Finite Group Databasebeta

← C59×#13423 #28425532

Subgroups — C59×#13423 #28425532

Order 15104.

558 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 558 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#2709C211yesmaximal, characteristic
2C2×C59×#353C211yesmaximal, characteristic
3C2×C59×#352C211yesmaximal, characteristic, complemented
4C59×#1890C211yesmaximal, characteristic, complemented
5C59×#1887C211yesmaximal, characteristic
6C59×#1867C211yesmaximal, characteristic, complemented
7C59×#1390C211yesmaximal, characteristic, complemented
8C2×#127×C59C2211yescharacteristic
9C2×#123×C59C2211yescharacteristic
10C59×#518C2211yescharacteristic
11C59×#418—21no—
12C2×#100×C59C2211yescharacteristic
13C2×#99×C59C2211yescharacteristic
14C2×#99×C59C2211yescharacteristic
15C59×#394—21no—
16C59×#394—21no—
17C59×#394—21no—
18C59×#387—21no—
19C59×#386—21no—
20C59×#386—21no—
21C59×#386C2211yescharacteristic
22C59×#385—21no—
23C59×#381—21no—
24C59×#353—22no—
25C59×#352—22no—
26C59×#342—21no—
27C59×#342—21no—
28C59×#339—21no—
29C22×D4×C59—21no—
30C22×D4×C59—21no—
31C22×D4×C59D411yescharacteristic
32C22×D4×C59C2311yescharacteristic
33C23×C4×C59D411yescharacteristic
34C23×C4×C59D411yescharacteristic
35C2×M16×C59—21no—
36#127×C59—21no—
37#127×C59—21no—
38#127×C59—21no—
39#127×C59—21no—
40#123×C59—21no—
41#123×C59—21no—
42#123×C59—21no—
43#123×C59—21no—
44C4×D4×C59—41no—
45C4×D4×C59—41no—
46#117×C59—21no—
47C2×C4⋊C4×C59—21no—
48C2×C4⋊C4×C59—21no—
49C2×C4⋊C4×C59—41no—
50C2×C22⋊C4×C59—21no—
51C2×C22⋊C4×C59—21no—
52C2×C22⋊C4×C59—21no—
53C2×C22⋊C4×C59—21no—
54C2×C22⋊C4×C59—21no—
55C2×C22⋊C4×C59—21no—
56C2×C22⋊C4×C59—21no—
57C2×C22⋊C4×C59—21no—
58C2×C22⋊C4×C59—21no—
59C2×C22⋊C4×C59—21no—
60C2×C22⋊C4×C59D411yescharacteristic
61C2×C22⋊C4×C59D411yescharacteristic
62C2×C42×C59D411yescharacteristic
63#102×C59—41no—
64#102×C59—41no—
65#100×C59—21no—
66#100×C59—21no—
67#99×C59—21no—
68#99×C59—21no—
69#99×C59—21no—
70#99×C59D412yes—
71#95×C59—21no—
72#95×C59—21no—
73#95×C59—21no—
74#95×C59—21no—
75#95×C59—41no—
76#95×C59—41no—
77#95×C59—41no—
78C24×C59—21no—
79C24×C59C2×D411yescharacteristic
80C24×C59C2×D411yescharacteristic
81C2×D4×C59—21no—
82C2×D4×C59—21no—
83C2×D4×C59—41no—
84C2×D4×C59—41no—
85C2×D4×C59—41no—
86C2×D4×C59—41no—
87C2×D4×C59—42no—
88C2×D4×C59—42no—
89C2×D4×C59—41no—
90C2×D4×C59—41no—
91C2×D4×C59—41no—
92C2×D4×C59—41no—
93C2×D4×C59—81no—
94C2×D4×C59—81no—
95C2×D4×C59C2×D411yescharacteristic
96C2×D4×C59#4111yescharacteristic
97C2×D4×C59#4111yescharacteristic
98C2×D4×C59#4111yescharacteristic
99C22×C4×C59—21no—
100C22×C4×C59—21no—
101C22×C4×C59—21no—
102C22×C4×C59—21no—
103C22×C4×C59—21no—
104C22×C4×C59—21no—
105C22×C4×C59—21no—
106C22×C4×C59—21no—
107C22×C4×C59—21no—
108C22×C4×C59—21no—
109C22×C4×C59—21no—
110C22×C4×C59—41no—
111C22×C4×C59—41no—
112C22×C4×C59—41no—
113C22×C4×C59—41no—
114C22×C4×C59—41no—
115C22×C4×C59—81no—
116C22×C4×C59C2×D411yescharacteristic
117M16×C59—41no—
118M16×C59—41no—
119C2×C8×C59—41no—
120C4⋊C4×C59—21no—
121C4⋊C4×C59—21no—
122C4⋊C4×C59—42no—
123C4⋊C4×C59—41no—
124C4⋊C4×C59—41no—
125C4⋊C4×C59—82no—
126C22⋊C4×C59—22no—
127C22⋊C4×C59—21no—
128C22⋊C4×C59—21no—
129C22⋊C4×C59—41no—
130C22⋊C4×C59—41no—
131C22⋊C4×C59—41no—
132C22⋊C4×C59—41no—
133C22⋊C4×C59—41no—
134C22⋊C4×C59—41no—
135C22⋊C4×C59—41no—
136C22⋊C4×C59—41no—
137C22⋊C4×C59—41no—
138C22⋊C4×C59—81no—
139C22⋊C4×C59—81no—
140C22⋊C4×C59—81no—
141C22⋊C4×C59—81no—
142C22⋊C4×C59—81no—
143C42×C59—21no—
144C42×C59—21no—
145C42×C59—41no—
146C23×C59—21no—
147C23×C59—21no—
148C23×C59—21no—
149C23×C59—21no—
150C23×C59—41no—
151C23×C59—41no—
152C23×C59—41no—
153C23×C59—41no—
154C23×C59—41no—
155C23×C59—41no—
156C23×C59—41no—
157C23×C59—41no—
158C23×C59—41no—
159C23×C59—41no—
160C23×C59—41no—
161C23×C59#12011yescharacteristic
162C23×C59#12111yescharacteristic
163C23×C59#12111yescharacteristic
164C23×C59#12311yescharacteristic
165C23×C59#12411yescharacteristic
166D4×C59—41no—
167D4×C59—41no—
168D4×C59—41no—
169D4×C59—41no—
170D4×C59—42no—
171D4×C59—81no—
172D4×C59—82no—
173D4×C59—82no—
174D4×C59—82no—
175D4×C59—82no—
176C2×C4×C59—21no—
177C2×C4×C59—21no—
178C2×C4×C59—22no—
179C2×C4×C59—41no—
180C2×C4×C59—41no—
181C2×C4×C59—42no—
182C2×C4×C59—41no—
183C2×C4×C59—41no—
184C2×C4×C59—41no—
185C2×C4×C59—41no—
186C2×C4×C59—41no—
187C2×C4×C59—41no—
188C2×C4×C59—42no—
189C2×C4×C59—42no—
190C2×C4×C59—41no—
191C2×C4×C59—41no—
192C2×C4×C59—41no—
193C2×C4×C59—41no—
194C2×C4×C59—41no—
195C2×C4×C59—41no—
196C2×C4×C59—41no—
197C2×C4×C59—41no—
198C2×C4×C59—81no—
199C2×C4×C59—81no—
200C2×C4×C59—81no—
201C2×C4×C59—81no—
202C2×C4×C59—81no—
203C2×C4×C59—81no—
204C2×C4×C59—81no—
205C2×C4×C59—81no—
206C2×C4×C59—81no—
207C2×C4×C59—81no—
208C2×C4×C59—81no—
209C2×C4×C59#12111yescharacteristic
210C2×C4×C59#12311yescharacteristic
211C8×C59—81no—
212#13423C5911yesmaximal, characteristic, direct product factor, Sylow
213C22×C59—21no—
214C22×C59—21no—
215C22×C59—21no—
216C22×C59—21no—
217C22×C59—21no—
218C22×C59—21no—
219C22×C59—41no—
220C22×C59—41no—
221C22×C59—41no—
222C22×C59—41no—
223C22×C59—41no—
224C22×C59—41no—
225C22×C59—41no—
226C22×C59—41no—
227C22×C59—81no—
228C22×C59—81no—
229C22×C59—81no—
230C22×C59—81no—
231C22×C59—81no—
232C22×C59—81no—
233C22×C59—81no—
234C22×C59—81no—
235C22×C59—81no—
236C22×C59#39411yescharacteristic
237C22×C59B(4,𝔽2)11yescharacteristic
238C22×C59#45811yescharacteristic
239C4×C59—21no—
240C4×C59—21no—
241C4×C59—42no—
242C4×C59—81no—
243C4×C59—81no—
244C4×C59—82no—
245C4×C59—81no—
246C4×C59—81no—
247C4×C59—81no—
248C4×C59—81no—
249C4×C59—161no—
250#2709C2×C5911yescharacteristic
251C2×#353C2×C5911yescharacteristic
252C2×#352C2×C5911yescharacteristic, complemented
253#1890C2×C5911yescharacteristic, complemented
254#1887C2×C5911yescharacteristic
255#1867C2×C5911yescharacteristic, complemented
256#1390C2×C5911yescharacteristic, complemented
257C2×C59—21no—
258C2×C59—21no—
259C2×C59—41no—
260C2×C59—41no—
261C2×C59—41no—
262C2×C59—41no—
263C2×C59—161no—
264C2×C59#204411yescharacteristic
265C2×C59#219811yescharacteristic
266C2×C59#220011yescharacteristic
267C2×#127C22×C5911yescharacteristic
268C2×#123C22×C5911yescharacteristic
269#518C22×C5911yescharacteristic
270#418—21no—
271C2×#100C22×C5911yescharacteristic
272C2×#99C22×C5911yescharacteristic
273C2×#99C22×C5911yescharacteristic
274#394—21no—
275#394—21no—
276#394—21no—
277#387—21no—
278#386—21no—
279#386—21no—
280#386C22×C5911yescharacteristic
281#385—21no—
282#381—21no—
283#353—22no—
284#352—22no—
285#342—21no—
286#342—21no—
287#339—21no—
288C59#1342311yescharacteristic, direct product factor, Sylow
289C22×D4—21no—
290C22×D4—21no—
291C22×D4D4×C5911yescharacteristic
292C22×D4C23×C5911yescharacteristic
293C23×C4D4×C5911yescharacteristic
294C23×C4D4×C5911yescharacteristic
295C2×M16—21no—
296#127—21no—
297#127—21no—
298#127—21no—
299#127—21no—
300#123—21no—
301#123—21no—
302#123—21no—
303#123—21no—
304C4×D4—41no—
305C4×D4—41no—
306#117—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—41no—
310C2×C22⋊C4—21no—
311C2×C22⋊C4—21no—
312C2×C22⋊C4—21no—
313C2×C22⋊C4—21no—
314C2×C22⋊C4—21no—
315C2×C22⋊C4—21no—
316C2×C22⋊C4—21no—
317C2×C22⋊C4—21no—
318C2×C22⋊C4—21no—
319C2×C22⋊C4—21no—
320C2×C22⋊C4D4×C5911yescharacteristic
321C2×C22⋊C4D4×C5911yescharacteristic
322C2×C42D4×C5911yescharacteristic
323#102—41no—
324#102—41no—
325#100—21no—
326#100—21no—
327#99—21no—
328#99—21no—
329#99—21no—
330#99D4×C5912yes—
331#95—21no—
332#95—21no—
333#95—21no—
334#95—21no—
335#95—41no—
336#95—41no—
337#95—41no—
338C24—21no—
339C24C2×D4×C5911yescharacteristic
340C24C2×D4×C5911yescharacteristic
341C2×D4—21no—
342C2×D4—21no—
343C2×D4—41no—
344C2×D4—41no—
345C2×D4—41no—
346C2×D4—41no—
347C2×D4—42no—
348C2×D4—42no—
349C2×D4—41no—
350C2×D4—41no—
351C2×D4—41no—
352C2×D4—41no—
353C2×D4—81no—
354C2×D4—81no—
355C2×D4C2×D4×C5911yescharacteristic
356C2×D4#41×C5911yescharacteristic
357C2×D4#41×C5911yescharacteristic
358C2×D4#41×C5911yescharacteristic
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—41no—
371C22×C4—41no—
372C22×C4—41no—
373C22×C4—41no—
374C22×C4—41no—
375C22×C4—81no—
376C22×C4C2×D4×C5911yescharacteristic
377M16—41no—
378M16—41no—
379C2×C8—41no—
380C4⋊C4—21no—
381C4⋊C4—21no—
382C4⋊C4—42no—
383C4⋊C4—41no—
384C4⋊C4—41no—
385C4⋊C4—82no—
386C22⋊C4—22no—
387C22⋊C4—21no—
388C22⋊C4—21no—
389C22⋊C4—41no—
390C22⋊C4—41no—
391C22⋊C4—41no—
392C22⋊C4—41no—
393C22⋊C4—41no—
394C22⋊C4—41no—
395C22⋊C4—41no—
396C22⋊C4—41no—
397C22⋊C4—41no—
398C22⋊C4—81no—
399C22⋊C4—81no—
400C22⋊C4—81no—
401C22⋊C4—81no—
402C22⋊C4—81no—
403C42—21no—
404C42—21no—
405C42—41no—
406C23—21no—
407C23—21no—
408C23—21no—
409C23—21no—
410C23—41no—
411C23—41no—
412C23—41no—
413C23—41no—
414C23—41no—
415C23—41no—
416C23—41no—
417C23—41no—
418C23—41no—
419C23—41no—
420C23—41no—
421C23#120×C5911yescharacteristic
422C23#121×C5911yescharacteristic
423C23#121×C5911yescharacteristic
424C23#123×C5911yescharacteristic
425C23#124×C5911yescharacteristic
426D4—41no—
427D4—41no—
428D4—41no—
429D4—41no—
430D4—42no—
431D4—81no—
432D4—82no—
433D4—82no—
434D4—82no—
435D4—82no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—22no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—42no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—81no—
459C2×C4—81no—
460C2×C4—81no—
461C2×C4—81no—
462C2×C4—81no—
463C2×C4—81no—
464C2×C4—81no—
465C2×C4—81no—
466C2×C4—81no—
467C2×C4—81no—
468C2×C4—81no—
469C2×C4#121×C5911yescharacteristic
470C2×C4#123×C5911yescharacteristic
471C8—81no—
472C22—21no—
473C22—21no—
474C22—21no—
475C22—21no—
476C22—21no—
477C22—21no—
478C22—41no—
479C22—41no—
480C22—41no—
481C22—41no—
482C22—41no—
483C22—41no—
484C22—41no—
485C22—41no—
486C22—81no—
487C22—81no—
488C22—81no—
489C22—81no—
490C22—81no—
491C22—81no—
492C22—81no—
493C22—81no—
494C22—81no—
495C22C59×#39411yescharacteristic
496C22C59×B(4,𝔽2)11yescharacteristic
497C22C59×#45811yescharacteristic
498C4—21no—
499C4—21no—
500C4—42no—
501C4—81no—
502C4—81no—
503C4—82no—
504C4—81no—
505C4—81no—
506C4—81no—
507C4—81no—
508C4—161no—
509C2—21no—
510C2—21no—
511C2—41no—
512C2—41no—
513C2—41no—
514C2—41no—
515C2—161no—
516C2C59×#204411yescharacteristic
517C2C59×#219811yescharacteristic
518C2C59×#220011yescharacteristic
subgroupG/H
center, socleC22×C59B(4,𝔽2)
commutator, Frattini, cosocleC22×D4C23×C59
prime radicalC2×#127×C59C22
LCSG ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C59 ◁ C23×C59 ◁ C22×D4×C59 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C59×#352C2semidirect
4. C59×#1890C2semidirect
6. C59×#1867C2semidirect
7. C59×#1390C2semidirect
212. #13423C59direct (N × H)
252. C2×#352C2×C59semidirect
253. #1890C2×C59semidirect
255. #1867C2×C59semidirect
256. #1390C2×C59semidirect
288. C59#13423direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#27092
C2×C59×#3532
C2×C59×#3522
C59×#18902
C59×#18872
C59×#18672
C59×#13902
#1342359