Finite Group Databasebeta

← C59×#18294 #28430403

Subgroups — C59×#18294 #28430403

Order 15104.

1002 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×#544C211yesmaximal, characteristic, complemented
2C59×#3187C212yesmaximal
3C59×#2618C211yesmaximal, characteristic
4C59×#1611C214yesmaximal, complemented
5C59×#1599C214yesmaximal, complemented
6C59×#1520C212yesmaximal, complemented
7C2×C59×#324C211yesmaximal, characteristic, complemented
8C59×#544—24no—
9C59×#544—22no—
10C59×#544C2214yes—
11C2×C4⋊Q8×C59—22no—
12C2×#125×C59—22no—
13C2×#123×C59—21no—
14C2×C22⋊Q8×C59—21no—
15C2×C22⋊Q8×C59C2212yes—
16C2×#121×C59C2211yescharacteristic
17C2×#117×C59—21no—
18C22×C4⋊C4×C59C2211yescharacteristic
19C59×#483C2214yes—
20C59×#481—22no—
21C59×#465—24no—
22C59×#450C2214yes—
23C59×#448—22no—
24C2×C22⋊C8×C59C2212yes—
25C59×#398C2212yes—
26C59×#396—22no—
27C59×#394C2212yes—
28C59×#386—21no—
29C59×#380C2211yescharacteristic
30C59×#328C2218yes—
31C59×#324C2214yes—
32C22×Q8×C59—21no—
33C22×Q8×C59D412yes—
34C22×D4×C59—21no—
35C22×D4×C59C2311yescharacteristic
36C23×C4×C59D411yescharacteristic
37C23×C4×C59D411yescharacteristic
38C23×C4×C59C2311yescharacteristic
39C2×SD16×C59—24no—
40C22×C8×C59—22no—
41C4⋊Q8×C59—28no—
42C4⋊Q8×C59—28no—
43#125×C59—28no—
44#125×C59—28no—
45#123×C59—44no—
46C22⋊Q8×C59—24no—
47C22⋊Q8×C59—24no—
48C22⋊Q8×C59—22no—
49C22⋊Q8×C59—22no—
50C22⋊Q8×C59D414yes—
51C22⋊Q8×C59C2314yes—
52#121×C59—22no—
53#121×C59—22no—
54#117×C59—24no—
55#117×C59—24no—
56C2×C4⋊C4×C59—21no—
57C2×C4⋊C4×C59—21no—
58C2×C4⋊C4×C59—21no—
59C2×C4⋊C4×C59—22no—
60C2×C4⋊C4×C59—22no—
61C2×C4⋊C4×C59—22no—
62C2×C4⋊C4×C59—22no—
63C2×C4⋊C4×C59—22no—
64C2×C4⋊C4×C59—21no—
65C2×C4⋊C4×C59D412yes—
66C2×C4⋊C4×C59D412yes—
67C2×C4⋊C4×C59C2311yescharacteristic
68C2×C4⋊C4×C59C2312yes—
69C2×C22⋊C4×C59—22no—
70C2×C22⋊C4×C59—21no—
71C2×C22⋊C4×C59—22no—
72C2×C22⋊C4×C59—21no—
73C2×C22⋊C4×C59—22no—
74C2×C42×C59—22no—
75#106×C59—24no—
76#103×C59—24no—
77#102×C59—24no—
78C22⋊C8×C59—22no—
79C22⋊C8×C59C2314yes—
80#95×C59—22no—
81#95×C59C2312yes—
82C24×C59—21no—
83C24×C59C2×D411yescharacteristic
84C2×Q8×C59—24no—
85C2×Q8×C59—22no—
86C2×Q8×C59—82no—
87C2×Q8×C59—82no—
88C2×Q8×C59C2×D414yes—
89C2×D4×C59—22no—
90C2×D4×C59—41no—
91C2×D4×C59—41no—
92C2×D4×C59—42no—
93C2×D4×C59—42no—
94C2×D4×C59—81no—
95C22×C4×C59—21no—
96C22×C4×C59—21no—
97C22×C4×C59—22no—
98C22×C4×C59—22no—
99C22×C4×C59—22no—
100C22×C4×C59—21no—
101C22×C4×C59—21no—
102C22×C4×C59—21no—
103C22×C4×C59—22no—
104C22×C4×C59—81no—
105C22×C4×C59—81no—
106C22×C4×C59SD1614yescomplemented
107C22×C4×C59C2×D412yes—
108C22×C4×C59C2×D412yes—
109C22×C4×C59C2×D411yescharacteristic
110C22×C4×C59C2×D412yes—
111C22×C4×C59C2×D412yes—
112C22×C4×C59C2411yescharacteristic
113SD16×C59—84no—
114C2×C8×C59—24no—
115C2×C8×C59—82no—
116C4⋊C4×C59—24no—
117C4⋊C4×C59—24no—
118C4⋊C4×C59—24no—
119C4⋊C4×C59—28no—
120C4⋊C4×C59—24no—
121C4⋊C4×C59—24no—
122C4⋊C4×C59—22no—
123C4⋊C4×C59—24no—
124C4⋊C4×C59—24no—
125C4⋊C4×C59—22no—
126C4⋊C4×C59—44no—
127C4⋊C4×C59—81no—
128C4⋊C4×C59C2×D414yes—
129C22⋊C4×C59—24no—
130C22⋊C4×C59—24no—
131C22⋊C4×C59—42no—
132C22⋊C4×C59—42no—
133C22⋊C4×C59—44no—
134C22⋊C4×C59—82no—
135C42×C59—28no—
136C23×C59—41no—
137C23×C59—41no—
138C23×C59—42no—
139C23×C59—42no—
140C23×C59—41no—
141C23×C59—41no—
142C23×C59—41no—
143C23×C59#12011yescharacteristic
144C23×C59#12011yescharacteristic
145C23×C59C2×SD1612yes—
146C23×C59#13712yes—
147C23×C59C22×D411yescharacteristic
148Q8×C59—44no—
149Q8×C59—82no—
150Q8×C59—84no—
151D4×C59—44no—
152D4×C59—82no—
153D4×C59—82no—
154C2×C4×C59—22no—
155C2×C4×C59—22no—
156C2×C4×C59—24no—
157C2×C4×C59—24no—
158C2×C4×C59—24no—
159C2×C4×C59—24no—
160C2×C4×C59—22no—
161C2×C4×C59—41no—
162C2×C4×C59—42no—
163C2×C4×C59—42no—
164C2×C4×C59—41no—
165C2×C4×C59—44no—
166C2×C4×C59—42no—
167C2×C4×C59—44no—
168C2×C4×C59—42no—
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—81no—
176C2×C4×C59#12012yes—
177C2×C4×C59C2×SD1614yes—
178C2×C4×C59C22×D412yes—
179C8×C59—44no—
180#18294C5911yesmaximal, characteristic, direct product factor, Sylow
181C22×C59—21no—
182C22×C59—21no—
183C22×C59—21no—
184C22×C59—21no—
185C22×C59—21no—
186C22×C59—21no—
187C22×C59—42no—
188C22×C59—42no—
189C22×C59—82no—
190C22×C59—82no—
191C22×C59—81no—
192C22×C59—81no—
193C22×C59—81no—
194C22×C59#44812yes—
195C22×C59#44812yes—
196C22×C59C2×#12011yescharacteristic
197C22×C59C22×SD1611yescharacteristic
198C22×C59C2×#13711yescharacteristic
199C4×C59—24no—
200C4×C59—22no—
201C4×C59—22no—
202C4×C59—44no—
203C4×C59—42no—
204C4×C59—44no—
205C4×C59—82no—
206C4×C59—81no—
207C2×#544C2×C5911yescharacteristic, complemented
208#3187C2×C5912yes—
209#2618C2×C5911yescharacteristic
210#1611C2×C5914yescomplemented
211#1599C2×C5914yescomplemented
212#1520C2×C5912yescomplemented
213C2×#324C2×C5911yescharacteristic, complemented
214C2×C59—21no—
215C2×C59—21no—
216C2×C59—22no—
217C2×C59—22no—
218C2×C59—161no—
219C2×C59C2×#44811yescharacteristic
220C2×C59#302011yescharacteristic
221C2×C59#302611yescharacteristic
222#544—24no—
223#544—22no—
224#544C22×C5914yes—
225C2×C4⋊Q8—22no—
226C2×#125—22no—
227C2×#123—21no—
228C2×C22⋊Q8—21no—
229C2×C22⋊Q8C22×C5912yes—
230C2×#121C22×C5911yescharacteristic
231C2×#117—21no—
232C22×C4⋊C4C22×C5911yescharacteristic
233#483C22×C5914yes—
234#481—22no—
235#465—24no—
236#450C22×C5914yes—
237#448—22no—
238C2×C22⋊C8C22×C5912yes—
239#398C22×C5912yes—
240#396—22no—
241#394C22×C5912yes—
242#386—21no—
243#380C22×C5911yescharacteristic
244#328C22×C5918yes—
245#324C22×C5914yes—
246C59#1829411yescharacteristic, direct product factor, Sylow
247C22×Q8—21no—
248C22×Q8D4×C5912yes—
249C22×D4—21no—
250C22×D4C23×C5911yescharacteristic
251C23×C4D4×C5911yescharacteristic
252C23×C4D4×C5911yescharacteristic
253C23×C4C23×C5911yescharacteristic
254C2×SD16—24no—
255C22×C8—22no—
256C4⋊Q8—28no—
257C4⋊Q8—28no—
258#125—28no—
259#125—28no—
260#123—44no—
261C22⋊Q8—24no—
262C22⋊Q8—24no—
263C22⋊Q8—22no—
264C22⋊Q8—22no—
265C22⋊Q8D4×C5914yes—
266C22⋊Q8C23×C5914yes—
267#121—22no—
268#121—22no—
269#117—24no—
270#117—24no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4D4×C5912yes—
281C2×C4⋊C4D4×C5912yes—
282C2×C4⋊C4C23×C5911yescharacteristic
283C2×C4⋊C4C23×C5912yes—
284C2×C22⋊C4—22no—
285C2×C22⋊C4—21no—
286C2×C22⋊C4—21no—
287C2×C22⋊C4—22no—
288C2×C22⋊C4—22no—
289C2×C42—22no—
290#106—24no—
291#103—24no—
292#102—24no—
293C22⋊C8—22no—
294C22⋊C8C23×C5914yes—
295#95—22no—
296#95C23×C5912yes—
297C24—21no—
298C24C2×D4×C5911yescharacteristic
299C2×Q8—24no—
300C2×Q8—22no—
301C2×Q8—82no—
302C2×Q8—82no—
303C2×Q8C2×D4×C5914yes—
304C2×D4—22no—
305C2×D4—41no—
306C2×D4—41no—
307C2×D4—42no—
308C2×D4—42no—
309C2×D4—81no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—22no—
313C22×C4—22no—
314C22×C4—22no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—22no—
319C22×C4—81no—
320C22×C4—81no—
321C22×C4SD16×C5914yescomplemented
322C22×C4C2×D4×C5912yes—
323C22×C4C2×D4×C5912yes—
324C22×C4C2×D4×C5911yescharacteristic
325C22×C4C2×D4×C5912yes—
326C22×C4C2×D4×C5912yes—
327C22×C4C24×C5911yescharacteristic
328SD16—84no—
329C2×C8—24no—
330C2×C8—82no—
331C4⋊C4—24no—
332C4⋊C4—24no—
333C4⋊C4—24no—
334C4⋊C4—28no—
335C4⋊C4—24no—
336C4⋊C4—24no—
337C4⋊C4—22no—
338C4⋊C4—24no—
339C4⋊C4—24no—
340C4⋊C4—22no—
341C4⋊C4—44no—
342C4⋊C4—81no—
343C4⋊C4C2×D4×C5914yes—
344C22⋊C4—24no—
345C22⋊C4—24no—
346C22⋊C4—42no—
347C22⋊C4—42no—
348C22⋊C4—44no—
349C22⋊C4—82no—
350C42—28no—
351C23—41no—
352C23—41no—
353C23—42no—
354C23—42no—
355C23—41no—
356C23—41no—
357C23—41no—
358C23#120×C5911yescharacteristic
359C23#120×C5911yescharacteristic
360C23C2×SD16×C5912yes—
361C23#137×C5912yes—
362C23C22×D4×C5911yescharacteristic
363Q8—44no—
364Q8—82no—
365Q8—84no—
366D4—44no—
367D4—82no—
368D4—82no—
369C2×C4—24no—
370C2×C4—24no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—24no—
374C2×C4—24no—
375C2×C4—22no—
376C2×C4—41no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—41no—
380C2×C4—44no—
381C2×C4—42no—
382C2×C4—44no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—41no—
387C2×C4—42no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—81no—
391C2×C4#120×C5912yes—
392C2×C4C2×SD16×C5914yes—
393C2×C4C22×D4×C5912yes—
394C8—44no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—42no—
402C22—42no—
403C22—82no—
404C22—82no—
405C22—81no—
406C22—81no—
407C22—81no—
408C22C59×#44812yes—
409C22C59×#44812yes—
410C22C2×#120×C5911yescharacteristic
411C22C22×SD16×C5911yescharacteristic
412C22C2×#137×C5911yescharacteristic
413C4—24no—
414C4—22no—
415C4—22no—
416C4—44no—
417C4—42no—
418C4—44no—
419C4—82no—
420C4—81no—
421C2—21no—
422C2—21no—
423C2—22no—
424C2—22no—
425C2—161no—
426C2C2×C59×#44811yescharacteristic
427C2C59×#302011yescharacteristic
428C2C59×#302611yescharacteristic
subgroupG/H
center, socleC22×C59C2×#120
commutator, Frattini, cosocleC22×C4C24×C59
prime radicalC2×#121×C59C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C59 ◁ C23×C4×C59 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C59×#544C2semidirect
4. C59×#1611C2semidirect
5. C59×#1599C2semidirect
6. C59×#1520C2semidirect
7. C2×C59×#324C2semidirect
106. C22×C4×C59SD16semidirect
180. #18294C59direct (N × H)
207. C2×#544C2×C59semidirect
210. #1611C2×C59semidirect
211. #1599C2×C59semidirect
212. #1520C2×C59semidirect
213. C2×#324C2×C59semidirect
246. C59#18294direct (N × H)
321. C22×C4SD16×C59semidirect

Maximal subgroups

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

subgroupindex
C2×C59×#5442
C59×#31872
C59×#26182
C59×#16112
C59×#15992
C59×#15202
C2×C59×#3242
#1829459