
141C42×C59C2×D411yescharacteristic
142C42×C59C2×D411yescharacteristic
143C42×C59#4111yescharacteristic
144C23×C59—22no—
145C23×C59—41no—
146C23×C59—41no—
147C23×C59—41no—
148C23×C59—41no—
149C23×C59—41no—
150C23×C59—41no—
151C23×C59#12011yescharacteristic
152Q8×C59—22no—
153Q8×C59—22no—
154Q8×C59—44no—
155Q8×C59—41no—
156Q8×C59—41no—
157Q8×C59—82no—
158D4×C59—22no—
159D4×C59—22no—
160D4×C59—41no—
161D4×C59—41no—
162C2×C4×C59—21no—
163C2×C4×C59—21no—
164C2×C4×C59—22no—
165C2×C4×C59—41no—
166C2×C4×C59—41no—
167C2×C4×C59—41no—
168C2×C4×C59—41no—
169C2×C4×C59—42no—
170C2×C4×C59—42no—
171C2×C4×C59—41no—
172C2×C4×C59—42no—
173C2×C4×C59—41no—
174C2×C4×C59—41no—
175C2×C4×C59—42no—
176C2×C4×C59—41no—
177C2×C4×C59—81no—
178C2×C4×C59—81no—
179C2×C4×C59—81no—
180C2×C4×C59—81no—
181C2×C4×C59—81no—
182C2×C4×C59—81no—
183C2×C4×C59#12011yescharacteristic
184C2×C4×C59#12011yescharacteristic
185C2×C4×C59#12111yescharacteristic
186C2×C4×C59#12111yescharacteristic
187C2×C4×C59#12111yescharacteristic
188C2×C4×C59#12711yescharacteristic
189C2×C4×C59C2×SD1611yescharacteristic
190C2×C4×C59C2×Q1611yescharacteristic
191C2×C4×C59#13511yescharacteristic
192C2×C4×C59#13511yescharacteristic
193C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
194C2×C4×C59#13711yescharacteristic
195C2×C4×C59#13711yescharacteristic
196C2×C4×C59#13711yescharacteristic
197C8×C59—42no—
198C8×C59—42no—
199C8×C59—42no—
200#10236C5911yesmaximal, characteristic, direct product factor, Sylow
201C22×C59—42no—
202C22×C59—42no—
203C22×C59—42no—
204C22×C59—81no—
205C22×C59—81no—
206C22×C59—81no—
207C22×C59—81no—
208C22×C59#39211yescharacteristic
209C22×C59#45011yescharacteristic
210C22×C59#45111yescharacteristic
211C22×C59#45211yescharacteristic
212C22×C59#45211yescharacteristic
213C22×C59#45311yescharacteristic
214C22×C59#45411yescharacteristic
215C4×C59—21no—
216C4×C59—21no—
217C4×C59—42no—
218C4×C59—82no—
219C4×C59—81no—
220C4×C59—81no—
221C4×C59—82no—
222C4×C59#44811yescharacteristic
223C4×C59#44911yescharacteristic
224C4×C59#45111yescharacteristic
225C4×C59#45211yescharacteristic
226C4×C59#46511yescharacteristic
227C4×C59#46711yescharacteristic
228C4×C59#46811yescharacteristic
229C4×C59#47011yescharacteristic
230C2×#477C2×C5911yescharacteristic, complemented
231C2×#476C2×C5911yescharacteristic
232#2538C2×C5911yescharacteristic
233#1956C2×C5911yescharacteristic, complemented
234C2×Q8⋊C8C2×C5911yescharacteristic, complemented
235C2×D4⋊C8C2×C5911yescharacteristic
236#1296C2×C5911yescharacteristic, complemented
237C2×C59—82no—
238C2×C59#163111yescharacteristic
239C2×C59#163211yescharacteristic
240C2×C59#163711yescharacteristic
241C2×C59#163811yescharacteristic
242C2×C59#200011yescharacteristic
243C2×C59#200111yescharacteristic
244C2×C59#200611yescharacteristic
245C2×C4⋊Q8C22×C5911yescharacteristic
246C2×C22⋊Q8—21no—
247C2×C4×Q8C22×C5911yescharacteristic
248C2×C4×D4C22×C5911yescharacteristic
249#477—22no—
250#477—22no—
251#476—22no—
252#476—22no—
253C2×#107—21no—
254C2×#106—21no—
255C2×C4⋊C8C22×C5911yescharacteristic
256C2×C4⋊C8C22×C5911yescharacteristic
257C2×#103—21no—
258C2×#103—22no—
259C2×#102—21no—
260C2×C4×C8C22×C5911yescharacteristic
261#396—22no—
262#390—21no—
263#389—21no—
264#384C22×C5911yescharacteristic
265#380—21no—
266Q8⋊C8—22no—
267D4⋊C8—22no—
268C59#1023611yescharacteristic, direct product factor, Sylow
269C22×Q8—21no—
270C22×Q8D4×C5911yescharacteristic
271C22×D4D4×C5911yescharacteristic
272C23×C4—21no—
273C22×C8—21no—
274C22×C8—21no—
275C22×C8—21no—
276C4⋊Q8—21no—
277C4⋊Q8—21no—
278C4⋊Q8—21no—
279C4⋊Q8D4×C5912yes—
280C22⋊Q8—42no—
281C22⋊Q8—42no—
282C4×Q8—21no—
283C4×Q8—21no—
284C4×Q8—21no—
285C4×Q8—21no—
286C4×D4—21no—
287C4×D4—21no—
288C4×D4—21no—
289C4×D4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4D4×C5911yescharacteristic
297C2×C4⋊C4D4×C5911yescharacteristic
298C2×C4⋊C4D4×C5912yes—
299C2×C22⋊C4—22no—
300C2×C22⋊C4—21no—
301C2×C22⋊C4—22no—
302C2×C42—21no—
303C2×C42C23×C5911yescharacteristic
304#107—24no—
305#106—24no—
306C4⋊C8—21no—
307C4⋊C8—21no—
308C4⋊C8D4×C5912yes—
309C4⋊C8D4×C5912yes—
310#103—24no—
311#103—44no—
312#102—24no—
313C4×C8—21no—
314C4×C8—21no—
315#95—22no—
316C24—21no—
317C2×Q8—21no—
318C2×Q8—21no—
319C2×Q8—21no—
320C2×Q8—22no—
321C2×Q8—21no—
322C2×Q8—21no—
323C2×Q8—42no—
324C2×Q8—42no—
325C2×Q8—41no—
326C2×Q8SD16×C5912yes—
327C2×D4—21no—
328C2×D4—21no—
329C2×D4—21no—
330C2×D4—21no—
331C2×D4—21no—
332C2×D4Q16×C5912yes—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—22no—
337C22×C4—41no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—41no—
341C22×C4—41no—
342C22×C4—41no—
343C22×C4—41no—
344C22×C4C2×D4×C5911yescharacteristic
345C22×C4C2×D4×C5911yescharacteristic
346C22×C4C2×D4×C5911yescharacteristic
347C2×C8—22no—
348C2×C8—22no—
349C2×C8—22no—
350C2×C8—41no—
351C2×C8—41no—
352C2×C8—41no—
353C2×C8—41no—
354C2×C8—41no—
355C2×C8—41no—
356C4⋊C4—22no—
357C4⋊C4—22no—
358C4⋊C4—21no—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4—21no—
362C4⋊C4—42no—
363C4⋊C4—44no—
364C4⋊C4—41no—
365C4⋊C4—41no—
366C4⋊C4—41no—
367C4⋊C4—41no—
368C4⋊C4—41no—
369C4⋊C4—41no—
370C4⋊C4—41no—
371C4⋊C4—41no—
372C22⋊C4—44no—
373C22⋊C4—41no—
374C22⋊C4—41no—
375C22⋊C4—82no—
376C42—41no—
377C42—41no—
378C42C2×D4×C5911yescharacteristic
379C42C2×D4×C5911yescharacteristic
380C42C2×D4×C5911yescharacteristic
381C42#41×C5911yescharacteristic
382C23—22no—
383C23—41no—
384C23—41no—
385C23—41no—
386C23—41no—
387C23—41no—
388C23—41no—
389C23#120×C5911yescharacteristic
390Q8—22no—
391Q8—22no—
392Q8—44no—
393Q8—41no—
394Q8—41no—
395Q8—82no—
396D4—22no—
397D4—22no—
398D4—41no—
399D4—41no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—22no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—41no—
410C2×C4—42no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—42no—
414C2×C4—41no—
415C2×C4—81no—
416C2×C4—81no—
417C2×C4—81no—
418C2×C4—81no—
419C2×C4—81no—
420C2×C4—81no—
421C2×C4#120×C5911yescharacteristic
422C2×C4#120×C5911yescharacteristic
423C2×C4#121×C5911yescharacteristic
424C2×C4#121×C5911yescharacteristic
425C2×C4#121×C5911yescharacteristic
426C2×C4#127×C5911yescharacteristic
427C2×C4C2×SD16×C5911yescharacteristic
428C2×C4C2×Q16×C5911yescharacteristic
429C2×C4#135×C5911yescharacteristic
430C2×C4#135×C5911yescharacteristic
431C2×C4AGL(1,ℤ/8)×C5911yescharacteristic
432C2×C4#137×C5911yescharacteristic
433C2×C4#137×C5911yescharacteristic
434C2×C4#137×C5911yescharacteristic
435C8—42no—
436C8—42no—
437C8—42no—
438C22—42no—
439C22—42no—
440C22—42no—
441C22—81no—
442C22—81no—
443C22—81no—
444C22—81no—
445C22C59×#39211yescharacteristic
446C22C59×#45011yescharacteristic
447C22C59×#45111yescharacteristic
448C22C59×#45211yescharacteristic
449C22C59×#45211yescharacteristic
450C22C59×#45311yescharacteristic
451C22C59×#45411yescharacteristic
452C4—21no—
453C4—21no—
454C4—42no—
455C4—81no—
456C4—81no—
457C4—82no—
458C4—82no—
459C4C59×#44811yescharacteristic
460C4C59×#44911yescharacteristic
461C4C59×#45111yescharacteristic
462C4C59×#45211yescharacteristic
463C4C59×#46511yescharacteristic
464C4C59×#46711yescharacteristic
465C4C59×#46811yescharacteristic
466C4C59×#47011yescharacteristic
467C2—82no—
468C2C59×#163111yescharacteristic
469C2C59×#163211yescharacteristic
470C2C59×#163711yescharacteristic
471C2C59×#163811yescharacteristic
472C2C59×#200011yescharacteristic
473C2C59×#200111yescharacteristic
474C2C59×#200611yescharacteristic
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×#477C2semidirect
4. C59×#1956C2semidirect
5. C2×C59×Q8⋊C8C2semidirect
7. C59×#1296C2semidirect
200. #10236C59direct (N × H)
230. C2×#477C2×C59semidirect
233. #1956C2×C59semidirect
234. C2×Q8⋊C8C2×C59semidirect
236. #1296C2×C59semidirect
268. C59#10236direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C59×#4772
C2×C59×#4762
C59×#25382
C59×#19562
C2×C59×Q8⋊C82
C2×C59×D4⋊C82
C59×#12962
#1023659