Finite Group Databasebeta

← C59×#19288 #28431397

Subgroups — C59×#19288 #28431397

Order 15104.

608 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
1C59×#3167C211yesmaximal, characteristic
2C59×#3113C211yesmaximal, characteristic, complemented
3C59×#3112C211yesmaximal, characteristic
4C2×C59×#446C211yesmaximal, characteristic, complemented
5C59×#1704C212yesmaximal, complemented
6C59×#1702C212yesmaximal, complemented
7C59×#1692C212yesmaximal, complemented
8C59×#1686C212yesmaximal, complemented
9C59×#1568C211yesmaximal, characteristic, complemented
10C59×#1552C211yesmaximal, characteristic, complemented
11C59×#1551C211yesmaximal, characteristic
12C59×#533C2211yescharacteristic
13C59×#532C2211yescharacteristic
14C2×C4×Q8×C59C2211yescharacteristic
15C59×#498C2211yescharacteristic
16C59×#492C2211yescharacteristic
17C59×#487C2211yescharacteristic
18C59×#486C2211yescharacteristic
19C59×#483—21no—
20C59×#480—21no—
21C59×#477C2212yes—
22C59×#475C2212yes—
23C59×#465—21no—
24C59×#465—21no—
25C59×#462C2212yes—
26C59×#460C2212yes—
27C59×#451—21no—
28C59×#448—21no—
29C59×#446—21no—
30C59×#446—21no—
31C59×#446C2212yes—
32C59×#446C2212yes—
33C59×#441—22no—
34C59×#440—22no—
35C4×SD16×C59—21no—
36C4×SD16×C59—21no—
37C59×#432C2211yescharacteristic
38C59×#432C2211yescharacteristic
39C2×C4⋊C8×C59—21no—
40C2×C4⋊C8×C59C2211yescharacteristic
41C2×#97×C59—21no—
42C2×C4×C8×C59C2211yescharacteristic
43C59×#335C2212yes—
44C59×#334C2212yes—
45C59×#333C2212yes—
46C59×#332C2212yes—
47C59×#332C2212yes—
48C59×#331C2212yes—
49C2×#41×C59—21no—
50C22×Q8×C59D411yescharacteristic
51C2×Q16×C59—22no—
52C2×SD16×C59—22no—
53C2×SD16×C59—21no—
54C2×SD16×C59—21no—
55C22×C8×C59—21no—
56C22×C8×C59D411yescharacteristic
57C22×C8×C59D411yescharacteristic
58C4⋊Q8×C59C2311yescharacteristic
59C4⋊Q8×C59C2311yescharacteristic
60C4⋊Q8×C59C2311yescharacteristic
61#127×C59C2311yescharacteristic
62#125×C59—21no—
63#124×C59—21no—
64C22⋊Q8×C59—21no—
65C22⋊Q8×C59—21no—
66#121×C59—21no—
67#121×C59—21no—
68C4×Q8×C59—21no—
69C4×Q8×C59—21no—
70C4×Q8×C59—21no—
71C4×Q8×C59—21no—
72C4×Q8×C59D412yes—
73C4×Q8×C59C2312yes—
74C4×D4×C59—21no—
75C4×D4×C59—21no—
76#117×C59—21no—
77C2×C4⋊C4×C59—21no—
78C2×C4⋊C4×C59D411yescharacteristic
79C2×C42×C59—21no—
80C2×C42×C59C2311yescharacteristic
81#107×C59—22no—
82#106×C59—21no—
83#106×C59—21no—
84#106×C59—22no—
85C4⋊C8×C59—22no—
86C4⋊C8×C59—22no—
87C4⋊C8×C59—21no—
88C4⋊C8×C59C2312yes—
89C4⋊C8×C59C2312yes—
90C4⋊C8×C59C2312yes—
91#103×C59—22no—
92#103×C59—22no—
93#103×C59—21no—
94#103×C59—21no—
95#103×C59—22no—
96#102×C59—21no—
97#102×C59—21no—
98#102×C59—22no—
99C22⋊C8×C59—21no—
100C22⋊C8×C59—21no—
101#97×C59—22no—
102#97×C59—22no—
103#97×C59—21no—
104#97×C59—21no—
105C4×C8×C59D411yescharacteristic
106C4×C8×C59D411yescharacteristic
107C4×C8×C59C2311yescharacteristic
108C4×C8×C59C2311yescharacteristic
109#41×C59—82no—
110C2×Q8×C59—21no—
111C2×Q8×C59—21no—
112C2×Q8×C59—21no—
113C2×Q8×C59—21no—
114C2×Q8×C59—42no—
115C2×Q8×C59C2×D412yes—
116C2×D4×C59—21no—
117C2×D4×C59—21no—
118C2×D4×C59—21no—
119C2×D4×C59—41no—
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—44no—
127SD16×C59—42no—
128SD16×C59—44no—
129SD16×C59—42no—
130C2×C8×C59—22no—
131C2×C8×C59—22no—
132C2×C8×C59—22no—
133C2×C8×C59—22no—
134C2×C8×C59—41no—
135C2×C8×C59—42no—
136C2×C8×C59C2×D411yescharacteristic
137C2×C8×C59C2×D411yescharacteristic
138C2×C8×C59C2×D411yescharacteristic
139C2×C8×C59C2×D411yescharacteristic
140C4⋊C4×C59—22no—
141C4⋊C4×C59—21no—
142C4⋊C4×C59—22no—
143C4⋊C4×C59—21no—
144C4⋊C4×C59—21no—
145C4⋊C4×C59—21no—
146C4⋊C4×C59—21no—
147C4⋊C4×C59—21no—
148C4⋊C4×C59—21no—
149C4⋊C4×C59—41no—
150C4⋊C4×C59—41no—
151C4⋊C4×C59C2×D412yes—
152C22⋊C4×C59—41no—
153C22⋊C4×C59—41no—
154C22⋊C4×C59—41no—
155C42×C59—22no—
156C42×C59—22no—
157C42×C59—41no—
158C42×C59C2×D411yescharacteristic
159C42×C59C2×D411yescharacteristic
160C42×C59#4111yescharacteristic
161C42×C59C2411yescharacteristic
162C23×C59—41no—
163C23×C59#12111yescharacteristic
164Q8×C59—22no—
165Q8×C59—22no—
166Q8×C59—42no—
167Q8×C59—41no—
168Q8×C59—41no—
169Q8×C59—42no—
170Q8×C59—81no—
171D4×C59—41no—
172D4×C59—41no—
173D4×C59—42no—
174D4×C59—81no—
175D4×C59—82no—
176C2×C4×C59—22no—
177C2×C4×C59—21no—
178C2×C4×C59—21no—
179C2×C4×C59—22no—
180C2×C4×C59—22no—
181C2×C4×C59—22no—
182C2×C4×C59—42no—
183C2×C4×C59—42no—
184C2×C4×C59—41no—
185C2×C4×C59—41no—
186C2×C4×C59—41no—
187C2×C4×C59—82no—
188C2×C4×C59#12111yescharacteristic
189C2×C4×C59#12111yescharacteristic
190C2×C4×C59#12111yescharacteristic
191C2×C4×C59C22×D411yescharacteristic
192C2×C4×C59C22×D411yescharacteristic
193C2×C4×C59C2×#4111yescharacteristic
194C8×C59—21no—
195C8×C59—21no—
196C8×C59—21no—
197C8×C59—42no—
198C8×C59—42no—
199C8×C59—42no—
200C8×C59#13712yes—
201#19288C5911yesmaximal, characteristic, direct product factor, Sylow
202C22×C59—21no—
203C22×C59—21no—
204C22×C59—81no—
205C22×C59—81no—
206C22×C59—81no—
207C22×C59#47112yes—
208C22×C59C2×#12111yescharacteristic
209C4×C59—21no—
210C4×C59—21no—
211C4×C59—21no—
212C4×C59—21no—
213C4×C59—42no—
214C4×C59—42no—
215C4×C59—81no—
216C4×C59—81no—
217C4×C59—81no—
218C4×C59C2×#13711yescharacteristic
219C4×C59#57511yescharacteristic
220C4×C59#57512yes—
221#3167C2×C5911yescharacteristic
222#3113C2×C5911yescharacteristic, complemented
223#3112C2×C5911yescharacteristic
224C2×#446C2×C5911yescharacteristic, complemented
225#1704C2×C5912yescomplemented
226#1702C2×C5912yescomplemented
227#1692C2×C5912yescomplemented
228#1686C2×C5912yescomplemented
229#1568C2×C5911yescharacteristic, complemented
230#1552C2×C5911yescharacteristic, complemented
231#1551C2×C5911yescharacteristic
232C2×C59—22no—
233C2×C59—161no—
234C2×C59#303711yescharacteristic
235C2×C59#305411yescharacteristic
236C2×C59C2×#47111yescharacteristic
237#533C22×C5911yescharacteristic
238#532C22×C5911yescharacteristic
239C2×C4×Q8C22×C5911yescharacteristic
240#498C22×C5911yescharacteristic
241#492C22×C5911yescharacteristic
242#487C22×C5911yescharacteristic
243#486C22×C5911yescharacteristic
244#483—21no—
245#480—21no—
246#477C22×C5912yes—
247#475C22×C5912yes—
248#465—21no—
249#465—21no—
250#462C22×C5912yes—
251#460C22×C5912yes—
252#451—21no—
253#448—21no—
254#446—21no—
255#446—21no—
256#446C22×C5912yes—
257#446C22×C5912yes—
258#441—22no—
259#440—22no—
260C4×SD16—21no—
261C4×SD16—21no—
262#432C22×C5911yescharacteristic
263#432C22×C5911yescharacteristic
264C2×C4⋊C8—21no—
265C2×C4⋊C8C22×C5911yescharacteristic
266C2×#97—21no—
267C2×C4×C8C22×C5911yescharacteristic
268#335C22×C5912yes—
269#334C22×C5912yes—
270#333C22×C5912yes—
271#332C22×C5912yes—
272#332C22×C5912yes—
273#331C22×C5912yes—
274C59#1928811yescharacteristic, direct product factor, Sylow
275C2×#41—21no—
276C22×Q8D4×C5911yescharacteristic
277C2×Q16—22no—
278C2×SD16—22no—
279C2×SD16—21no—
280C2×SD16—21no—
281C22×C8—21no—
282C22×C8D4×C5911yescharacteristic
283C22×C8D4×C5911yescharacteristic
284C4⋊Q8C23×C5911yescharacteristic
285C4⋊Q8C23×C5911yescharacteristic
286C4⋊Q8C23×C5911yescharacteristic
287#127C23×C5911yescharacteristic
288#125—21no—
289#124—21no—
290C22⋊Q8—21no—
291C22⋊Q8—21no—
292#121—21no—
293#121—21no—
294C4×Q8—21no—
295C4×Q8—21no—
296C4×Q8—21no—
297C4×Q8—21no—
298C4×Q8D4×C5912yes—
299C4×Q8C23×C5912yes—
300C4×D4—21no—
301C4×D4—21no—
302#117—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4D4×C5911yescharacteristic
305C2×C42—21no—
306C2×C42C23×C5911yescharacteristic
307#107—22no—
308#106—21no—
309#106—21no—
310#106—22no—
311C4⋊C8—22no—
312C4⋊C8—22no—
313C4⋊C8—21no—
314C4⋊C8C23×C5912yes—
315C4⋊C8C23×C5912yes—
316C4⋊C8C23×C5912yes—
317#103—22no—
318#103—22no—
319#103—21no—
320#103—21no—
321#103—22no—
322#102—21no—
323#102—21no—
324#102—22no—
325C22⋊C8—21no—
326C22⋊C8—21no—
327#97—22no—
328#97—22no—
329#97—21no—
330#97—21no—
331C4×C8D4×C5911yescharacteristic
332C4×C8D4×C5911yescharacteristic
333C4×C8C23×C5911yescharacteristic
334C4×C8C23×C5911yescharacteristic
335#41—82no—
336C2×Q8—21no—
337C2×Q8—21no—
338C2×Q8—21no—
339C2×Q8—21no—
340C2×Q8—42no—
341C2×Q8C2×D4×C5912yes—
342C2×D4—21no—
343C2×D4—21no—
344C2×D4—21no—
345C2×D4—41no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—41no—
349C22×C4C2×D4×C5911yescharacteristic
350C22×C4C2×D4×C5911yescharacteristic
351C22×C4#41×C5911yescharacteristic
352Q16—44no—
353SD16—42no—
354SD16—44no—
355SD16—42no—
356C2×C8—22no—
357C2×C8—22no—
358C2×C8—22no—
359C2×C8—22no—
360C2×C8—41no—
361C2×C8—42no—
362C2×C8C2×D4×C5911yescharacteristic
363C2×C8C2×D4×C5911yescharacteristic
364C2×C8C2×D4×C5911yescharacteristic
365C2×C8C2×D4×C5911yescharacteristic
366C4⋊C4—22no—
367C4⋊C4—21no—
368C4⋊C4—22no—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—41no—
376C4⋊C4—41no—
377C4⋊C4C2×D4×C5912yes—
378C22⋊C4—41no—
379C22⋊C4—41no—
380C22⋊C4—41no—
381C42—22no—
382C42—22no—
383C42—41no—
384C42C2×D4×C5911yescharacteristic
385C42C2×D4×C5911yescharacteristic
386C42#41×C5911yescharacteristic
387C42C24×C5911yescharacteristic
388C23—41no—
389C23#121×C5911yescharacteristic
390Q8—22no—
391Q8—22no—
392Q8—42no—
393Q8—41no—
394Q8—41no—
395Q8—42no—
396Q8—81no—
397D4—41no—
398D4—41no—
399D4—42no—
400D4—81no—
401D4—82no—
402C2×C4—22no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—82no—
414C2×C4#121×C5911yescharacteristic
415C2×C4#121×C5911yescharacteristic
416C2×C4#121×C5911yescharacteristic
417C2×C4C22×D4×C5911yescharacteristic
418C2×C4C22×D4×C5911yescharacteristic
419C2×C4C2×#41×C5911yescharacteristic
420C8—21no—
421C8—21no—
422C8—21no—
423C8—42no—
424C8—42no—
425C8—42no—
426C8#137×C5912yes—
427C22—21no—
428C22—21no—
429C22—81no—
430C22—81no—
431C22—81no—
432C22C59×#47112yes—
433C22C2×#121×C5911yescharacteristic
434C4—21no—
435C4—21no—
436C4—21no—
437C4—21no—
438C4—42no—
439C4—42no—
440C4—81no—
441C4—81no—
442C4—81no—
443C4C2×#137×C5911yescharacteristic
444C4C59×#57511yescharacteristic
445C4C59×#57512yes—
446C2—22no—
447C2—161no—
448C2C59×#303711yescharacteristic
449C2C59×#305411yescharacteristic
450C2C2×C59×#47111yescharacteristic
subgroupG/H
center, socleC22×C59C2×#121
commutator, Frattini, cosocleC42C24×C59
prime radicalC59×#532C22
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
2. C59×#3113C2semidirect
4. C2×C59×#446C2semidirect
5. C59×#1704C2semidirect
6. C59×#1702C2semidirect
7. C59×#1692C2semidirect
8. C59×#1686C2semidirect
9. C59×#1568C2semidirect
10. C59×#1552C2semidirect
201. #19288C59direct (N × H)
222. #3113C2×C59semidirect
224. C2×#446C2×C59semidirect
225. #1704C2×C59semidirect
226. #1702C2×C59semidirect
227. #1692C2×C59semidirect
228. #1686C2×C59semidirect
229. #1568C2×C59semidirect
230. #1552C2×C59semidirect
274. C59#19288direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#31672
C59×#31132
C59×#31122
C2×C59×#4462
C59×#17042
C59×#17022
C59×#16922
C59×#16862
C59×#15682
C59×#15522
C59×#15512
#1928859