Finite Group Databasebeta

← C2×C59×#2044 #28435622

Subgroups — C2×C59×#2044 #28435622

Order 15104.

2046 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×#534C211yesmaximal, characteristic
2C22×#99×C59C212yesmaximal, complemented
3C2×C59×#386C212yesmaximal, complemented
4C2×C59×#385C211yesmaximal, characteristic, complemented
5C59×#2044C218yesmaximal, direct product factor
6C2×C59×#342C211yesmaximal, characteristic, complemented
7C23×D4×C59C2212yes—
8C24×C4×C59C2211yescharacteristic
9C59×#534—24no—
10C59×#534—22no—
11C59×#534C2214yes—
12C2×#123×C59—22no—
13C2×#121×C59—21no—
14C2×#121×C59—21no—
15C2×#120×C59—22no—
16C22×C4⋊C4×C59—21no—
17C22×C22⋊C4×C59—22no—
18C22×C22⋊C4×C59C2212yes—
19C22×C22⋊C4×C59C2211yescharacteristic
20C22×C22⋊C4×C59C2211yescharacteristic
21C2×#99×C59—28no—
22C2×#99×C59C2218yescomplemented
23C59×#386—24no—
24C59×#386C2218yescomplemented
25C59×#385—22no—
26C59×#385C2214yescomplemented
27C2×#95×C59—21no—
28C2×#95×C59—22no—
29C59×#342C2214yescomplemented
30C25×C59D412yes—
31C25×C59C2311yescharacteristic
32C22×D4×C59—24no—
33C22×D4×C59—22no—
34C22×D4×C59—22no—
35C22×D4×C59—22no—
36C22×D4×C59—22no—
37C22×D4×C59—24no—
38C22×D4×C59—24no—
39C22×D4×C59—24no—
40C22×D4×C59—21no—
41C22×D4×C59—21no—
42C22×D4×C59D414yes—
43C22×D4×C59C2314yes—
44C23×C4×C59—22no—
45C23×C4×C59—21no—
46C23×C4×C59—21no—
47C23×C4×C59—22no—
48C23×C4×C59—21no—
49C23×C4×C59—22no—
50C23×C4×C59—44no—
51C23×C4×C59D412yes—
52C23×C4×C59D411yescharacteristic
53C23×C4×C59D411yescharacteristic
54C23×C4×C59C2312yes—
55#123×C59—28no—
56#123×C59—28no—
57#121×C59—24no—
58#121×C59—24no—
59#121×C59—24no—
60#121×C59—24no—
61#120×C59—28no—
62#120×C59—28no—
63C2×C4⋊C4×C59—21no—
64C2×C4⋊C4×C59—21no—
65C2×C4⋊C4×C59—24no—
66C2×C4⋊C4×C59—44no—
67C2×C22⋊C4×C59—22no—
68C2×C22⋊C4×C59—22no—
69C2×C22⋊C4×C59—21no—
70C2×C22⋊C4×C59—22no—
71C2×C22⋊C4×C59—22no—
72C2×C22⋊C4×C59—22no—
73C2×C22⋊C4×C59—24no—
74C2×C22⋊C4×C59—24no—
75C2×C22⋊C4×C59—22no—
76C2×C22⋊C4×C59—28no—
77C2×C22⋊C4×C59—48no—
78C2×C22⋊C4×C59D412yes—
79C2×C22⋊C4×C59D414yescomplemented
80C2×C22⋊C4×C59C2314yes—
81C2×C22⋊C4×C59C2312yes—
82C2×C22⋊C4×C59C2312yes—
83#99×C59—216no—
84#95×C59—24no—
85#95×C59—28no—
86C24×C59—22no—
87C24×C59—24no—
88C24×C59—22no—
89C24×C59—24no—
90C24×C59—42no—
91C24×C59—42no—
92C24×C59—44no—
93C24×C59—44no—
94C24×C59C2×D412yes—
95C24×C59C2×D411yescharacteristic
96C24×C59C2×D414yes—
97C24×C59C2×D412yes—
98C24×C59C2×D411yescharacteristic
99C24×C59C2×D412yes—
100C24×C59#4112yes—
101C24×C59#4114yes—
102C24×C59C2411yescharacteristic
103C2×D4×C59—24no—
104C2×D4×C59—24no—
105C2×D4×C59—28no—
106C2×D4×C59—28no—
107C2×D4×C59—24no—
108C2×D4×C59—24no—
109C2×D4×C59—24no—
110C2×D4×C59—24no—
111C2×D4×C59—24no—
112C2×D4×C59—24no—
113C2×D4×C59—24no—
114C2×D4×C59—24no—
115C2×D4×C59—44no—
116C2×D4×C59—44no—
117C2×D4×C59—44no—
118C2×D4×C59—44no—
119C2×D4×C59—44no—
120C2×D4×C59—44no—
121C2×D4×C59—44no—
122C2×D4×C59—44no—
123C2×D4×C59—82no—
124C2×D4×C59—82no—
125C22×C4×C59—28no—
126C22×C4×C59—24no—
127C22×C4×C59—22no—
128C22×C4×C59—21no—
129C22×C4×C59—21no—
130C22×C4×C59—22no—
131C22×C4×C59—24no—
132C22×C4×C59—24no—
133C22×C4×C59—24no—
134C22×C4×C59—24no—
135C22×C4×C59—22no—
136C22×C4×C59—22no—
137C22×C4×C59—21no—
138C22×C4×C59—21no—
139C22×C4×C59—24no—
140C22×C4×C59—44no—
141C22×C4×C59—48no—
142C22×C4×C59—44no—
143C22×C4×C59—42no—
144C22×C4×C59—42no—
145C22×C4×C59—42no—
146C22×C4×C59—44no—
147C22×C4×C59—42no—
148C22×C4×C59—41no—
149C22×C4×C59—41no—
150C22×C4×C59—42no—
151C22×C4×C59—42no—
152C22×C4×C59—44no—
153C22×C4×C59—44no—
154C22×C4×C59—44no—
155C22×C4×C59C2×D414yes—
156C22×C4×C59C2×D412yes—
157C22×C4×C59C2×D412yes—
158C4⋊C4×C59—24no—
159C4⋊C4×C59—24no—
160C4⋊C4×C59—48no—
161C22⋊C4×C59—28no—
162C22⋊C4×C59—28no—
163C22⋊C4×C59—24no—
164C22⋊C4×C59—24no—
165C22⋊C4×C59—24no—
166C22⋊C4×C59—22no—
167C22⋊C4×C59—24no—
168C22⋊C4×C59—24no—
169C22⋊C4×C59—416no—
170C22⋊C4×C59—44no—
171C22⋊C4×C59C2×D414yescomplemented
172C23×C59—22no—
173C23×C59—24no—
174C23×C59—22no—
175C23×C59—24no—
176C23×C59—24no—
177C23×C59—24no—
178C23×C59—24no—
179C23×C59—41no—
180C23×C59—42no—
181C23×C59—41no—
182C23×C59—41no—
183C23×C59—42no—
184C23×C59—44no—
185C23×C59—44no—
186C23×C59—48no—
187C23×C59—41no—
188C23×C59—44no—
189C23×C59—44no—
190C23×C59—416no—
191C23×C59—44no—
192C23×C59—44no—
193C23×C59—44no—
194C23×C59—44no—
195C23×C59—82no—
196C23×C59—82no—
197C23×C59—88no—
198C23×C59#12012yes—
199C23×C59#12011yescharacteristic
200C23×C59#12011yescharacteristic
201C23×C59#12112yes—
202C23×C59#12114yes—
203C23×C59#12112yes—
204C23×C59#12114yes—
205C23×C59#12314yes—
206C23×C59#12314yes—
207C23×C59#12412yes—
208C23×C59#12412yes—
209C23×C59C22×D412yes—
210C23×C59C22×D411yescharacteristic
211C23×C59C22×D411yescharacteristic
212C23×C59C2×#4111yescharacteristic
213C23×C59C2×#4112yes—
214D4×C59—44no—
215D4×C59—44no—
216D4×C59—44no—
217D4×C59—44no—
218D4×C59—48no—
219D4×C59—48no—
220D4×C59—84no—
221D4×C59—84no—
222C2×C4×C59—28no—
223C2×C4×C59—24no—
224C2×C4×C59—22no—
225C2×C4×C59—22no—
226C2×C4×C59—24no—
227C2×C4×C59—24no—
228C2×C4×C59—24no—
229C2×C4×C59—24no—
230C2×C4×C59—42no—
231C2×C4×C59—42no—
232C2×C4×C59—48no—
233C2×C4×C59—42no—
234C2×C4×C59—44no—
235C2×C4×C59—44no—
236C2×C4×C59—48no—
237C2×C4×C59—42no—
238C2×C4×C59—44no—
239C2×C4×C59—44no—
240C2×C4×C59—44no—
241C2×C4×C59—42no—
242C2×C4×C59—42no—
243C2×C4×C59—42no—
244C2×C4×C59—42no—
245C2×C4×C59—44no—
246C2×C4×C59—44no—
247C2×C4×C59—44no—
248C2×C4×C59—81no—
249C2×C4×C59—81no—
250C2×C4×C59—88no—
251C2×#2044C5911yesmaximal, characteristic, direct product factor, Sylow
252C22×C59—21no—
253C22×C59—22no—
254C22×C59—21no—
255C22×C59—22no—
256C22×C59—21no—
257C22×C59—22no—
258C22×C59—21no—
259C22×C59—22no—
260C22×C59—24no—
261C22×C59—28no—
262C22×C59—28no—
263C22×C59—24no—
264C22×C59—42no—
265C22×C59—44no—
266C22×C59—44no—
267C22×C59—42no—
268C22×C59—41no—
269C22×C59—41no—
270C22×C59—42no—
271C22×C59—48no—
272C22×C59—44no—
273C22×C59—44no—
274C22×C59—44no—
275C22×C59—84no—
276C22×C59—88no—
277C22×C59—88no—
278C22×C59#39414yes—
279C22×C59#39412yes—
280C22×C59#39412yes—
281C22×C59B(4,𝔽2)12yes—
282C22×C59#45812yes—
283C22×C59C2×#12011yescharacteristic
284C22×C59C2×#12111yescharacteristic
285C22×C59C2×#12112yes—
286C22×C59C2×#12312yes—
287C22×C59C2×#12411yescharacteristic
288C4×C59—44no—
289C4×C59—44no—
290C4×C59—44no—
291C4×C59—42no—
292C4×C59—42no—
293C4×C59—84no—
294C2×#534C2×C5911yescharacteristic
295C22×#99C2×C5912yescomplemented
296C2×#386C2×C5912yescomplemented
297C2×#385C2×C5911yescharacteristic, complemented
298#2044C2×C5918yesdirect product factor
299C2×#342C2×C5911yescharacteristic, complemented
300C2×C59—21no—
301C2×C59—22no—
302C2×C59—22no—
303C2×C59—24no—
304C2×C59—21no—
305C2×C59—22no—
306C2×C59—84no—
307C2×C59#204414yesdirect product factor
308C2×C59C2×#39411yescharacteristic
309C2×C59C2×B(4,𝔽2)11yescharacteristic
310C2×C59C2×#45811yescharacteristic
311C23×D4C22×C5912yes—
312C24×C4C22×C5911yescharacteristic
313#534—24no—
314#534—22no—
315#534C22×C5914yes—
316C2×#123—22no—
317C2×#121—21no—
318C2×#121—21no—
319C2×#120—22no—
320C22×C4⋊C4—21no—
321C22×C22⋊C4—22no—
322C22×C22⋊C4C22×C5912yes—
323C22×C22⋊C4C22×C5911yescharacteristic
324C22×C22⋊C4C22×C5911yescharacteristic
325C2×#99—28no—
326C2×#99C22×C5918yescomplemented
327#386—24no—
328#386C22×C5918yescomplemented
329#385—22no—
330#385C22×C5914yescomplemented
331C2×#95—21no—
332C2×#95—22no—
333#342C22×C5914yescomplemented
334C59C2×#204411yescharacteristic, direct product factor, Sylow
335C25D4×C5912yes—
336C25C23×C5911yescharacteristic
337C22×D4—22no—
338C22×D4—22no—
339C22×D4—22no—
340C22×D4—22no—
341C22×D4—24no—
342C22×D4—24no—
343C22×D4—24no—
344C22×D4—24no—
345C22×D4—21no—
346C22×D4—21no—
347C22×D4D4×C5914yes—
348C22×D4C23×C5914yes—
349C23×C4—22no—
350C23×C4—21no—
351C23×C4—21no—
352C23×C4—22no—
353C23×C4—21no—
354C23×C4—22no—
355C23×C4—44no—
356C23×C4D4×C5912yes—
357C23×C4D4×C5911yescharacteristic
358C23×C4D4×C5911yescharacteristic
359C23×C4C23×C5912yes—
360#123—28no—
361#123—28no—
362#121—24no—
363#121—24no—
364#121—24no—
365#121—24no—
366#120—28no—
367#120—28no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—24no—
371C2×C4⋊C4—44no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—28no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—48no—
383C2×C22⋊C4D4×C5912yes—
384C2×C22⋊C4D4×C5914yescomplemented
385C2×C22⋊C4C23×C5914yes—
386C2×C22⋊C4C23×C5912yes—
387C2×C22⋊C4C23×C5912yes—
388#99—216no—
389#95—24no—
390#95—28no—
391C24—22no—
392C24—24no—
393C24—22no—
394C24—24no—
395C24—42no—
396C24—42no—
397C24—44no—
398C24—44no—
399C24C2×D4×C5912yes—
400C24C2×D4×C5911yescharacteristic
401C24C2×D4×C5914yes—
402C24C2×D4×C5912yes—
403C24C2×D4×C5911yescharacteristic
404C24C2×D4×C5912yes—
405C24#41×C5912yes—
406C24#41×C5914yes—
407C24C24×C5911yescharacteristic
408C2×D4—24no—
409C2×D4—24no—
410C2×D4—28no—
411C2×D4—28no—
412C2×D4—24no—
413C2×D4—24no—
414C2×D4—24no—
415C2×D4—24no—
416C2×D4—24no—
417C2×D4—24no—
418C2×D4—24no—
419C2×D4—24no—
420C2×D4—44no—
421C2×D4—44no—
422C2×D4—44no—
423C2×D4—44no—
424C2×D4—44no—
425C2×D4—44no—
426C2×D4—44no—
427C2×D4—44no—
428C2×D4—82no—
429C2×D4—82no—
430C22×C4—28no—
431C22×C4—24no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—24no—
437C22×C4—24no—
438C22×C4—24no—
439C22×C4—24no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—24no—
445C22×C4—44no—
446C22×C4—48no—
447C22×C4—44no—
448C22×C4—42no—
449C22×C4—42no—
450C22×C4—44no—
451C22×C4—42no—
452C22×C4—42no—
453C22×C4—41no—
454C22×C4—41no—
455C22×C4—42no—
456C22×C4—42no—
457C22×C4—44no—
458C22×C4—44no—
459C22×C4—44no—
460C22×C4C2×D4×C5914yes—
461C22×C4C2×D4×C5912yes—
462C22×C4C2×D4×C5912yes—
463C4⋊C4—24no—
464C4⋊C4—24no—
465C4⋊C4—48no—
466C22⋊C4—28no—
467C22⋊C4—28no—
468C22⋊C4—24no—
469C22⋊C4—24no—
470C22⋊C4—24no—
471C22⋊C4—22no—
472C22⋊C4—24no—
473C22⋊C4—24no—
474C22⋊C4—416no—
475C22⋊C4—44no—
476C22⋊C4C2×D4×C5914yescomplemented
477C23—22no—
478C23—24no—
479C23—22no—
480C23—24no—
481C23—24no—
482C23—24no—
483C23—24no—
484C23—41no—
485C23—42no—
486C23—41no—
487C23—41no—
488C23—42no—
489C23—44no—
490C23—44no—
491C23—48no—
492C23—41no—
493C23—44no—
494C23—44no—
495C23—416no—
496C23—44no—
497C23—44no—
498C23—44no—
499C23—44no—
500C23—82no—
501C23—82no—
502C23—88no—
503C23#120×C5912yes—
504C23#120×C5911yescharacteristic
505C23#120×C5911yescharacteristic
506C23#121×C5912yes—
507C23#121×C5914yes—
508C23#121×C5912yes—
509C23#121×C5914yes—
510C23#123×C5914yes—
511C23#123×C5914yes—
512C23#124×C5912yes—
513C23#124×C5912yes—
514C23C22×D4×C5912yes—
515C23C22×D4×C5911yescharacteristic
516C23C22×D4×C5911yescharacteristic
517C23C2×#41×C5911yescharacteristic
518C23C2×#41×C5912yes—
519D4—48no—
520D4—48no—
521D4—44no—
522D4—44no—
523D4—44no—
524D4—44no—
525D4—84no—
526D4—84no—
527C2×C4—28no—
528C2×C4—24no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—24no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—24no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—48no—
538C2×C4—42no—
539C2×C4—44no—
540C2×C4—44no—
541C2×C4—48no—
542C2×C4—44no—
543C2×C4—44no—
544C2×C4—44no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—44no—
551C2×C4—44no—
552C2×C4—44no—
553C2×C4—81no—
554C2×C4—81no—
555C2×C4—88no—
556C22—21no—
557C22—22no—
558C22—21no—
559C22—22no—
560C22—21no—
561C22—22no—
562C22—21no—
563C22—22no—
564C22—24no—
565C22—28no—
566C22—28no—
567C22—24no—
568C22—42no—
569C22—44no—
570C22—44no—
571C22—42no—
572C22—41no—
573C22—41no—
574C22—42no—
575C22—48no—
576C22—44no—
577C22—44no—
578C22—44no—
579C22—84no—
580C22—88no—
581C22—88no—
582C22C59×#39414yes—
583C22C59×#39412yes—
584C22C59×#39412yes—
585C22C59×B(4,𝔽2)12yes—
586C22C59×#45812yes—
587C22C2×#120×C5911yescharacteristic
588C22C2×#121×C5911yescharacteristic
589C22C2×#121×C5912yes—
590C22C2×#123×C5912yes—
591C22C2×#124×C5911yescharacteristic
592C4—44no—
593C4—44no—
594C4—42no—
595C4—42no—
596C4—44no—
597C4—84no—
598C2—21no—
599C2—22no—
600C2—22no—
601C2—24no—
602C2—22no—
603C2—21no—
604C2—84no—
605C2C59×#204414yesdirect product factor
606C2C2×C59×#39411yescharacteristic
607C2C2×C59×B(4,𝔽2)11yescharacteristic
608C2C2×C59×#45811yescharacteristic
subgroupG/H
center, socleC23×C59#120
commutator, Frattini, cosocleC24C24×C59
prime radicalC2×C59×#534C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C59 ◁ C25×C59 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×#99×C59C2semidirect
3. C2×C59×#386C2semidirect
4. C2×C59×#385C2semidirect
5. C59×#2044C2direct (N × H)
6. C2×C59×#342C2semidirect
22. C2×#99×C59C22semidirect
24. C59×#386C22semidirect
26. C59×#385C22semidirect
29. C59×#342C22semidirect
79. C2×C22⋊C4×C59D4semidirect
171. C22⋊C4×C59C2×D4semidirect
251. C2×#2044C59direct (N × H)
295. C22×#99C2×C59semidirect
296. C2×#386C2×C59semidirect
297. C2×#385C2×C59semidirect
298. #2044C2×C59direct (N × H)
299. C2×#342C2×C59semidirect
307. C2×C59#2044direct (N × H)
326. C2×#99C22×C59semidirect
328. #386C22×C59semidirect
330. #385C22×C59semidirect
333. #342C22×C59semidirect
334. C59C2×#2044direct (N × H)
384. C2×C22⋊C4D4×C59semidirect
476. C22⋊C4C2×D4×C59semidirect
605. C2C59×#2044direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C59×#5342
C22×#99×C592
C2×C59×#3862
C2×C59×#3852
C59×#20442
C2×C59×#3422
C2×#204459