Finite Group Databasebeta

← C59×#9114 #28421223

Subgroups — C59×#9114 #28421223

Order 15104.

694 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×#431C211yesmaximal, characteristic, complemented
2C59×#2854C211yesmaximal, characteristic
3C2×C59×#327C212yesmaximal
4C59×#1434C211yesmaximal, characteristic, complemented
5C59×#1294C212yesmaximal, complemented
6C2×#123×C59—21no—
7C2×#121×C59C2211yescharacteristic
8C22×C42×C59C2211yescharacteristic
9C59×#431—24no—
10C2×C4⋊C8×C59—21no—
11C2×C22⋊C8×C59C2212yes—
12C2×C4×C8×C59—21no—
13C59×#390C411yescharacteristic, complemented
14C59×#390C411yescharacteristic, complemented
15C59×#389C411yescharacteristic, complemented
16C59×#389C411yescharacteristic, complemented
17C59×#388—21no—
18C59×#388—21no—
19C59×#386—21no—
20C59×#380C2211yescharacteristic
21C2×#95×C59—21no—
22C2×#95×C59—21no—
23C2×#95×C59C2212yes—
24C59×#327—24no—
25C22×D4×C59—21no—
26C22×D4×C59C2×C411yescharacteristic
27C23×C4×C59—22no—
28C23×C4×C59D411yescharacteristic
29C23×C4×C59D411yescharacteristic
30C23×C4×C59C2311yescharacteristic
31C22×C8×C59—22no—
32#123×C59—42no—
33#123×C59—42no—
34#121×C59—22no—
35#121×C59—22no—
36C2×C4⋊C4×C59—21no—
37C2×C4⋊C4×C59—21no—
38C2×C4⋊C4×C59C2×C411yescharacteristic
39C2×C4⋊C4×C59C2×C411yescharacteristic
40C2×C4⋊C4×C59C2×C411yescharacteristic
41C2×C22⋊C4×C59—21no—
42C2×C22⋊C4×C59—21no—
43C2×C22⋊C4×C59—21no—
44C2×C22⋊C4×C59—21no—
45C2×C22⋊C4×C59—21no—
46C2×C22⋊C4×C59—21no—
47C2×C42×C59—22no—
48C2×C42×C59—22no—
49C2×C42×C59C2×C411yescharacteristic
50C2×C42×C59C2×C411yescharacteristic
51C2×C42×C59D411yescharacteristic
52C2×C42×C59D411yescharacteristic
53C4⋊C8×C59—24no—
54C22⋊C8×C59—22no—
55C22⋊C8×C59D414yes—
56C4×C8×C59—24no—
57#95×C59—24no—
58#95×C59—21no—
59#95×C59—21no—
60#95×C59—21no—
61#95×C59—22no—
62#95×C59—22no—
63#95×C59—42no—
64C24×C59—21no—
65C24×C59C2×D411yescharacteristic
66C2×D4×C59—22no—
67C2×D4×C59—41no—
68C2×D4×C59—41no—
69C2×D4×C59—42no—
70C2×D4×C59—41no—
71C2×D4×C59—41no—
72C2×D4×C59—42no—
73C22×C4×C59—22no—
74C22×C4×C59—22no—
75C22×C4×C59—22no—
76C22×C4×C59—22no—
77C22×C4×C59—24no—
78C22×C4×C59—21no—
79C22×C4×C59—21no—
80C22×C4×C59—21no—
81C22×C4×C59—41no—
82C22×C4×C59—41no—
83C22×C4×C59—41no—
84C22×C4×C59—42no—
85C22×C4×C59—42no—
86C22×C4×C59—42no—
87C22×C4×C59—42no—
88C22×C4×C59—42no—
89C22×C4×C59—42no—
90C22×C4×C59C22⋊C411yescharacteristic
91C22×C4×C59C22⋊C411yescharacteristic
92C22×C4×C59C22⋊C411yescharacteristic
93C22×C4×C59C22⋊C411yescharacteristic
94C22×C4×C59D812yes—
95C22×C4×C59SD1612yes—
96C22×C4×C59C22×C411yescharacteristic
97C22×C4×C59C2×D411yescharacteristic
98C22×C4×C59C2×D412yes—
99C22×C4×C59#4112yes—
100C2×C8×C59—24no—
101C2×C8×C59—42no—
102C2×C8×C59—42no—
103C4⋊C4×C59—22no—
104C4⋊C4×C59—41no—
105C4⋊C4×C59—41no—
106C4⋊C4×C59—42no—
107C4⋊C4×C59—42no—
108C22⋊C4×C59—42no—
109C22⋊C4×C59—41no—
110C22⋊C4×C59—41no—
111C22⋊C4×C59—42no—
112C22⋊C4×C59—42no—
113C22⋊C4×C59—42no—
114C22⋊C4×C59—41no—
115C22⋊C4×C59—41no—
116C42×C59—22no—
117C42×C59—22no—
118C42×C59—21no—
119C42×C59—21no—
120C42×C59—21no—
121C42×C59—21no—
122C23×C59—21no—
123C23×C59—21no—
124C23×C59—21no—
125C23×C59—21no—
126C23×C59—41no—
127C23×C59—41no—
128C23×C59—41no—
129C23×C59—41no—
130C23×C59—41no—
131C23×C59—41no—
132C23×C59—41no—
133C23×C59C2×C22⋊C411yescharacteristic
134C23×C59#12112yes—
135C23×C59C2×D811yescharacteristic
136C23×C59C2×SD1611yescharacteristic
137C23×C59#13512yes—
138D4×C59—82no—
139D4×C59—82no—
140D4×C59—82no—
141C2×C4×C59—21no—
142C2×C4×C59—21no—
143C2×C4×C59—21no—
144C2×C4×C59—21no—
145C2×C4×C59—21no—
146C2×C4×C59—21no—
147C2×C4×C59—21no—
148C2×C4×C59—21no—
149C2×C4×C59—21no—
150C2×C4×C59—21no—
151C2×C4×C59—24no—
152C2×C4×C59—24no—
153C2×C4×C59—21no—
154C2×C4×C59—21no—
155C2×C4×C59—21no—
156C2×C4×C59—42no—
157C2×C4×C59—42no—
158C2×C4×C59—44no—
159C2×C4×C59—44no—
160C2×C4×C59—44no—
161C2×C4×C59—44no—
162C2×C4×C59—41no—
163C2×C4×C59—41no—
164C2×C4×C59—41no—
165C2×C4×C59—41no—
166C2×C4×C59—41no—
167C2×C4×C59—41no—
168C2×C4×C59—41no—
169C2×C4×C59—41no—
170C2×C4×C59—41no—
171C2×C4×C59—82no—
172C2×C4×C59—82no—
173C2×C4×C59—82no—
174C2×C4×C59—82no—
175C2×C4×C59#10212yes—
176C2×C4×C59#10212yes—
177C2×C4×C59#10412yes—
178C2×C4×C59C4×D412yes—
179C2×C4×C59#12011yescharacteristic
180C2×C4×C59#12311yescharacteristic
181C8×C59—44no—
182#9114C5911yesmaximal, characteristic, direct product factor, Sylow
183C22×C59—22no—
184C22×C59—22no—
185C22×C59—22no—
186C22×C59—21no—
187C22×C59—21no—
188C22×C59—21no—
189C22×C59—21no—
190C22×C59—22no—
191C22×C59—81no—
192C22×C59—81no—
193C22×C59—81no—
194C22×C59—81no—
195C22×C59—81no—
196C22×C59—81no—
197C22×C59—81no—
198C22×C59#38611yescharacteristic
199C22×C59#41011yescharacteristic
200C22×C59#41011yescharacteristic
201C22×C59C2×#10211yescharacteristic
202C22×C59#41611yescharacteristic
203C22×C59C2×#10411yescharacteristic
204C22×C59#42111yescharacteristic
205C22×C59#46512yes—
206C22×C59#46612yes—
207C4×C59—22no—
208C4×C59—22no—
209C4×C59—22no—
210C4×C59—21no—
211C4×C59—22no—
212C4×C59—21no—
213C4×C59—41no—
214C4×C59—84no—
215C4×C59—81no—
216C4×C59—81no—
217C4×C59—81no—
218C2×#431C2×C5911yescharacteristic, complemented
219#2854C2×C5911yescharacteristic
220C2×#327C2×C5912yes—
221#1434C2×C5911yescharacteristic, complemented
222#1294C2×C5912yescomplemented
223C2×C59—22no—
224C2×C59—22no—
225C2×C59—161no—
226C2×C59#150011yescharacteristic
227C2×C59#150211yescharacteristic
228C2×C59#151711yescharacteristic
229C2×C59#152111yescharacteristic
230C2×C59#187111yescharacteristic
231C2×C59#189311yescharacteristic
232C2×C59#189911yescharacteristic
233C2×#123—21no—
234C2×#121C22×C5911yescharacteristic
235C22×C42C22×C5911yescharacteristic
236#431—24no—
237C2×C4⋊C8—21no—
238C2×C22⋊C8C22×C5912yes—
239C2×C4×C8—21no—
240#390C4×C5911yescharacteristic, complemented
241#390C4×C5911yescharacteristic, complemented
242#389C4×C5911yescharacteristic, complemented
243#389C4×C5911yescharacteristic, complemented
244#388—21no—
245#388—21no—
246#386—21no—
247#380C22×C5911yescharacteristic
248C2×#95—21no—
249C2×#95—21no—
250C2×#95C22×C5912yes—
251#327—24no—
252C59#911411yescharacteristic, direct product factor, Sylow
253C22×D4—21no—
254C22×D4C2×C4×C5911yescharacteristic
255C23×C4—22no—
256C23×C4D4×C5911yescharacteristic
257C23×C4D4×C5911yescharacteristic
258C23×C4C23×C5911yescharacteristic
259C22×C8—22no—
260#123—42no—
261#123—42no—
262#121—22no—
263#121—22no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4C2×C4×C5911yescharacteristic
267C2×C4⋊C4C2×C4×C5911yescharacteristic
268C2×C4⋊C4C2×C4×C5911yescharacteristic
269C2×C22⋊C4—21no—
270C2×C22⋊C4—21no—
271C2×C22⋊C4—21no—
272C2×C22⋊C4—21no—
273C2×C22⋊C4—21no—
274C2×C22⋊C4—21no—
275C2×C42—22no—
276C2×C42—22no—
277C2×C42C2×C4×C5911yescharacteristic
278C2×C42C2×C4×C5911yescharacteristic
279C2×C42D4×C5911yescharacteristic
280C2×C42D4×C5911yescharacteristic
281C4⋊C8—24no—
282C22⋊C8—22no—
283C22⋊C8D4×C5914yes—
284C4×C8—24no—
285#95—24no—
286#95—21no—
287#95—21no—
288#95—21no—
289#95—22no—
290#95—22no—
291#95—42no—
292C24—21no—
293C24C2×D4×C5911yescharacteristic
294C2×D4—22no—
295C2×D4—41no—
296C2×D4—41no—
297C2×D4—42no—
298C2×D4—41no—
299C2×D4—41no—
300C2×D4—42no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—24no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—42no—
313C22×C4—42no—
314C22×C4—42no—
315C22×C4—42no—
316C22×C4—42no—
317C22×C4—42no—
318C22×C4C22⋊C4×C5911yescharacteristic
319C22×C4C22⋊C4×C5911yescharacteristic
320C22×C4C22⋊C4×C5911yescharacteristic
321C22×C4C22⋊C4×C5911yescharacteristic
322C22×C4D8×C5912yes—
323C22×C4SD16×C5912yes—
324C22×C4C22×C4×C5911yescharacteristic
325C22×C4C2×D4×C5911yescharacteristic
326C22×C4C2×D4×C5912yes—
327C22×C4#41×C5912yes—
328C2×C8—24no—
329C2×C8—42no—
330C2×C8—42no—
331C4⋊C4—22no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C4⋊C4—42no—
335C4⋊C4—42no—
336C22⋊C4—42no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—42no—
340C22⋊C4—42no—
341C22⋊C4—42no—
342C22⋊C4—41no—
343C22⋊C4—41no—
344C42—22no—
345C42—22no—
346C42—21no—
347C42—21no—
348C42—21no—
349C42—21no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—41no—
355C23—41no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—41no—
361C23C2×C22⋊C4×C5911yescharacteristic
362C23#121×C5912yes—
363C23C2×D8×C5911yescharacteristic
364C23C2×SD16×C5911yescharacteristic
365C23#135×C5912yes—
366D4—82no—
367D4—82no—
368D4—82no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—24no—
380C2×C4—24no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—44no—
387C2×C4—44no—
388C2×C4—44no—
389C2×C4—44no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—82no—
400C2×C4—82no—
401C2×C4—82no—
402C2×C4—82no—
403C2×C4#102×C5912yes—
404C2×C4#102×C5912yes—
405C2×C4#104×C5912yes—
406C2×C4C4×D4×C5912yes—
407C2×C4#120×C5911yescharacteristic
408C2×C4#123×C5911yescharacteristic
409C8—44no—
410C22—22no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—22no—
416C22—22no—
417C22—22no—
418C22—81no—
419C22—81no—
420C22—81no—
421C22—81no—
422C22—81no—
423C22—81no—
424C22—81no—
425C22C59×#38611yescharacteristic
426C22C59×#41011yescharacteristic
427C22C59×#41011yescharacteristic
428C22C2×#102×C5911yescharacteristic
429C22C59×#41611yescharacteristic
430C22C2×#104×C5911yescharacteristic
431C22C59×#42111yescharacteristic
432C22C59×#46512yes—
433C22C59×#46612yes—
434C4—22no—
435C4—22no—
436C4—22no—
437C4—21no—
438C4—22no—
439C4—21no—
440C4—41no—
441C4—84no—
442C4—81no—
443C4—81no—
444C4—81no—
445C2—22no—
446C2—22no—
447C2—161no—
448C2C59×#150011yescharacteristic
449C2C59×#150211yescharacteristic
450C2C59×#151711yescharacteristic
451C2C59×#152111yescharacteristic
452C2C59×#187111yescharacteristic
453C2C59×#189311yescharacteristic
454C2C59×#189911yescharacteristic
subgroupG/H
center, socleC23×C59C2×C22⋊C4
commutatorC22×C4C22×C4×C59
Frattini, cosocleC23×C4C23×C59
prime radicalC2×#121×C59C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C59 ◁ C22×C42×C59 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C59×#431C2semidirect
4. C59×#1434C2semidirect
5. C59×#1294C2semidirect
13. C59×#390C4semidirect
14. C59×#390C4semidirect
15. C59×#389C4semidirect
16. C59×#389C4semidirect
182. #9114C59direct (N × H)
218. C2×#431C2×C59semidirect
221. #1434C2×C59semidirect
222. #1294C2×C59semidirect
240. #390C4×C59semidirect
241. #390C4×C59semidirect
242. #389C4×C59semidirect
243. #389C4×C59semidirect
252. C59#9114direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C59×#4312
C59×#28542
C2×C59×#3272
C59×#14342
C59×#12942
#911459