Finite Group Databasebeta

← C2×C59×#1615 #28430215

Subgroups — C2×C59×#1615 #28430215

Order 15104.

1016 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×#539C211yesmaximal, characteristic
2C2×C59×#484C211yesmaximal, characteristic, complemented
3C2×C59×#481C211yesmaximal, characteristic
4C2×C59×#400C211yesmaximal, characteristic, complemented
5C59×#1615C218yesmaximal, direct product factor
6C2×C59×#328C211yesmaximal, characteristic, complemented
7C2×C59×#327C211yesmaximal, characteristic
8C2×C59×#324C211yesmaximal, characteristic, complemented
9C59×#539—22no—
10C59×#539—22no—
11C59×#539—22no—
12C59×#539C2214yes—
13C2×#126×C59—21no—
14C2×#125×C59—21no—
15C2×#123×C59—21no—
16C2×#123×C59—21no—
17C2×C22⋊Q8×C59—21no—
18C2×C22⋊Q8×C59C2211yescharacteristic
19C2×#121×C59C2211yescharacteristic
20C2×C4×D4×C59—21no—
21C22×C4⋊C4×C59C2211yescharacteristic
22C22×C4⋊C4×C59C2211yescharacteristic
23C59×#484—22no—
24C59×#484C2214yescomplemented
25C59×#481—22no—
26C59×#481C2214yes—
27C2×#107×C59—21no—
28C2×#106×C59—21no—
29C2×#103×C59—21no—
30C2×#102×C59—21no—
31C2×C22⋊C8×C59C2211yescharacteristic
32C2×C22⋊C8×C59C2211yescharacteristic
33C59×#400—22no—
34C59×#400C2214yescomplemented
35C2×#95×C59—21no—
36C2×#95×C59—21no—
37C2×#95×C59C2211yescharacteristic
38C59×#328C2214yescomplemented
39C59×#327C2214yes—
40C59×#324C2214yescomplemented
41C22×Q8×C59D411yescharacteristic
42C22×D4×C59—21no—
43C22×D4×C59D411yescharacteristic
44C23×C4×C59—21no—
45C23×C4×C59—21no—
46C23×C4×C59—21no—
47C23×C4×C59D411yescharacteristic
48C23×C4×C59D411yescharacteristic
49C23×C4×C59C2311yescharacteristic
50C22×C8×C59—21no—
51C22×C8×C59—21no—
52#126×C59—24no—
53#126×C59—24no—
54#125×C59—24no—
55#125×C59—24no—
56#123×C59—24no—
57#123×C59—24no—
58#123×C59—24no—
59#123×C59—24no—
60C22⋊Q8×C59—24no—
61C22⋊Q8×C59—24no—
62C22⋊Q8×C59—21no—
63C22⋊Q8×C59—21no—
64C22⋊Q8×C59D412yes—
65C22⋊Q8×C59C2312yes—
66#121×C59—21no—
67#121×C59—21no—
68#121×C59D412yes—
69#121×C59C2312yes—
70C4×D4×C59—24no—
71C4×D4×C59—24no—
72C2×C4⋊C4×C59—21no—
73C2×C4⋊C4×C59—21no—
74C2×C4⋊C4×C59—21no—
75C2×C4⋊C4×C59—21no—
76C2×C4⋊C4×C59—21no—
77C2×C4⋊C4×C59—21no—
78C2×C4⋊C4×C59—21no—
79C2×C4⋊C4×C59—21no—
80C2×C4⋊C4×C59—21no—
81C2×C4⋊C4×C59—21no—
82C2×C4⋊C4×C59—21no—
83C2×C4⋊C4×C59—21no—
84C2×C4⋊C4×C59—21no—
85C2×C4⋊C4×C59D412yes—
86C2×C4⋊C4×C59D411yescharacteristic
87C2×C4⋊C4×C59D411yescharacteristic
88C2×C4⋊C4×C59C2312yes—
89C2×C4⋊C4×C59C2312yes—
90C2×C22⋊C4×C59—21no—
91C2×C22⋊C4×C59—21no—
92C2×C22⋊C4×C59—21no—
93C2×C22⋊C4×C59—21no—
94C2×C22⋊C4×C59—21no—
95C2×C42×C59—21no—
96#107×C59—24no—
97#106×C59—24no—
98#103×C59—24no—
99#102×C59—24no—
100C22⋊C8×C59—21no—
101C22⋊C8×C59—21no—
102C22⋊C8×C59C2312yes—
103C22⋊C8×C59C2312yes—
104#95×C59—24no—
105#95×C59—24no—
106#95×C59—21no—
107#95×C59C2312yes—
108C24×C59—21no—
109C24×C59C2×D411yescharacteristic
110C2×Q8×C59—21no—
111C2×Q8×C59—42no—
112C2×Q8×C59C2×D412yes—
113C2×D4×C59—22no—
114C2×D4×C59—22no—
115C2×D4×C59—21no—
116C2×D4×C59—42no—
117C2×D4×C59—42no—
118C2×D4×C59—42no—
119C2×D4×C59C2×D412yes—
120C22×C4×C59—21no—
121C22×C4×C59—21no—
122C22×C4×C59—21no—
123C22×C4×C59—21no—
124C22×C4×C59—21no—
125C22×C4×C59—21no—
126C22×C4×C59—22no—
127C22×C4×C59—22no—
128C22×C4×C59—24no—
129C22×C4×C59—21no—
130C22×C4×C59—22no—
131C22×C4×C59—22no—
132C22×C4×C59—42no—
133C22×C4×C59—42no—
134C22×C4×C59—42no—
135C22×C4×C59—42no—
136C22×C4×C59—44no—
137C22×C4×C59—41no—
138C22×C4×C59—41no—
139C22×C4×C59—42no—
140C22×C4×C59—82no—
141C22×C4×C59C2×D412yes—
142C22×C4×C59C2×D411yescharacteristic
143C22×C4×C59C2×D411yescharacteristic
144C22×C4×C59C2×D412yes—
145C22×C4×C59C2×D411yescharacteristic
146C22×C4×C59C2×D411yescharacteristic
147C22×C4×C59C2×D411yescharacteristic
148C22×C4×C59C2411yescharacteristic
149C2×C8×C59—22no—
150C2×C8×C59—22no—
151C2×C8×C59—42no—
152C2×C8×C59—42no—
153C4⋊C4×C59—24no—
154C4⋊C4×C59—24no—
155C4⋊C4×C59—24no—
156C4⋊C4×C59—22no—
157C4⋊C4×C59—22no—
158C4⋊C4×C59—22no—
159C4⋊C4×C59—21no—
160C4⋊C4×C59—21no—
161C4⋊C4×C59—22no—
162C4⋊C4×C59—22no—
163C4⋊C4×C59—22no—
164C4⋊C4×C59—22no—
165C4⋊C4×C59—22no—
166C4⋊C4×C59—41no—
167C4⋊C4×C59—41no—
168C4⋊C4×C59C2×D412yes—
169C4⋊C4×C59C2×D412yes—
170C22⋊C4×C59—24no—
171C22⋊C4×C59—24no—
172C22⋊C4×C59—24no—
173C22⋊C4×C59—22no—
174C22⋊C4×C59—22no—
175C22⋊C4×C59—22no—
176C22⋊C4×C59—22no—
177C42×C59—24no—
178C23×C59—22no—
179C23×C59—22no—
180C23×C59—22no—
181C23×C59—42no—
182C23×C59—42no—
183C23×C59—42no—
184C23×C59#12011yescharacteristic
185C23×C59#12011yescharacteristic
186C23×C59#13512yes—
187C23×C59#13712yes—
188C23×C59C22×D411yescharacteristic
189Q8×C59—42no—
190Q8×C59—81no—
191D4×C59—42no—
192D4×C59—42no—
193D4×C59—42no—
194D4×C59—44no—
195D4×C59—81no—
196C2×C4×C59—22no—
197C2×C4×C59—22no—
198C2×C4×C59—22no—
199C2×C4×C59—22no—
200C2×C4×C59—22no—
201C2×C4×C59—22no—
202C2×C4×C59—22no—
203C2×C4×C59—22no—
204C2×C4×C59—22no—
205C2×C4×C59—41no—
206C2×C4×C59—41no—
207C2×C4×C59—41no—
208C2×C4×C59—41no—
209C2×C4×C59—42no—
210C2×C4×C59—42no—
211C2×C4×C59—42no—
212C2×C4×C59—42no—
213C2×C4×C59—42no—
214C2×C4×C59—42no—
215C2×C4×C59—42no—
216C2×C4×C59—42no—
217C2×C4×C59—42no—
218C2×C4×C59—44no—
219C2×C4×C59—42no—
220C2×C4×C59—42no—
221C2×C4×C59—81no—
222C2×C4×C59—84no—
223C2×C4×C59—84no—
224C2×C4×C59—82no—
225C2×C4×C59—82no—
226C2×C4×C59#12011yescharacteristic
227C2×C4×C59#12011yescharacteristic
228C2×C4×C59C22×D411yescharacteristic
229C2×C4×C59C22×D411yescharacteristic
230C8×C59—42no—
231C8×C59—42no—
232C2×#1615C5911yesmaximal, characteristic, direct product factor, Sylow
233C22×C59—24no—
234C22×C59—24no—
235C22×C59—21no—
236C22×C59—21no—
237C22×C59—21no—
238C22×C59—21no—
239C22×C59—42no—
240C22×C59—42no—
241C22×C59—42no—
242C22×C59—84no—
243C22×C59#45212yes—
244C22×C59#45212yes—
245C22×C59#45412yes—
246C22×C59#45812yes—
247C22×C59C2×#12011yescharacteristic
248C22×C59C2×#13511yescharacteristic
249C22×C59C2×#13711yescharacteristic
250C4×C59—21no—
251C4×C59—21no—
252C4×C59—21no—
253C4×C59—21no—
254C4×C59—42no—
255C4×C59—42no—
256C4×C59—42no—
257C4×C59—42no—
258C4×C59—42no—
259C4×C59—82no—
260C4×C59—82no—
261C2×#539C2×C5911yescharacteristic
262C2×#484C2×C5911yescharacteristic, complemented
263C2×#481C2×C5911yescharacteristic
264C2×#400C2×C5911yescharacteristic, complemented
265#1615C2×C5918yesdirect product factor
266C2×#328C2×C5911yescharacteristic, complemented
267C2×#327C2×C5911yescharacteristic
268C2×#324C2×C5911yescharacteristic, complemented
269C2×C59—21no—
270C2×C59—21no—
271C2×C59—22no—
272C2×C59—82no—
273C2×C59#161514yesdirect product factor
274C2×C59C2×#45211yescharacteristic
275C2×C59C2×#45411yescharacteristic
276C2×C59C2×#45811yescharacteristic
277#539—22no—
278#539—22no—
279#539—22no—
280#539C22×C5914yes—
281C2×#126—21no—
282C2×#125—21no—
283C2×#123—21no—
284C2×#123—21no—
285C2×C22⋊Q8—21no—
286C2×C22⋊Q8C22×C5911yescharacteristic
287C2×#121C22×C5911yescharacteristic
288C2×C4×D4—21no—
289C22×C4⋊C4C22×C5911yescharacteristic
290C22×C4⋊C4C22×C5911yescharacteristic
291#484—22no—
292#484C22×C5914yescomplemented
293#481—22no—
294#481C22×C5914yes—
295C2×#107—21no—
296C2×#106—21no—
297C2×#103—21no—
298C2×#102—21no—
299C2×C22⋊C8C22×C5911yescharacteristic
300C2×C22⋊C8C22×C5911yescharacteristic
301#400—22no—
302#400C22×C5914yescomplemented
303C2×#95—21no—
304C2×#95—21no—
305C2×#95C22×C5911yescharacteristic
306#328C22×C5914yescomplemented
307#327C22×C5914yes—
308#324C22×C5914yescomplemented
309C59C2×#161511yescharacteristic, direct product factor, Sylow
310C22×Q8D4×C5911yescharacteristic
311C22×D4—21no—
312C22×D4D4×C5911yescharacteristic
313C23×C4—21no—
314C23×C4—21no—
315C23×C4—21no—
316C23×C4D4×C5911yescharacteristic
317C23×C4D4×C5911yescharacteristic
318C23×C4C23×C5911yescharacteristic
319C22×C8—21no—
320C22×C8—21no—
321#126—24no—
322#126—24no—
323#125—24no—
324#125—24no—
325#123—24no—
326#123—24no—
327#123—24no—
328#123—24no—
329C22⋊Q8—24no—
330C22⋊Q8—24no—
331C22⋊Q8—21no—
332C22⋊Q8—21no—
333C22⋊Q8D4×C5912yes—
334C22⋊Q8C23×C5912yes—
335#121—21no—
336#121—21no—
337#121D4×C5912yes—
338#121C23×C5912yes—
339C4×D4—24no—
340C4×D4—24no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4D4×C5912yes—
355C2×C4⋊C4D4×C5911yescharacteristic
356C2×C4⋊C4D4×C5911yescharacteristic
357C2×C4⋊C4C23×C5912yes—
358C2×C4⋊C4C23×C5912yes—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—21no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C42—21no—
365#107—24no—
366#106—24no—
367#103—24no—
368#102—24no—
369C22⋊C8—21no—
370C22⋊C8—21no—
371C22⋊C8C23×C5912yes—
372C22⋊C8C23×C5912yes—
373#95—24no—
374#95—24no—
375#95—21no—
376#95C23×C5912yes—
377C24—21no—
378C24C2×D4×C5911yescharacteristic
379C2×Q8—21no—
380C2×Q8—42no—
381C2×Q8C2×D4×C5912yes—
382C2×D4—22no—
383C2×D4—22no—
384C2×D4—21no—
385C2×D4—42no—
386C2×D4—42no—
387C2×D4—42no—
388C2×D4C2×D4×C5912yes—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—24no—
398C22×C4—21no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—42no—
402C22×C4—42no—
403C22×C4—42no—
404C22×C4—42no—
405C22×C4—44no—
406C22×C4—41no—
407C22×C4—41no—
408C22×C4—42no—
409C22×C4—82no—
410C22×C4C2×D4×C5912yes—
411C22×C4C2×D4×C5911yescharacteristic
412C22×C4C2×D4×C5911yescharacteristic
413C22×C4C2×D4×C5912yes—
414C22×C4C2×D4×C5911yescharacteristic
415C22×C4C2×D4×C5911yescharacteristic
416C22×C4C2×D4×C5911yescharacteristic
417C22×C4C24×C5911yescharacteristic
418C2×C8—22no—
419C2×C8—22no—
420C2×C8—42no—
421C2×C8—42no—
422C4⋊C4—24no—
423C4⋊C4—24no—
424C4⋊C4—24no—
425C4⋊C4—22no—
426C4⋊C4—22no—
427C4⋊C4—22no—
428C4⋊C4—21no—
429C4⋊C4—21no—
430C4⋊C4—22no—
431C4⋊C4—22no—
432C4⋊C4—22no—
433C4⋊C4—22no—
434C4⋊C4—22no—
435C4⋊C4—41no—
436C4⋊C4—41no—
437C4⋊C4C2×D4×C5912yes—
438C4⋊C4C2×D4×C5912yes—
439C22⋊C4—24no—
440C22⋊C4—24no—
441C22⋊C4—24no—
442C22⋊C4—22no—
443C22⋊C4—22no—
444C22⋊C4—22no—
445C22⋊C4—22no—
446C42—24no—
447C23—22no—
448C23—22no—
449C23—22no—
450C23—42no—
451C23—42no—
452C23—42no—
453C23#120×C5911yescharacteristic
454C23#120×C5911yescharacteristic
455C23#135×C5912yes—
456C23#137×C5912yes—
457C23C22×D4×C5911yescharacteristic
458Q8—42no—
459Q8—81no—
460D4—42no—
461D4—44no—
462D4—42no—
463D4—42no—
464D4—81no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—44no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—81no—
491C2×C4—84no—
492C2×C4—84no—
493C2×C4—82no—
494C2×C4—82no—
495C2×C4#120×C5911yescharacteristic
496C2×C4#120×C5911yescharacteristic
497C2×C4C22×D4×C5911yescharacteristic
498C2×C4C22×D4×C5911yescharacteristic
499C8—42no—
500C8—42no—
501C22—21no—
502C22—21no—
503C22—21no—
504C22—21no—
505C22—24no—
506C22—24no—
507C22—42no—
508C22—42no—
509C22—42no—
510C22—84no—
511C22C59×#45212yes—
512C22C59×#45212yes—
513C22C59×#45412yes—
514C22C59×#45812yes—
515C22C2×#120×C5911yescharacteristic
516C22C2×#135×C5911yescharacteristic
517C22C2×#137×C5911yescharacteristic
518C4—21no—
519C4—21no—
520C4—21no—
521C4—21no—
522C4—42no—
523C4—42no—
524C4—42no—
525C4—42no—
526C4—42no—
527C4—82no—
528C4—82no—
529C2—21no—
530C2—22no—
531C2—21no—
532C2—82no—
533C2C59×#161514yesdirect product factor
534C2C2×C59×#45211yescharacteristic
535C2C2×C59×#45411yescharacteristic
536C2C2×C59×#45811yescharacteristic
subgroupG/H
center, socleC23×C59#120
commutator, Frattini, cosocleC22×C4C24×C59
prime radicalC2×#121×C59C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C59 ◁ C23×C4×C59 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C59×#484C2semidirect
4. C2×C59×#400C2semidirect
5. C59×#1615C2direct (N × H)
6. C2×C59×#328C2semidirect
8. C2×C59×#324C2semidirect
24. C59×#484C22semidirect
34. C59×#400C22semidirect
38. C59×#328C22semidirect
40. C59×#324C22semidirect
232. C2×#1615C59direct (N × H)
262. C2×#484C2×C59semidirect
264. C2×#400C2×C59semidirect
265. #1615C2×C59direct (N × H)
266. C2×#328C2×C59semidirect
268. C2×#324C2×C59semidirect
273. C2×C59#1615direct (N × H)
292. #484C22×C59semidirect
302. #400C22×C59semidirect
306. #328C22×C59semidirect
308. #324C22×C59semidirect
309. C59C2×#1615direct (N × H)
533. C2C59×#1615direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C59×#5392
C2×C59×#4842
C2×C59×#4812
C2×C59×#4002
C59×#16152
C2×C59×#3282
C2×C59×#3272
C2×C59×#3242
C2×#161559