Finite Group Databasebeta

← C59×#19317 #28431426

Subgroups — C59×#19317 #28431426

Order 15104.

598 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3139C211yesmaximal, characteristic, complemented
2C59×#3116C211yesmaximal, characteristic
3C59×#3079C211yesmaximal, characteristic
4C59×#2970C211yesmaximal, characteristic
5C59×#1704C212yesmaximal, complemented
6C59×#1700C212yesmaximal, complemented
7C59×#1683C212yesmaximal, complemented
8C59×#1679C212yesmaximal, complemented
9C59×#1569C211yesmaximal, characteristic, complemented
10C59×#1559C211yesmaximal, characteristic, complemented
11C59×#1556C211yesmaximal, characteristic, complemented
12C59×#533C2211yescharacteristic
13C2×C4⋊Q8×C59C2211yescharacteristic
14C4×#41×C59C2211yescharacteristic
15C59×#491—21no—
16C59×#491—21no—
17C59×#487C2212yes—
18C59×#487C2212yes—
19C59×#485—21no—
20C59×#477—21no—
21C59×#477C2211yescharacteristic
22C59×#476—21no—
23C59×#476C2211yescharacteristic
24C59×#475C2212yes—
25C59×#474C2212yes—
26C59×#462C2211yescharacteristic
27C59×#461C2211yescharacteristic
28C59×#452—21no—
29C59×#446C2212yes—
30C59×#441—21no—
31C59×#440—21no—
32C59×#435—22no—
33C8×D4×C59C2212yes—
34C59×#432—21no—
35C59×#432C2211yescharacteristic
36C59×#432C2211yescharacteristic
37C59×#428—21no—
38C59×#423C2211yescharacteristic
39C59×#419—22no—
40C59×#417—21no—
41C4×M16×C59C2211yescharacteristic
42C2×#97×C59—21no—
43C59×#335C2212yes—
44C59×#334C2212yes—
45C59×#333C2212yes—
46C59×#332C2212yes—
47C59×#332C2212yes—
48C59×#332C2212yes—
49C2×#41×C59D411yescharacteristic
50C22×Q8×C59—21no—
51C2×Q16×C59—21no—
52C2×SD16×C59—21no—
53C2×M16×C59—21no—
54C2×M16×C59D412yes—
55C22×C8×C59—22no—
56C4⋊Q8×C59—21no—
57C4⋊Q8×C59—21no—
58C4⋊Q8×C59—21no—
59C4⋊Q8×C59C2311yescharacteristic
60C4⋊Q8×C59C2312yes—
61C4⋊Q8×C59C2311yescharacteristic
62#125×C59—21no—
63C22⋊Q8×C59—21no—
64C22⋊Q8×C59—21no—
65C4×Q8×C59—21no—
66C4×Q8×C59—21no—
67C4×Q8×C59D411yescharacteristic
68C4×Q8×C59C2311yescharacteristic
69C4×D4×C59—21no—
70C4×D4×C59—21no—
71C4×D4×C59D411yescharacteristic
72C4×D4×C59C2311yescharacteristic
73#117×C59—21no—
74#117×C59—21no—
75#117×C59D411yescharacteristic
76C2×C4⋊C4×C59—21no—
77C2×C4⋊C4×C59—21no—
78C2×C42×C59—21no—
79C2×C42×C59C2311yescharacteristic
80#107×C59—22no—
81#107×C59—21no—
82#106×C59—22no—
83#106×C59—21no—
84C4⋊C8×C59—22no—
85C4⋊C8×C59—21no—
86C4⋊C8×C59C2312yes—
87C4⋊C8×C59C2311yescharacteristic
88C4⋊C8×C59C2311yescharacteristic
89C4⋊C8×C59C2312yes—
90#103×C59—22no—
91#103×C59—21no—
92#103×C59—22no—
93#103×C59—22no—
94#103×C59—22no—
95#103×C59—22no—
96#103×C59—21no—
97#103×C59—21no—
98#102×C59—22no—
99#102×C59—21no—
100C22⋊C8×C59—21no—
101C22⋊C8×C59—21no—
102C22⋊C8×C59—22no—
103#97×C59—22no—
104#97×C59—21no—
105#97×C59—21no—
106#97×C59D411yescharacteristic
107#97×C59D411yescharacteristic
108C4×C8×C59C2312yes—
109#41×C59—22no—
110#41×C59—41no—
111C2×Q8×C59—22no—
112C2×Q8×C59—21no—
113C2×Q8×C59—21no—
114C2×Q8×C59—44no—
115C2×Q8×C59—41no—
116C2×Q8×C59C2×D411yescharacteristic
117C2×D4×C59—21no—
118C2×D4×C59C2×D411yescharacteristic
119C22×C4×C59—21no—
120C22×C4×C59—21no—
121C22×C4×C59—21no—
122C22×C4×C59—41no—
123C22×C4×C59C2×D411yescharacteristic
124C22×C4×C59C2×D411yescharacteristic
125C22×C4×C59#4111yescharacteristic
126Q16×C59—42no—
127SD16×C59—42no—
128M16×C59—42no—
129M16×C59—42no—
130C2×C8×C59—22no—
131C2×C8×C59—21no—
132C2×C8×C59—21no—
133C2×C8×C59—22no—
134C2×C8×C59—44no—
135C2×C8×C59C2×D412yes—
136C2×C8×C59C2×D412yes—
137C4⋊C4×C59—21no—
138C4⋊C4×C59—21no—
139C4⋊C4×C59—22no—
140C4⋊C4×C59—21no—
141C4⋊C4×C59—21no—
142C4⋊C4×C59—21no—
143C4⋊C4×C59—22no—
144C4⋊C4×C59—21no—
145C4⋊C4×C59—41no—
146C4⋊C4×C59—41no—
147C4⋊C4×C59—41no—
148C4⋊C4×C59—41no—
149C4⋊C4×C59C2×D411yescharacteristic
150C4⋊C4×C59C2×D411yescharacteristic
151C22⋊C4×C59—21no—
152C22⋊C4×C59—21no—
153C22⋊C4×C59—21no—
154C22⋊C4×C59—41no—
155C42×C59—21no—
156C42×C59—21no—
157C42×C59—21no—
158C42×C59—41no—
159C42×C59C2×D411yescharacteristic
160C42×C59C2×D411yescharacteristic
161C42×C59#4111yescharacteristic
162C42×C59C2411yescharacteristic
163C23×C59—21no—
164C23×C59#12111yescharacteristic
165Q8×C59—21no—
166Q8×C59—21no—
167Q8×C59—41no—
168Q8×C59—41no—
169Q8×C59—44no—
170Q8×C59—81no—
171Q8×C59—82no—
172D4×C59—21no—
173D4×C59—42no—
174D4×C59#13712yes—
175C2×C4×C59—21no—
176C2×C4×C59—21no—
177C2×C4×C59—22no—
178C2×C4×C59—21no—
179C2×C4×C59—21no—
180C2×C4×C59—21no—
181C2×C4×C59—41no—
182C2×C4×C59—42no—
183C2×C4×C59—42no—
184C2×C4×C59—41no—
185C2×C4×C59—41no—
186C2×C4×C59—42no—
187C2×C4×C59—81no—
188C2×C4×C59—82no—
189C2×C4×C59#12111yescharacteristic
190C2×C4×C59#12111yescharacteristic
191C2×C4×C59#12111yescharacteristic
192C2×C4×C59C22×D411yescharacteristic
193C2×C4×C59C22×D411yescharacteristic
194C2×C4×C59C2×#4111yescharacteristic
195C8×C59—22no—
196C8×C59—22no—
197C8×C59—41no—
198C8×C59—42no—
199C8×C59—42no—
200C8×C59—41no—
201#19317C5911yesmaximal, characteristic, direct product factor, Sylow
202C22×C59—21no—
203C22×C59—21no—
204C22×C59—22no—
205C22×C59—21no—
206C22×C59—41no—
207C22×C59—41no—
208C22×C59C2×#12111yescharacteristic
209C4×C59—21no—
210C4×C59—21no—
211C4×C59—21no—
212C4×C59—21no—
213C4×C59—41no—
214C4×C59—41no—
215C4×C59—41no—
216C4×C59—82no—
217C4×C59—81no—
218C4×C59—81no—
219C4×C59C2×#13711yescharacteristic
220C4×C59#57512yes—
221C4×C59#57511yescharacteristic
222#3139C2×C5911yescharacteristic, complemented
223#3116C2×C5911yescharacteristic
224#3079C2×C5911yescharacteristic
225#2970C2×C5911yescharacteristic
226#1704C2×C5912yescomplemented
227#1700C2×C5912yescomplemented
228#1683C2×C5912yescomplemented
229#1679C2×C5912yescomplemented
230#1569C2×C5911yescharacteristic, complemented
231#1559C2×C5911yescharacteristic, complemented
232#1556C2×C5911yescharacteristic, complemented
233C2×C59—41no—
234C2×C59—42no—
235C2×C59#304011yescharacteristic
236C2×C59#305611yescharacteristic
237C2×C59#306911yescharacteristic
238#533C22×C5911yescharacteristic
239C2×C4⋊Q8C22×C5911yescharacteristic
240C4×#41C22×C5911yescharacteristic
241#491—21no—
242#491—21no—
243#487C22×C5912yes—
244#487C22×C5912yes—
245#485—21no—
246#477—21no—
247#477C22×C5911yescharacteristic
248#476—21no—
249#476C22×C5911yescharacteristic
250#475C22×C5912yes—
251#474C22×C5912yes—
252#462C22×C5911yescharacteristic
253#461C22×C5911yescharacteristic
254#452—21no—
255#446C22×C5912yes—
256#441—21no—
257#440—21no—
258#435—22no—
259C8×D4C22×C5912yes—
260#432—21no—
261#432C22×C5911yescharacteristic
262#432C22×C5911yescharacteristic
263#428—21no—
264#423C22×C5911yescharacteristic
265#419—22no—
266#417—21no—
267C4×M16C22×C5911yescharacteristic
268C2×#97—21no—
269#335C22×C5912yes—
270#334C22×C5912yes—
271#333C22×C5912yes—
272#332C22×C5912yes—
273#332C22×C5912yes—
274#332C22×C5912yes—
275C59#1931711yescharacteristic, direct product factor, Sylow
276C2×#41D4×C5911yescharacteristic
277C22×Q8—21no—
278C2×Q16—21no—
279C2×SD16—21no—
280C2×M16—21no—
281C2×M16D4×C5912yes—
282C22×C8—22no—
283C4⋊Q8—21no—
284C4⋊Q8—21no—
285C4⋊Q8—21no—
286C4⋊Q8C23×C5912yes—
287C4⋊Q8C23×C5911yescharacteristic
288C4⋊Q8C23×C5911yescharacteristic
289#125—21no—
290C22⋊Q8—21no—
291C22⋊Q8—21no—
292C4×Q8—21no—
293C4×Q8—21no—
294C4×Q8D4×C5911yescharacteristic
295C4×Q8C23×C5911yescharacteristic
296C4×D4—21no—
297C4×D4—21no—
298C4×D4D4×C5911yescharacteristic
299C4×D4C23×C5911yescharacteristic
300#117—21no—
301#117—21no—
302#117D4×C5911yescharacteristic
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C42—21no—
306C2×C42C23×C5911yescharacteristic
307#107—22no—
308#107—21no—
309#106—22no—
310#106—21no—
311C4⋊C8—22no—
312C4⋊C8—21no—
313C4⋊C8C23×C5912yes—
314C4⋊C8C23×C5911yescharacteristic
315C4⋊C8C23×C5911yescharacteristic
316C4⋊C8C23×C5912yes—
317#103—22no—
318#103—21no—
319#103—22no—
320#103—22no—
321#103—22no—
322#103—22no—
323#103—21no—
324#103—21no—
325#102—22no—
326#102—21no—
327C22⋊C8—21no—
328C22⋊C8—21no—
329C22⋊C8—22no—
330#97—22no—
331#97—21no—
332#97—21no—
333#97D4×C5911yescharacteristic
334#97D4×C5911yescharacteristic
335C4×C8C23×C5912yes—
336#41—22no—
337#41—41no—
338C2×Q8—22no—
339C2×Q8—21no—
340C2×Q8—21no—
341C2×Q8—44no—
342C2×Q8—41no—
343C2×Q8C2×D4×C5911yescharacteristic
344C2×D4—21no—
345C2×D4C2×D4×C5911yescharacteristic
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—41no—
350C22×C4C2×D4×C5911yescharacteristic
351C22×C4C2×D4×C5911yescharacteristic
352C22×C4#41×C5911yescharacteristic
353Q16—42no—
354SD16—42no—
355M16—42no—
356M16—42no—
357C2×C8—22no—
358C2×C8—21no—
359C2×C8—21no—
360C2×C8—22no—
361C2×C8—44no—
362C2×C8C2×D4×C5912yes—
363C2×C8C2×D4×C5912yes—
364C4⋊C4—21no—
365C4⋊C4—21no—
366C4⋊C4—22no—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—22no—
371C4⋊C4—21no—
372C4⋊C4—41no—
373C4⋊C4—41no—
374C4⋊C4—41no—
375C4⋊C4—41no—
376C4⋊C4C2×D4×C5911yescharacteristic
377C4⋊C4C2×D4×C5911yescharacteristic
378C22⋊C4—21no—
379C22⋊C4—21no—
380C22⋊C4—21no—
381C22⋊C4—41no—
382C42—21no—
383C42—21no—
384C42—21no—
385C42—41no—
386C42C2×D4×C5911yescharacteristic
387C42C2×D4×C5911yescharacteristic
388C42#41×C5911yescharacteristic
389C42C24×C5911yescharacteristic
390C23—21no—
391C23#121×C5911yescharacteristic
392Q8—21no—
393Q8—21no—
394Q8—41no—
395Q8—41no—
396Q8—44no—
397Q8—81no—
398Q8—82no—
399D4—21no—
400D4—42no—
401D4#137×C5912yes—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—22no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—41no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—42no—
414C2×C4—81no—
415C2×C4—82no—
416C2×C4#121×C5911yescharacteristic
417C2×C4#121×C5911yescharacteristic
418C2×C4#121×C5911yescharacteristic
419C2×C4C22×D4×C5911yescharacteristic
420C2×C4C22×D4×C5911yescharacteristic
421C2×C4C2×#41×C5911yescharacteristic
422C8—22no—
423C8—22no—
424C8—41no—
425C8—42no—
426C8—42no—
427C8—41no—
428C22—21no—
429C22—21no—
430C22—22no—
431C22—21no—
432C22—41no—
433C22—41no—
434C22C2×#121×C5911yescharacteristic
435C4—21no—
436C4—21no—
437C4—21no—
438C4—21no—
439C4—41no—
440C4—41no—
441C4—41no—
442C4—82no—
443C4—81no—
444C4—81no—
445C4C2×#137×C5911yescharacteristic
446C4C59×#57512yes—
447C4C59×#57511yescharacteristic
448C2—41no—
449C2—42no—
450C2C59×#304011yescharacteristic
451C2C59×#305611yescharacteristic
452C2C59×#306911yescharacteristic
subgroupG/H
center, socleC22×C59C2×#121
commutator, Frattini, cosocleC42C24×C59
prime radicalC2×#41×C59D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C59 ◁ C2×C42×C59 ◁ G

Complements

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

NH ≅ G/Ntype
1. C59×#3139C2semidirect
5. C59×#1704C2semidirect
6. C59×#1700C2semidirect
7. C59×#1683C2semidirect
8. C59×#1679C2semidirect
9. C59×#1569C2semidirect
10. C59×#1559C2semidirect
11. C59×#1556C2semidirect
201. #19317C59direct (N × H)
222. #3139C2×C59semidirect
226. #1704C2×C59semidirect
227. #1700C2×C59semidirect
228. #1683C2×C59semidirect
229. #1679C2×C59semidirect
230. #1569C2×C59semidirect
231. #1559C2×C59semidirect
232. #1556C2×C59semidirect
275. C59#19317direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#31392
C59×#31162
C59×#30792
C59×#29702
C59×#17042
C59×#17002
C59×#16832
C59×#16792
C59×#15692
C59×#15592
C59×#15562
#1931759