Finite Group Databasebeta

← C2×C59×#1390 #28424681

Subgroups — C2×C59×#1390 #28424681

Order 15104.

1202 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#100×C59C211yesmaximal, characteristic
2C22×#99×C59C211yesmaximal, characteristic
3C2×C59×#386C211yesmaximal, characteristic
4C59×#1390C214yesmaximal, direct product factor
5C23×D4×C59C2211yescharacteristic
6C24×C4×C59C411yescharacteristic, complemented
7C22×M16×C59—21no—
8C22×C22⋊C4×C59—21no—
9C22×C22⋊C4×C59—21no—
10C22×C22⋊C4×C59C411yescharacteristic, complemented
11C2×#100×C59—21no—
12C2×#100×C59—22no—
13C2×#100×C59C414yescomplemented
14C2×#100×C59C2212yes—
15C2×#99×C59—21no—
16C2×#99×C59—22no—
17C2×#99×C59C414yescomplemented
18C2×#99×C59C2212yes—
19C59×#386—21no—
20C59×#386—21no—
21C59×#386C412yescomplemented
22C59×#386C2212yes—
23C2×#95×C59—21no—
24C25×C59C2×C411yescharacteristic
25C25×C59D411yescharacteristic
26C22×D4×C59—42no—
27C22×D4×C59—41no—
28C22×D4×C59—41no—
29C22×D4×C59C2×C411yescharacteristic
30C22×D4×C59C2×C412yes—
31C22×D4×C59C2×C412yes—
32C22×D4×C59D411yescharacteristic
33C22×D4×C59D412yes—
34C22×D4×C59D411yescharacteristic
35C22×D4×C59Q812yes—
36C22×D4×C59C2311yescharacteristic
37C23×C4×C59—21no—
38C23×C4×C59—21no—
39C23×C4×C59—21no—
40C23×C4×C59—44no—
41C23×C4×C59—41no—
42C23×C4×C59—41no—
43C23×C4×C59—41no—
44C23×C4×C59C2×C412yescomplemented
45C23×C4×C59D411yescharacteristic
46C2×M16×C59—24no—
47C2×M16×C59—22no—
48C2×M16×C59—42no—
49C2×M16×C59—41no—
50C22×C8×C59—41no—
51C2×C22⋊C4×C59—24no—
52C2×C22⋊C4×C59—22no—
53C2×C22⋊C4×C59—21no—
54C2×C22⋊C4×C59—22no—
55C2×C22⋊C4×C59—22no—
56C2×C22⋊C4×C59—44no—
57C2×C22⋊C4×C59—41no—
58C2×C22⋊C4×C59—42no—
59C2×C22⋊C4×C59—42no—
60C2×C22⋊C4×C59C2×C412yescomplemented
61#100×C59—24no—
62#100×C59—22no—
63#100×C59C2×C414yescomplemented
64#99×C59—24no—
65#99×C59—22no—
66#99×C59C2×C414yescomplemented
67#95×C59—22no—
68#95×C59—22no—
69C24×C59—22no—
70C24×C59—21no—
71C24×C59—21no—
72C24×C59—21no—
73C24×C59—22no—
74C24×C59—21no—
75C24×C59—42no—
76C24×C59—42no—
77C24×C59—42no—
78C24×C59—42no—
79C24×C59C4212yes—
80C24×C59C22⋊C412yes—
81C24×C59C22⋊C411yescharacteristic
82C24×C59C22⋊C411yescharacteristic
83C24×C59C22⋊C411yescharacteristic
84C24×C59C4⋊C412yes—
85C24×C59C4⋊C412yes—
86C24×C59C22×C411yescharacteristic
87C24×C59C2×D411yescharacteristic
88C2×D4×C59—42no—
89C2×D4×C59—42no—
90C2×D4×C59—42no—
91C2×D4×C59—42no—
92C2×D4×C59—41no—
93C2×D4×C59—41no—
94C2×D4×C59—42no—
95C2×D4×C59—42no—
96C2×D4×C59—41no—
97C2×D4×C59—41no—
98C2×D4×C59—41no—
99C2×D4×C59—41no—
100C2×D4×C59—42no—
101C2×D4×C59—42no—
102C2×D4×C59—41no—
103C2×D4×C59—41no—
104C2×D4×C59C4212yes—
105C2×D4×C59C22⋊C412yes—
106C2×D4×C59C22⋊C412yes—
107C2×D4×C59C4⋊C412yes—
108C2×D4×C59C4⋊C412yes—
109C2×D4×C59C4⋊C412yes—
110C2×D4×C59C22×C411yescharacteristic
111C2×D4×C59C22×C411yescharacteristic
112C2×D4×C59C2×D411yescharacteristic
113C2×D4×C59C2×Q811yescharacteristic
114C22×C4×C59—22no—
115C22×C4×C59—21no—
116C22×C4×C59—21no—
117C22×C4×C59—24no—
118C22×C4×C59—22no—
119C22×C4×C59—22no—
120C22×C4×C59—44no—
121C22×C4×C59—44no—
122C22×C4×C59—42no—
123C22×C4×C59—42no—
124C22×C4×C59—48no—
125C22×C4×C59—44no—
126C22×C4×C59—41no—
127C22×C4×C59—41no—
128C22×C4×C59—42no—
129C22×C4×C59—44no—
130C22×C4×C59—44no—
131C22×C4×C59—42no—
132C22×C4×C59—42no—
133C22×C4×C59—42no—
134C22×C4×C59—42no—
135C22×C4×C59—82no—
136C22×C4×C59—82no—
137C22×C4×C59C22⋊C411yescharacteristic
138C22×C4×C59C22⋊C412yes—
139C22×C4×C59C4⋊C412yes—
140C22×C4×C59C2×D411yescharacteristic
141M16×C59—24no—
142M16×C59—44no—
143M16×C59—42no—
144C2×C8×C59—44no—
145C2×C8×C59—42no—
146C22⋊C4×C59—24no—
147C22⋊C4×C59—44no—
148C22⋊C4×C59—44no—
149C22⋊C4×C59—44no—
150C22⋊C4×C59—42no—
151C22⋊C4×C59—42no—
152C22⋊C4×C59—42no—
153C23×C59—22no—
154C23×C59—22no—
155C23×C59—22no—
156C23×C59—22no—
157C23×C59—22no—
158C23×C59—22no—
159C23×C59—22no—
160C23×C59—22no—
161C23×C59—21no—
162C23×C59—21no—
163C23×C59—21no—
164C23×C59—21no—
165C23×C59—21no—
166C23×C59—21no—
167C23×C59—22no—
168C23×C59—22no—
169C23×C59—21no—
170C23×C59—21no—
171C23×C59—41no—
172C23×C59—41no—
173C23×C59—44no—
174C23×C59—41no—
175C23×C59—44no—
176C23×C59—41no—
177C23×C59—42no—
178C23×C59—42no—
179C23×C59—48no—
180C23×C59—41no—
181C23×C59—41no—
182C23×C59—41no—
183C23×C59—44no—
184C23×C59—44no—
185C23×C59—41no—
186C23×C59—42no—
187C23×C59—42no—
188C23×C59—42no—
189C23×C59—42no—
190C23×C59—81no—
191C23×C59—81no—
192C23×C59—84no—
193C23×C59#9512yes—
194C23×C59#9512yes—
195C23×C59#9512yes—
196C23×C59#9911yescharacteristic
197C23×C59#9912yes—
198C23×C59#9911yescharacteristic
199C23×C59C2×C4211yescharacteristic
200C23×C59C2×C22⋊C411yescharacteristic
201C23×C59C2×C22⋊C411yescharacteristic
202C23×C59C2×C4⋊C411yescharacteristic
203C23×C59C2×C4⋊C411yescharacteristic
204D4×C59—42no—
205D4×C59—42no—
206D4×C59—42no—
207D4×C59—42no—
208D4×C59—42no—
209D4×C59—42no—
210D4×C59—41no—
211D4×C59—41no—
212D4×C59—41no—
213D4×C59—41no—
214C2×C4×C59—22no—
215C2×C4×C59—22no—
216C2×C4×C59—22no—
217C2×C4×C59—22no—
218C2×C4×C59—21no—
219C2×C4×C59—21no—
220C2×C4×C59—21no—
221C2×C4×C59—21no—
222C2×C4×C59—24no—
223C2×C4×C59—42no—
224C2×C4×C59—44no—
225C2×C4×C59—48no—
226C2×C4×C59—44no—
227C2×C4×C59—44no—
228C2×C4×C59—42no—
229C2×C4×C59—44no—
230C2×C4×C59—44no—
231C2×C4×C59—42no—
232C2×C4×C59—42no—
233C2×C4×C59—42no—
234C2×C4×C59—84no—
235C2×C4×C59—82no—
236C2×C4×C59—82no—
237C2×C4×C59—88no—
238C2×C4×C59#9512yes—
239C2×C4×C59C2×C22⋊C411yescharacteristic
240C2×C4×C59C2×C4⋊C411yescharacteristic
241C8×C59—44no—
242C2×#1390C5911yesmaximal, characteristic, direct product factor, Sylow
243C22×C59—21no—
244C22×C59—21no—
245C22×C59—21no—
246C22×C59—21no—
247C22×C59—24no—
248C22×C59—24no—
249C22×C59—21no—
250C22×C59—22no—
251C22×C59—22no—
252C22×C59—21no—
253C22×C59—21no—
254C22×C59—21no—
255C22×C59—42no—
256C22×C59—42no—
257C22×C59—41no—
258C22×C59—41no—
259C22×C59—41no—
260C22×C59—41no—
261C22×C59—42no—
262C22×C59—42no—
263C22×C59—44no—
264C22×C59—44no—
265C22×C59—41no—
266C22×C59—41no—
267C22×C59—41no—
268C22×C59—41no—
269C22×C59—41no—
270C22×C59—41no—
271C22×C59—41no—
272C22×C59—41no—
273C22×C59—44no—
274C22×C59—44no—
275C22×C59—44no—
276C22×C59—44no—
277C22×C59—81no—
278C22×C59—81no—
279C22×C59—82no—
280C22×C59—82no—
281C22×C59#34212yes—
282C22×C59#34212yes—
283C22×C59AΣL(1,𝔽16)12yes—
284C22×C59#35212yes—
285C22×C59C2×#9511yescharacteristic
286C22×C59C2×#9911yescharacteristic
287C22×C59C2×#9911yescharacteristic
288C4×C59—21no—
289C4×C59—22no—
290C4×C59—21no—
291C4×C59—44no—
292C4×C59—82no—
293C4×C59—84no—
294C22×#100C2×C5911yescharacteristic
295C22×#99C2×C5911yescharacteristic
296C2×#386C2×C5911yescharacteristic
297#1390C2×C5914yesdirect product factor
298C2×C59—21no—
299C2×C59—21no—
300C2×C59—22no—
301C2×C59—41no—
302C2×C59—42no—
303C2×C59—41no—
304C2×C59—41no—
305C2×C59—42no—
306C2×C59—41no—
307C2×C59#139014yesdirect product factor
308C2×C59C2×#34211yescharacteristic
309C2×C59C2×AΣL(1,𝔽16)11yescharacteristic
310C2×C59C2×#35211yescharacteristic
311C23×D4C22×C5911yescharacteristic
312C24×C4C4×C5911yescharacteristic, complemented
313C22×M16—21no—
314C22×C22⋊C4—21no—
315C22×C22⋊C4—21no—
316C22×C22⋊C4C4×C5911yescharacteristic, complemented
317C2×#100—21no—
318C2×#100—22no—
319C2×#100C4×C5914yescomplemented
320C2×#100C22×C5912yes—
321C2×#99—21no—
322C2×#99—22no—
323C2×#99C4×C5914yescomplemented
324C2×#99C22×C5912yes—
325#386—21no—
326#386—21no—
327#386C4×C5912yescomplemented
328#386C22×C5912yes—
329C2×#95—21no—
330C59C2×#139011yescharacteristic, direct product factor, Sylow
331C25C2×C4×C5911yescharacteristic
332C25D4×C5911yescharacteristic
333C22×D4—41no—
334C22×D4—42no—
335C22×D4—41no—
336C22×D4C2×C4×C5911yescharacteristic
337C22×D4C2×C4×C5912yes—
338C22×D4C2×C4×C5912yes—
339C22×D4D4×C5911yescharacteristic
340C22×D4D4×C5912yes—
341C22×D4D4×C5911yescharacteristic
342C22×D4Q8×C5912yes—
343C22×D4C23×C5911yescharacteristic
344C23×C4—21no—
345C23×C4—21no—
346C23×C4—21no—
347C23×C4—44no—
348C23×C4—41no—
349C23×C4—41no—
350C23×C4—41no—
351C23×C4C2×C4×C5912yescomplemented
352C23×C4D4×C5911yescharacteristic
353C2×M16—24no—
354C2×M16—22no—
355C2×M16—42no—
356C2×M16—41no—
357C22×C8—41no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—44no—
364C2×C22⋊C4—41no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4C2×C4×C5912yescomplemented
368#100—24no—
369#100—22no—
370#100C2×C4×C5914yescomplemented
371#99—24no—
372#99—22no—
373#99C2×C4×C5914yescomplemented
374#95—22no—
375#95—22no—
376C24—22no—
377C24—21no—
378C24—21no—
379C24—21no—
380C24—22no—
381C24—21no—
382C24—42no—
383C24—42no—
384C24—42no—
385C24—42no—
386C24C42×C5912yes—
387C24C22⋊C4×C5911yescharacteristic
388C24C22⋊C4×C5912yes—
389C24C22⋊C4×C5911yescharacteristic
390C24C22⋊C4×C5911yescharacteristic
391C24C4⋊C4×C5912yes—
392C24C4⋊C4×C5912yes—
393C24C22×C4×C5911yescharacteristic
394C24C2×D4×C5911yescharacteristic
395C2×D4—42no—
396C2×D4—42no—
397C2×D4—42no—
398C2×D4—42no—
399C2×D4—41no—
400C2×D4—41no—
401C2×D4—42no—
402C2×D4—42no—
403C2×D4—41no—
404C2×D4—41no—
405C2×D4—41no—
406C2×D4—41no—
407C2×D4—42no—
408C2×D4—42no—
409C2×D4—41no—
410C2×D4—41no—
411C2×D4C42×C5912yes—
412C2×D4C22⋊C4×C5912yes—
413C2×D4C22⋊C4×C5912yes—
414C2×D4C4⋊C4×C5912yes—
415C2×D4C4⋊C4×C5912yes—
416C2×D4C4⋊C4×C5912yes—
417C2×D4C22×C4×C5911yescharacteristic
418C2×D4C22×C4×C5911yescharacteristic
419C2×D4C2×D4×C5911yescharacteristic
420C2×D4C2×Q8×C5911yescharacteristic
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—21no—
424C22×C4—24no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—44no—
428C22×C4—44no—
429C22×C4—42no—
430C22×C4—42no—
431C22×C4—48no—
432C22×C4—44no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—42no—
436C22×C4—44no—
437C22×C4—44no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—82no—
443C22×C4—82no—
444C22×C4C22⋊C4×C5911yescharacteristic
445C22×C4C22⋊C4×C5912yes—
446C22×C4C4⋊C4×C5912yes—
447C22×C4C2×D4×C5911yescharacteristic
448M16—24no—
449M16—44no—
450M16—42no—
451C2×C8—44no—
452C2×C8—42no—
453C22⋊C4—24no—
454C22⋊C4—44no—
455C22⋊C4—44no—
456C22⋊C4—44no—
457C22⋊C4—42no—
458C22⋊C4—42no—
459C22⋊C4—42no—
460C23—22no—
461C23—22no—
462C23—22no—
463C23—22no—
464C23—22no—
465C23—22no—
466C23—22no—
467C23—22no—
468C23—21no—
469C23—21no—
470C23—21no—
471C23—21no—
472C23—21no—
473C23—21no—
474C23—22no—
475C23—22no—
476C23—21no—
477C23—21no—
478C23—41no—
479C23—41no—
480C23—44no—
481C23—41no—
482C23—44no—
483C23—41no—
484C23—42no—
485C23—42no—
486C23—48no—
487C23—41no—
488C23—41no—
489C23—41no—
490C23—44no—
491C23—44no—
492C23—41no—
493C23—42no—
494C23—42no—
495C23—42no—
496C23—42no—
497C23—81no—
498C23—81no—
499C23—84no—
500C23#95×C5912yes—
501C23#95×C5912yes—
502C23#95×C5912yes—
503C23#99×C5911yescharacteristic
504C23#99×C5912yes—
505C23#99×C5911yescharacteristic
506C23C2×C42×C5911yescharacteristic
507C23C2×C22⋊C4×C5911yescharacteristic
508C23C2×C22⋊C4×C5911yescharacteristic
509C23C2×C4⋊C4×C5911yescharacteristic
510C23C2×C4⋊C4×C5911yescharacteristic
511D4—42no—
512D4—42no—
513D4—42no—
514D4—42no—
515D4—42no—
516D4—42no—
517D4—41no—
518D4—41no—
519D4—41no—
520D4—41no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—24no—
530C2×C4—42no—
531C2×C4—44no—
532C2×C4—48no—
533C2×C4—44no—
534C2×C4—44no—
535C2×C4—42no—
536C2×C4—44no—
537C2×C4—44no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—84no—
542C2×C4—82no—
543C2×C4—82no—
544C2×C4—88no—
545C2×C4#95×C5912yes—
546C2×C4C2×C22⋊C4×C5911yescharacteristic
547C2×C4C2×C4⋊C4×C5911yescharacteristic
548C8—44no—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—21no—
553C22—24no—
554C22—24no—
555C22—21no—
556C22—22no—
557C22—22no—
558C22—21no—
559C22—21no—
560C22—21no—
561C22—42no—
562C22—42no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22—42no—
568C22—42no—
569C22—44no—
570C22—44no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—44no—
580C22—44no—
581C22—44no—
582C22—44no—
583C22—81no—
584C22—81no—
585C22—82no—
586C22—82no—
587C22C59×#34212yes—
588C22C59×#34212yes—
589C22C59×AΣL(1,𝔽16)12yes—
590C22C59×#35212yes—
591C22C2×#95×C5911yescharacteristic
592C22C2×#99×C5911yescharacteristic
593C22C2×#99×C5911yescharacteristic
594C4—21no—
595C4—22no—
596C4—21no—
597C4—44no—
598C4—82no—
599C4—84no—
600C2—21no—
601C2—21no—
602C2—22no—
603C2—41no—
604C2—42no—
605C2—41no—
606C2—41no—
607C2—42no—
608C2—41no—
609C2C59×#139014yesdirect product factor
610C2C2×C59×#34211yescharacteristic
611C2C2×C59×AΣL(1,𝔽16)11yescharacteristic
612C2C2×C59×#35211yescharacteristic
subgroupG/H
center, socleC23×C59#99
commutatorC23C2×C42×C59
Frattini, cosocleC22×D4C23×C59
prime radicalC23×D4×C59C22
LCSG ▷ C23 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C23×C59 ◁ C24×C59 ◁ C23×D4×C59 ◁ G

Complements

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

NH ≅ G/Ntype
4. C59×#1390C2direct (N × H)
6. C24×C4×C59C4semidirect
10. C22×C22⋊C4×C59C4semidirect
13. C2×#100×C59C4semidirect
17. C2×#99×C59C4semidirect
21. C59×#386C4semidirect
44. C23×C4×C59C2×C4semidirect
60. C2×C22⋊C4×C59C2×C4semidirect
63. #100×C59C2×C4semidirect
66. #99×C59C2×C4semidirect
242. C2×#1390C59direct (N × H)
297. #1390C2×C59direct (N × H)
307. C2×C59#1390direct (N × H)
312. C24×C4C4×C59semidirect
316. C22×C22⋊C4C4×C59semidirect
319. C2×#100C4×C59semidirect
323. C2×#99C4×C59semidirect
327. #386C4×C59semidirect
330. C59C2×#1390direct (N × H)
351. C23×C4C2×C4×C59semidirect
367. C2×C22⋊C4C2×C4×C59semidirect
370. #100C2×C4×C59semidirect
373. #99C2×C4×C59semidirect
609. C2C59×#1390direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#100×C592
C22×#99×C592
C2×C59×#3862
C59×#13902
C2×#139059