Finite Group Databasebeta

← C59×#13462 #28425571

Subgroups — C59×#13462 #28425571

Order 15104.

476 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 98 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×#2748C211yesmaximal, characteristic
2C59×#1867C211yesmaximal, characteristic
3C59×#1867C211yesmaximal, characteristic
4C59×#1856C211yesmaximal, characteristic
5C59×#1393C211yesmaximal, characteristic
6C59×#1390C211yesmaximal, characteristic
7C59×#1390C211yesmaximal, characteristic
8C59×#518C2211yescharacteristic
9C59×#428—21no—
10C2×#100×C59C2211yescharacteristic
11C2×#99×C59C2211yescharacteristic
12C2×#99×C59C2211yescharacteristic
13C59×#399—21no—
14C59×#398—21no—
15C59×#396—21no—
16C59×#390C2211yescharacteristic
17C59×#387—21no—
18C59×#386C2211yescharacteristic
19C59×#386C2211yescharacteristic
20C59×#385—21no—
21C59×#385—21no—
22C59×#385—21no—
23C59×#380—21no—
24C59×#342—21no—
25C59×#342—21no—
26C59×#339—21no—
27C22×D4×C59C2311yescharacteristic
28C23×C4×C59D411yescharacteristic
29C23×C4×C59D411yescharacteristic
30C2×M16×C59—21no—
31C4×D4×C59—41no—
32C4×D4×C59—41no—
33#117×C59—21no—
34C2×C4⋊C4×C59—21no—
35C2×C4⋊C4×C59—21no—
36C2×C4⋊C4×C59—21no—
37C2×C4⋊C4×C59—21no—
38C2×C4⋊C4×C59—21no—
39C2×C4⋊C4×C59—41no—
40C2×C4⋊C4×C59—41no—
41C2×C4⋊C4×C59D411yescharacteristic
42C2×C22⋊C4×C59—21no—
43C2×C22⋊C4×C59—21no—
44C2×C22⋊C4×C59—21no—
45C2×C22⋊C4×C59—21no—
46C2×C22⋊C4×C59—21no—
47C2×C22⋊C4×C59—21no—
48C2×C22⋊C4×C59—21no—
49C2×C22⋊C4×C59—21no—
50C2×C22⋊C4×C59D411yescharacteristic
51C2×C22⋊C4×C59D411yescharacteristic
52C2×C42×C59D411yescharacteristic
53#107×C59—41no—
54#106×C59—41no—
55#100×C59—21no—
56#100×C59Q812yes—
57#99×C59—21no—
58#99×C59—21no—
59#99×C59Q812yes—
60#99×C59Q812yes—
61#95×C59—21no—
62#95×C59—21no—
63#95×C59—21no—
64#95×C59—21no—
65#95×C59—21no—
66#95×C59—41no—
67#95×C59—41no—
68C24×C59C2×D411yescharacteristic
69C24×C59C2×D411yescharacteristic
70C2×D4×C59—41no—
71C2×D4×C59—41no—
72C2×D4×C59C2×Q811yescharacteristic
73C2×D4×C59C2×Q811yescharacteristic
74C2×D4×C59C2×Q811yescharacteristic
75C2×D4×C59#4111yescharacteristic
76C22×C4×C59—21no—
77C22×C4×C59—21no—
78C22×C4×C59—21no—
79C22×C4×C59—21no—
80C22×C4×C59—21no—
81C22×C4×C59—21no—
82C22×C4×C59—21no—
83C22×C4×C59—21no—
84C22×C4×C59—21no—
85C22×C4×C59—21no—
86C22×C4×C59—42no—
87C22×C4×C59—41no—
88C22×C4×C59—41no—
89C22×C4×C59—41no—
90C22×C4×C59—41no—
91C22×C4×C59—81no—
92C22×C4×C59C2×D411yescharacteristic
93M16×C59—22no—
94M16×C59—41no—
95C2×C8×C59—41no—
96C4⋊C4×C59—21no—
97C4⋊C4×C59—21no—
98C4⋊C4×C59—42no—
99C4⋊C4×C59—41no—
100C4⋊C4×C59—81no—
101C4⋊C4×C59—81no—
102C4⋊C4×C59—81no—
103C4⋊C4×C59—81no—
104C4⋊C4×C59—82no—
105C4⋊C4×C59—82no—
106C22⋊C4×C59—22no—
107C22⋊C4×C59—22no—
108C22⋊C4×C59—42no—
109C22⋊C4×C59—41no—
110C22⋊C4×C59—41no—
111C22⋊C4×C59—41no—
112C22⋊C4×C59—41no—
113C22⋊C4×C59—41no—
114C22⋊C4×C59—41no—
115C22⋊C4×C59—41no—
116C22⋊C4×C59—81no—
117C22⋊C4×C59—81no—
118C22⋊C4×C59—81no—
119C42×C59—41no—
120C42×C59—41no—
121C23×C59—21no—
122C23×C59—21no—
123C23×C59—21no—
124C23×C59—21no—
125C23×C59—41no—
126C23×C59—41no—
127C23×C59—41no—
128C23×C59—41no—
129C23×C59#12011yescharacteristic
130C23×C59C22⋊Q811yescharacteristic
131C23×C59C22⋊Q811yescharacteristic
132C23×C59C4⋊Q811yescharacteristic
133C23×C59C4⋊Q811yescharacteristic
134D4×C59—41no—
135D4×C59—41no—
136D4×C59—41no—
137D4×C59—41no—
138C2×C4×C59—21no—
139C2×C4×C59—21no—
140C2×C4×C59—22no—
141C2×C4×C59—41no—
142C2×C4×C59—41no—
143C2×C4×C59—42no—
144C2×C4×C59—42no—
145C2×C4×C59—42no—
146C2×C4×C59—41no—
147C2×C4×C59—41no—
148C2×C4×C59—41no—
149C2×C4×C59—41no—
150C2×C4×C59—41no—
151C2×C4×C59—41no—
152C2×C4×C59—41no—
153C2×C4×C59—41no—
154C2×C4×C59—41no—
155C2×C4×C59—41no—
156C2×C4×C59—42no—
157C2×C4×C59—41no—
158C2×C4×C59—41no—
159C2×C4×C59—41no—
160C2×C4×C59—41no—
161C2×C4×C59—41no—
162C2×C4×C59—41no—
163C2×C4×C59—41no—
164C2×C4×C59—81no—
165C2×C4×C59—81no—
166C2×C4×C59—81no—
167C2×C4×C59—81no—
168C2×C4×C59—81no—
169C2×C4×C59—81no—
170C2×C4×C59—81no—
171C2×C4×C59—81no—
172C2×C4×C59—81no—
173C2×C4×C59—81no—
174C2×C4×C59C22⋊Q811yescharacteristic
175C2×C4×C59C4⋊Q811yescharacteristic
176C8×C59—42no—
177#13462C5911yesmaximal, characteristic, direct product factor, Sylow
178C22×C59—21no—
179C22×C59—21no—
180C22×C59—21no—
181C22×C59—21no—
182C22×C59—21no—
183C22×C59—21no—
184C22×C59—41no—
185C22×C59—41no—
186C22×C59—41no—
187C22×C59—41no—
188C22×C59—41no—
189C22×C59—41no—
190C22×C59—41no—
191C22×C59—41no—
192C22×C59—81no—
193C22×C59—81no—
194C22×C59#39511yescharacteristic
195C22×C59B(4,𝔽2)11yescharacteristic
196C22×C59#45811yescharacteristic
197C4×C59—21no—
198C4×C59—21no—
199C4×C59—42no—
200C4×C59—81no—
201C4×C59—81no—
202C4×C59—81no—
203C4×C59—82no—
204C4×C59—82no—
205C4×C59—81no—
206C4×C59—81no—
207C4×C59—81no—
208C4×C59—81no—
209#2748C2×C5911yescharacteristic
210#1867C2×C5911yescharacteristic
211#1867C2×C5911yescharacteristic
212#1856C2×C5911yescharacteristic
213#1393C2×C5911yescharacteristic
214#1390C2×C5911yescharacteristic
215#1390C2×C5911yescharacteristic
216C2×C59—21no—
217C2×C59—21no—
218C2×C59—41no—
219C2×C59—41no—
220C2×C59—41no—
221C2×C59—41no—
222C2×C59#206211yescharacteristic
223C2×C59#219711yescharacteristic
224C2×C59#220011yescharacteristic
225#518C22×C5911yescharacteristic
226#428—21no—
227C2×#100C22×C5911yescharacteristic
228C2×#99C22×C5911yescharacteristic
229C2×#99C22×C5911yescharacteristic
230#399—21no—
231#398—21no—
232#396—21no—
233#390C22×C5911yescharacteristic
234#387—21no—
235#386C22×C5911yescharacteristic
236#386C22×C5911yescharacteristic
237#385—21no—
238#385—21no—
239#385—21no—
240#380—21no—
241#342—21no—
242#342—21no—
243#339—21no—
244C59#1346211yescharacteristic, direct product factor, Sylow
245C22×D4C23×C5911yescharacteristic
246C23×C4D4×C5911yescharacteristic
247C23×C4D4×C5911yescharacteristic
248C2×M16—21no—
249C4×D4—41no—
250C4×D4—41no—
251#117—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—41no—
258C2×C4⋊C4—41no—
259C2×C4⋊C4D4×C5911yescharacteristic
260C2×C22⋊C4—21no—
261C2×C22⋊C4—21no—
262C2×C22⋊C4—21no—
263C2×C22⋊C4—21no—
264C2×C22⋊C4—21no—
265C2×C22⋊C4—21no—
266C2×C22⋊C4—21no—
267C2×C22⋊C4—21no—
268C2×C22⋊C4D4×C5911yescharacteristic
269C2×C22⋊C4D4×C5911yescharacteristic
270C2×C42D4×C5911yescharacteristic
271#107—41no—
272#106—41no—
273#100—21no—
274#100Q8×C5912yes—
275#99—21no—
276#99—21no—
277#99Q8×C5912yes—
278#99Q8×C5912yes—
279#95—21no—
280#95—21no—
281#95—21no—
282#95—21no—
283#95—21no—
284#95—41no—
285#95—41no—
286C24C2×D4×C5911yescharacteristic
287C24C2×D4×C5911yescharacteristic
288C2×D4—41no—
289C2×D4—41no—
290C2×D4C2×Q8×C5911yescharacteristic
291C2×D4C2×Q8×C5911yescharacteristic
292C2×D4C2×Q8×C5911yescharacteristic
293C2×D4#41×C5911yescharacteristic
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—42no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—81no—
310C22×C4C2×D4×C5911yescharacteristic
311M16—22no—
312M16—41no—
313C2×C8—41no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—41no—
317C4⋊C4—42no—
318C4⋊C4—81no—
319C4⋊C4—81no—
320C4⋊C4—81no—
321C4⋊C4—81no—
322C4⋊C4—82no—
323C4⋊C4—82no—
324C22⋊C4—22no—
325C22⋊C4—22no—
326C22⋊C4—42no—
327C22⋊C4—41no—
328C22⋊C4—41no—
329C22⋊C4—41no—
330C22⋊C4—41no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—41no—
334C22⋊C4—81no—
335C22⋊C4—81no—
336C22⋊C4—81no—
337C42—41no—
338C42—41no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23#120×C5911yescharacteristic
348C23C22⋊Q8×C5911yescharacteristic
349C23C22⋊Q8×C5911yescharacteristic
350C23C4⋊Q8×C5911yescharacteristic
351C23C4⋊Q8×C5911yescharacteristic
352D4—41no—
353D4—41no—
354D4—41no—
355D4—41no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—22no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—42no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—81no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4—81no—
386C2×C4—81no—
387C2×C4—81no—
388C2×C4—81no—
389C2×C4—81no—
390C2×C4—81no—
391C2×C4—81no—
392C2×C4C22⋊Q8×C5911yescharacteristic
393C2×C4C4⋊Q8×C5911yescharacteristic
394C8—42no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—81no—
410C22—81no—
411C22C59×#39511yescharacteristic
412C22C59×B(4,𝔽2)11yescharacteristic
413C22C59×#45811yescharacteristic
414C4—21no—
415C4—21no—
416C4—42no—
417C4—81no—
418C4—81no—
419C4—81no—
420C4—82no—
421C4—82no—
422C4—81no—
423C4—81no—
424C4—81no—
425C4—81no—
426C2—21no—
427C2—21no—
428C2—41no—
429C2—41no—
430C2—41no—
431C2—41no—
432C2C59×#206211yescharacteristic
433C2C59×#219711yescharacteristic
434C2C59×#220011yescharacteristic
subgroupG/H
center, socleC22×C59B(4,𝔽2)
commutator, Frattini, cosocleC22×D4C23×C59
prime radicalC22×D4×C59C23
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
177. #13462C59direct (N × H)
244. C59#13462direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#27482
C59×#18672
C59×#18562
C59×#13932
C59×#13902
#1346259