Finite Group Databasebeta

← C59×#18405 #28430514

Subgroups — C59×#18405 #28430514

Order 15104.

1190 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3506C211yesmaximal, characteristic, complemented
2C59×#3208C211yesmaximal, characteristic, complemented
3C59×#3205C211yesmaximal, characteristic, complemented
4C59×#2541C211yesmaximal, characteristic, complemented
5C59×#1600C218yesmaximal, complemented
6C59×#1503C211yesmaximal, characteristic, complemented
7C59×#1502C211yesmaximal, characteristic, complemented
8C59×#1460C211yesmaximal, characteristic, complemented
9C59×#559—22no—
10C59×#556—21no—
11C59×#555—21no—
12C59×#553—22no—
13C59×#550—21no—
14C59×#547—21no—
15C59×#538C2214yes—
16C59×#535—21no—
17C59×#533C2211yescharacteristic
18C59×#532C2211yescharacteristic
19C2×#127×C59—21no—
20C2×#127×C59C2211yescharacteristic
21C59×#525—22no—
22C2×#121×C59—22no—
23C59×#520—21no—
24C2×C4×D4×C59C2211yescharacteristic
25C59×#493—21no—
26C59×#492—21no—
27C59×#486—21no—
28C59×#486—21no—
29C59×#460—22no—
30C59×#459—22no—
31C59×#450C2214yes—
32C59×#447C2214yes—
33C59×#431C2211yescharacteristic
34C59×#431C2211yescharacteristic
35C59×#392C2214yes—
36C59×#390—21no—
37C4×C4⋊C4×C59C2211yescharacteristic
38C59×#328C2214yes—
39C59×#327C2214yes—
40C59×#323C2214yes—
41C2×#41×C59—22no—
42C2×#41×C59—21no—
43C22×D4×C59—24no—
44C22×D4×C59—21no—
45C22×D4×C59—21no—
46C22×D4×C59D411yescharacteristic
47C22×D4×C59C2312yes—
48C23×C4×C59D412yes—
49C2×SD16×C59—24no—
50C2×D8×C59—24no—
51C4⋊Q8×C59D411yescharacteristic, complemented
52C4⋊Q8×C59D411yescharacteristic, complemented
53C4⋊Q8×C59D411yescharacteristic, complemented
54#127×C59—22no—
55#127×C59—21no—
56#127×C59—21no—
57#127×C59—21no—
58#127×C59—21no—
59#127×C59—44no—
60#127×C59D411yescharacteristic, complemented
61#126×C59—24no—
62#125×C59—21no—
63#124×C59—22no—
64#124×C59—24no—
65#124×C59—21no—
66#123×C59—24no—
67#123×C59—24no—
68C22⋊Q8×C59—22no—
69C22⋊Q8×C59—21no—
70C22⋊Q8×C59C2312yes—
71#121×C59—22no—
72#121×C59—22no—
73#121×C59—22no—
74#121×C59—24no—
75#121×C59—21no—
76#121×C59—48no—
77#121×C59C2312yes—
78#120×C59—24no—
79C4×Q8×C59—22no—
80C4×Q8×C59—21no—
81C4×Q8×C59D412yescomplemented
82C4×D4×C59—22no—
83C4×D4×C59—24no—
84C4×D4×C59—24no—
85C4×D4×C59—21no—
86C4×D4×C59—21no—
87C4×D4×C59—21no—
88C4×D4×C59—21no—
89C4×D4×C59—21no—
90C4×D4×C59D412yescomplemented
91#117×C59—22no—
92#117×C59—22no—
93#117×C59—21no—
94C2×C4⋊C4×C59—22no—
95C2×C4⋊C4×C59—21no—
96C2×C4⋊C4×C59D411yescharacteristic
97C2×C22⋊C4×C59—24no—
98C2×C22⋊C4×C59C2312yes—
99C2×C42×C59—21no—
100C2×C42×C59C2311yescharacteristic
101C4⋊C8×C59—21no—
102C4⋊C8×C59—21no—
103#102×C59—24no—
104#102×C59—24no—
105C22⋊C8×C59C2312yes—
106C22⋊C8×C59C2312yes—
107C4×C8×C59—21no—
108C4×C8×C59—21no—
109#95×C59C2312yes—
110C24×C59—22no—
111C24×C59C2×D412yes—
112#41×C59—42no—
113#41×C59—42no—
114#41×C59—84no—
115C2×Q8×C59—21no—
116C2×Q8×C59—21no—
117C2×Q8×C59C2×D412yes—
118C2×D4×C59—22no—
119C2×D4×C59—24no—
120C2×D4×C59—24no—
121C2×D4×C59—21no—
122C2×D4×C59—21no—
123C2×D4×C59—21no—
124C2×D4×C59—21no—
125C2×D4×C59—22no—
126C2×D4×C59—22no—
127C2×D4×C59—22no—
128C2×D4×C59—22no—
129C2×D4×C59—44no—
130C2×D4×C59—48no—
131C2×D4×C59—48no—
132C2×D4×C59—41no—
133C2×D4×C59—41no—
134C2×D4×C59—41no—
135C2×D4×C59—41no—
136C2×D4×C59—42no—
137C2×D4×C59—42no—
138C2×D4×C59—82no—
139C2×D4×C59—84no—
140C2×D4×C59C2×D412yes—
141C22×C4×C59—22no—
142C22×C4×C59—24no—
143C22×C4×C59—22no—
144C22×C4×C59—22no—
145C22×C4×C59—22no—
146C22×C4×C59—44no—
147C22×C4×C59C2×D411yescharacteristic
148C22×C4×C59C2×D412yes—
149C22×C4×C59C2×D411yescharacteristic
150C22×C4×C59C2411yescharacteristic
151SD16×C59—84no—
152D8×C59—84no—
153C2×C8×C59—22no—
154C2×C8×C59—22no—
155C4⋊C4×C59—24no—
156C4⋊C4×C59—24no—
157C4⋊C4×C59—21no—
158C4⋊C4×C59—21no—
159C4⋊C4×C59—21no—
160C4⋊C4×C59—21no—
161C4⋊C4×C59—21no—
162C4⋊C4×C59—21no—
163C4⋊C4×C59—22no—
164C4⋊C4×C59—22no—
165C4⋊C4×C59C2×D412yes—
166C4⋊C4×C59C2×D412yes—
167C22⋊C4×C59—24no—
168C22⋊C4×C59—24no—
169C22⋊C4×C59—24no—
170C22⋊C4×C59—22no—
171C22⋊C4×C59—22no—
172C22⋊C4×C59—22no—
173C22⋊C4×C59—22no—
174C22⋊C4×C59—22no—
175C22⋊C4×C59—48no—
176C42×C59—24no—
177C42×C59—22no—
178C42×C59—42no—
179C42×C59C2×D411yescharacteristic
180C42×C59C2×D411yescharacteristic
181C42×C59C2×D411yescharacteristic
182C42×C59C2×D411yescharacteristic
183C23×C59—22no—
184C23×C59—22no—
185C23×C59—22no—
186C23×C59—22no—
187C23×C59—42no—
188C23×C59—42no—
189C23×C59—44no—
190C23×C59—44no—
191C23×C59—42no—
192C23×C59—42no—
193C23×C59—42no—
194C23×C59C22×D411yescharacteristic
195Q8×C59—42no—
196Q8×C59—42no—
197Q8×C59—42no—
198D4×C59—42no—
199D4×C59—44no—
200D4×C59—44no—
201D4×C59—42no—
202D4×C59—42no—
203D4×C59—42no—
204D4×C59—42no—
205D4×C59—42no—
206D4×C59—42no—
207D4×C59—82no—
208D4×C59—84no—
209D4×C59—84no—
210D4×C59—816no—
211D4×C59—82no—
212D4×C59—82no—
213D4×C59—82no—
214C2×C4×C59—22no—
215C2×C4×C59—24no—
216C2×C4×C59—22no—
217C2×C4×C59—22no—
218C2×C4×C59—22no—
219C2×C4×C59—22no—
220C2×C4×C59—41no—
221C2×C4×C59—42no—
222C2×C4×C59—42no—
223C2×C4×C59—44no—
224C2×C4×C59—44no—
225C2×C4×C59—42no—
226C2×C4×C59—82no—
227C2×C4×C59—84no—
228C2×C4×C59#12011yescharacteristic
229C2×C4×C59#12011yescharacteristic
230C2×C4×C59#12011yescharacteristic
231C2×C4×C59#12011yescharacteristic
232C2×C4×C59#13512yes—
233C2×C4×C59AGL(1,ℤ/8)12yes—
234C2×C4×C59C22×D411yescharacteristic
235C2×C4×C59C22×D411yescharacteristic
236C8×C59—42no—
237C8×C59—42no—
238#18405C5911yesmaximal, characteristic, direct product factor, Sylow
239C22×C59—21no—
240C22×C59—21no—
241C22×C59—44no—
242C22×C59—42no—
243C22×C59—42no—
244C22×C59—42no—
245C22×C59—42no—
246C22×C59—42no—
247C22×C59—42no—
248C22×C59—82no—
249C22×C59—84no—
250C22×C59—84no—
251C22×C59—82no—
252C22×C59—82no—
253C22×C59—82no—
254C22×C59C2×#12011yescharacteristic
255C22×C59C2×#13511yescharacteristic
256C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
257C4×C59—21no—
258C4×C59—21no—
259C4×C59—21no—
260C4×C59—44no—
261C4×C59—42no—
262C4×C59—42no—
263C4×C59—42no—
264C4×C59—42no—
265C4×C59#44912yes—
266C4×C59#44912yes—
267C4×C59#45312yes—
268#3506C2×C5911yescharacteristic, complemented
269#3208C2×C5911yescharacteristic, complemented
270#3205C2×C5911yescharacteristic, complemented
271#2541C2×C5911yescharacteristic, complemented
272#1600C2×C5918yescomplemented
273#1503C2×C5911yescharacteristic, complemented
274#1502C2×C5911yescharacteristic, complemented
275#1460C2×C5911yescharacteristic, complemented
276C2×C59—21no—
277C2×C59—21no—
278C2×C59—82no—
279C2×C59—82no—
280C2×C59—162no—
281C2×C59C2×#44911yescharacteristic
282C2×C59C2×#45311yescharacteristic
283C2×C59#302711yescharacteristic
284#559—22no—
285#556—21no—
286#555—21no—
287#553—22no—
288#550—21no—
289#547—21no—
290#538C22×C5914yes—
291#535—21no—
292#533C22×C5911yescharacteristic
293#532C22×C5911yescharacteristic
294C2×#127—21no—
295C2×#127C22×C5911yescharacteristic
296#525—22no—
297C2×#121—22no—
298#520—21no—
299C2×C4×D4C22×C5911yescharacteristic
300#493—21no—
301#492—21no—
302#486—21no—
303#486—21no—
304#460—22no—
305#459—22no—
306#450C22×C5914yes—
307#447C22×C5914yes—
308#431C22×C5911yescharacteristic
309#431C22×C5911yescharacteristic
310#392C22×C5914yes—
311#390—21no—
312C4×C4⋊C4C22×C5911yescharacteristic
313#328C22×C5914yes—
314#327C22×C5914yes—
315#323C22×C5914yes—
316C59#1840511yescharacteristic, direct product factor, Sylow
317C2×#41—22no—
318C2×#41—21no—
319C22×D4—24no—
320C22×D4—21no—
321C22×D4—21no—
322C22×D4D4×C5911yescharacteristic
323C22×D4C23×C5912yes—
324C23×C4D4×C5912yes—
325C2×SD16—24no—
326C2×D8—24no—
327C4⋊Q8D4×C5911yescharacteristic, complemented
328C4⋊Q8D4×C5911yescharacteristic, complemented
329C4⋊Q8D4×C5911yescharacteristic, complemented
330#127—22no—
331#127—21no—
332#127—21no—
333#127—21no—
334#127—21no—
335#127—44no—
336#127D4×C5911yescharacteristic, complemented
337#126—24no—
338#125—21no—
339#124—22no—
340#124—24no—
341#124—21no—
342#123—24no—
343#123—24no—
344C22⋊Q8—22no—
345C22⋊Q8—21no—
346C22⋊Q8C23×C5912yes—
347#121—22no—
348#121—22no—
349#121—22no—
350#121—24no—
351#121—21no—
352#121—48no—
353#121C23×C5912yes—
354#120—24no—
355C4×Q8—22no—
356C4×Q8—21no—
357C4×Q8D4×C5912yescomplemented
358C4×D4—22no—
359C4×D4—24no—
360C4×D4—24no—
361C4×D4—21no—
362C4×D4—21no—
363C4×D4—21no—
364C4×D4—21no—
365C4×D4—21no—
366C4×D4D4×C5912yescomplemented
367#117—22no—
368#117—22no—
369#117—21no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4D4×C5911yescharacteristic
373C2×C22⋊C4—24no—
374C2×C22⋊C4C23×C5912yes—
375C2×C42—21no—
376C2×C42C23×C5911yescharacteristic
377C4⋊C8—21no—
378C4⋊C8—21no—
379#102—24no—
380#102—24no—
381C22⋊C8C23×C5912yes—
382C22⋊C8C23×C5912yes—
383C4×C8—21no—
384C4×C8—21no—
385#95C23×C5912yes—
386C24—22no—
387C24C2×D4×C5912yes—
388#41—42no—
389#41—42no—
390#41—84no—
391C2×Q8—21no—
392C2×Q8—21no—
393C2×Q8C2×D4×C5912yes—
394C2×D4—22no—
395C2×D4—24no—
396C2×D4—24no—
397C2×D4—21no—
398C2×D4—21no—
399C2×D4—21no—
400C2×D4—21no—
401C2×D4—22no—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—22no—
405C2×D4—44no—
406C2×D4—48no—
407C2×D4—48no—
408C2×D4—41no—
409C2×D4—41no—
410C2×D4—41no—
411C2×D4—41no—
412C2×D4—42no—
413C2×D4—42no—
414C2×D4—82no—
415C2×D4—84no—
416C2×D4C2×D4×C5912yes—
417C22×C4—22no—
418C22×C4—24no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—44no—
423C22×C4C2×D4×C5911yescharacteristic
424C22×C4C2×D4×C5912yes—
425C22×C4C2×D4×C5911yescharacteristic
426C22×C4C24×C5911yescharacteristic
427SD16—84no—
428D8—84no—
429C2×C8—22no—
430C2×C8—22no—
431C4⋊C4—24no—
432C4⋊C4—24no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4—21no—
437C4⋊C4—21no—
438C4⋊C4—21no—
439C4⋊C4—22no—
440C4⋊C4—22no—
441C4⋊C4C2×D4×C5912yes—
442C4⋊C4C2×D4×C5912yes—
443C22⋊C4—24no—
444C22⋊C4—24no—
445C22⋊C4—24no—
446C22⋊C4—22no—
447C22⋊C4—22no—
448C22⋊C4—22no—
449C22⋊C4—22no—
450C22⋊C4—22no—
451C22⋊C4—48no—
452C42—24no—
453C42—22no—
454C42—42no—
455C42C2×D4×C5911yescharacteristic
456C42C2×D4×C5911yescharacteristic
457C42C2×D4×C5911yescharacteristic
458C42C2×D4×C5911yescharacteristic
459C23—22no—
460C23—22no—
461C23—22no—
462C23—22no—
463C23—42no—
464C23—42no—
465C23—44no—
466C23—44no—
467C23—42no—
468C23—42no—
469C23—42no—
470C23C22×D4×C5911yescharacteristic
471Q8—42no—
472Q8—42no—
473Q8—42no—
474D4—42no—
475D4—44no—
476D4—44no—
477D4—42no—
478D4—42no—
479D4—42no—
480D4—42no—
481D4—42no—
482D4—42no—
483D4—82no—
484D4—84no—
485D4—84no—
486D4—816no—
487D4—82no—
488D4—82no—
489D4—82no—
490C2×C4—22no—
491C2×C4—24no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—41no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—44no—
500C2×C4—44no—
501C2×C4—42no—
502C2×C4—82no—
503C2×C4—84no—
504C2×C4#120×C5911yescharacteristic
505C2×C4#120×C5911yescharacteristic
506C2×C4#120×C5911yescharacteristic
507C2×C4#120×C5911yescharacteristic
508C2×C4#135×C5912yes—
509C2×C4AGL(1,ℤ/8)×C5912yes—
510C2×C4C22×D4×C5911yescharacteristic
511C2×C4C22×D4×C5911yescharacteristic
512C8—42no—
513C8—42no—
514C22—21no—
515C22—21no—
516C22—44no—
517C22—42no—
518C22—42no—
519C22—42no—
520C22—42no—
521C22—42no—
522C22—42no—
523C22—82no—
524C22—84no—
525C22—84no—
526C22—82no—
527C22—82no—
528C22—82no—
529C22C2×#120×C5911yescharacteristic
530C22C2×#135×C5911yescharacteristic
531C22C2×AGL(1,ℤ/8)×C5911yescharacteristic
532C4—21no—
533C4—21no—
534C4—21no—
535C4—44no—
536C4—42no—
537C4—42no—
538C4—42no—
539C4—42no—
540C4C59×#44912yes—
541C4C59×#44912yes—
542C4C59×#45312yes—
543C2—21no—
544C2—21no—
545C2—82no—
546C2—82no—
547C2—162no—
548C2C2×C59×#44911yescharacteristic
549C2C2×C59×#45311yescharacteristic
550C2C59×#302711yescharacteristic
subgroupG/H
center, socleC22×C59C2×#120
commutator, Frattini, cosocleC22×C4C24×C59
LCSG ▷ C22×C4 ▷ 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×#3506C2semidirect
2. C59×#3208C2semidirect
3. C59×#3205C2semidirect
4. C59×#2541C2semidirect
5. C59×#1600C2semidirect
6. C59×#1503C2semidirect
7. C59×#1502C2semidirect
8. C59×#1460C2semidirect
51. C4⋊Q8×C59D4semidirect
52. C4⋊Q8×C59D4semidirect
53. C4⋊Q8×C59D4semidirect
60. #127×C59D4semidirect
81. C4×Q8×C59D4semidirect
90. C4×D4×C59D4semidirect
238. #18405C59direct (N × H)
268. #3506C2×C59semidirect
269. #3208C2×C59semidirect
270. #3205C2×C59semidirect
271. #2541C2×C59semidirect
272. #1600C2×C59semidirect
273. #1503C2×C59semidirect
274. #1502C2×C59semidirect
275. #1460C2×C59semidirect
316. C59#18405direct (N × H)
327. C4⋊Q8D4×C59semidirect
328. C4⋊Q8D4×C59semidirect
329. C4⋊Q8D4×C59semidirect
336. #127D4×C59semidirect
357. C4×Q8D4×C59semidirect
366. C4×D4D4×C59semidirect

Maximal subgroups

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

subgroupindex
C59×#35062
C59×#32082
C59×#32052
C59×#25412
C59×#16002
C59×#15032
C59×#15022
C59×#14602
#1840559