Finite Group Databasebeta

← C59×#9881 #28421990

Subgroups — C59×#9881 #28421990

Order 15104.

556 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×#387C211yesmaximal, characteristic
2C59×#1797C211yesmaximal, characteristic
3C59×#1749C211yesmaximal, characteristic
4C59×#1280C212yesmaximal
5C59×#1280C212yesmaximal
6C22×C4⋊C4×C59C411yescharacteristic
7C22×C4⋊C4×C59C411yescharacteristic
8C22×C42×C59C2211yescharacteristic
9C2×C4⋊C8×C59—21no—
10C2×C22⋊C8×C59C2212yes—
11C2×C22⋊C8×C59C2212yes—
12C2×#97×C59—21no—
13C59×#387—21no—
14C59×#387—21no—
15C59×#387—21no—
16C59×#387—21no—
17C2×#95×C59C411yescharacteristic
18C2×#95×C59C411yescharacteristic
19C2×#95×C59C2211yescharacteristic
20C2×#95×C59C2211yescharacteristic
21C59×#336—21no—
22C59×#336—21no—
23C23×C4×C59C2×C411yescharacteristic
24C23×C4×C59C2×C411yescharacteristic
25C23×C4×C59C2×C411yescharacteristic
26C23×C4×C59C2×C411yescharacteristic
27C23×C4×C59C2×C411yescharacteristic
28C23×C4×C59C2×C411yescharacteristic
29C23×C4×C59C2311yescharacteristic
30C22×C8×C59—22no—
31C22×C8×C59—22no—
32C2×C4⋊C4×C59—21no—
33C2×C4⋊C4×C59—21no—
34C2×C4⋊C4×C59—22no—
35C2×C4⋊C4×C59—22no—
36C2×C4⋊C4×C59—21no—
37C2×C4⋊C4×C59—21no—
38C2×C4⋊C4×C59—42no—
39C2×C42×C59—42no—
40C2×C42×C59D411yescharacteristic
41C2×C42×C59D411yescharacteristic
42C2×C42×C59D411yescharacteristic
43C2×C42×C59D411yescharacteristic
44C4⋊C8×C59—42no—
45C22⋊C8×C59—22no—
46C22⋊C8×C59—24no—
47C22⋊C8×C59Q814yes—
48#97×C59—42no—
49#95×C59—21no—
50#95×C59—21no—
51#95×C59—21no—
52#95×C59—21no—
53#95×C59—21no—
54#95×C59—21no—
55#95×C59—21no—
56#95×C59—21no—
57C24×C59C22×C411yescharacteristic
58C22×C4×C59—21no—
59C22×C4×C59—21no—
60C22×C4×C59—21no—
61C22×C4×C59—21no—
62C22×C4×C59—21no—
63C22×C4×C59—21no—
64C22×C4×C59—22no—
65C22×C4×C59—22no—
66C22×C4×C59—21no—
67C22×C4×C59—21no—
68C22×C4×C59—22no—
69C22×C4×C59—22no—
70C22×C4×C59—41no—
71C22×C4×C59—41no—
72C22×C4×C59—41no—
73C22×C4×C59—41no—
74C22×C4×C59—41no—
75C22×C4×C59—41no—
76C22×C4×C59—41no—
77C22×C4×C59—41no—
78C22×C4×C59—41no—
79C22×C4×C59—41no—
80C22×C4×C59—41no—
81C22×C4×C59—41no—
82C22×C4×C59—41no—
83C22×C4×C59C22⋊C411yescharacteristic
84C22×C4×C59C22⋊C411yescharacteristic
85C22×C4×C59C22⋊C411yescharacteristic
86C22×C4×C59C22⋊C411yescharacteristic
87C22×C4×C59M1612yes—
88C22×C4×C59M1612yes—
89C22×C4×C59C2×D411yescharacteristic
90C22×C4×C59C2×D411yescharacteristic
91C22×C4×C59C2×Q812yes—
92C22×C4×C59#4112yes—
93C2×C8×C59—24no—
94C2×C8×C59—42no—
95C2×C8×C59—42no—
96C2×C8×C59—42no—
97C2×C8×C59—42no—
98C2×C8×C59—42no—
99C4⋊C4×C59—24no—
100C4⋊C4×C59—24no—
101C4⋊C4×C59—42no—
102C4⋊C4×C59—42no—
103C42×C59—22no—
104C42×C59—22no—
105C42×C59—41no—
106C42×C59—41no—
107C23×C59—21no—
108C23×C59—21no—
109C23×C59—21no—
110C23×C59—21no—
111C23×C59C2×C22⋊C411yescharacteristic
112C23×C59C4×Q812yes—
113C23×C59C2×M1611yescharacteristic
114C23×C59C2×M1611yescharacteristic
115C23×C59#13112yes—
116C2×C4×C59—21no—
117C2×C4×C59—21no—
118C2×C4×C59—21no—
119C2×C4×C59—21no—
120C2×C4×C59—21no—
121C2×C4×C59—21no—
122C2×C4×C59—21no—
123C2×C4×C59—21no—
124C2×C4×C59—22no—
125C2×C4×C59—22no—
126C2×C4×C59—21no—
127C2×C4×C59—21no—
128C2×C4×C59—21no—
129C2×C4×C59—21no—
130C2×C4×C59—21no—
131C2×C4×C59—21no—
132C2×C4×C59—21no—
133C2×C4×C59—42no—
134C2×C4×C59—42no—
135C2×C4×C59—44no—
136C2×C4×C59—42no—
137C2×C4×C59—42no—
138C2×C4×C59—42no—
139C2×C4×C59—42no—
140C2×C4×C59—41no—
141C2×C4×C59—41no—
142C2×C4×C59—41no—
143C2×C4×C59—41no—
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—82no—
153C2×C4×C59—82no—
154C2×C4×C59#9912yes—
155C2×C4×C59C22⋊Q812yes—
156C2×C4×C59#12411yescharacteristic
157C2×C4×C59C4⋊Q811yescharacteristic
158C8×C59—44no—
159C8×C59—82no—
160#9881C5911yesmaximal, characteristic, direct product factor, Sylow
161C22×C59—21no—
162C22×C59—21no—
163C22×C59—21no—
164C22×C59—21no—
165C22×C59—22no—
166C22×C59—22no—
167C22×C59—22no—
168C22×C59—22no—
169C22×C59#39111yescharacteristic
170C22×C59#40711yescharacteristic
171C22×C59#40811yescharacteristic
172C22×C59C2×#9911yescharacteristic
173C22×C59#41011yescharacteristic
174C22×C59#41311yescharacteristic
175C22×C59#41311yescharacteristic
176C22×C59#44612yes—
177C22×C59#44612yes—
178C4×C59—22no—
179C4×C59—22no—
180C4×C59—21no—
181C4×C59—21no—
182C4×C59—42no—
183C4×C59—41no—
184C4×C59—41no—
185C4×C59—42no—
186C4×C59—41no—
187C4×C59—81no—
188C4×C59—81no—
189C2×#387C2×C5911yescharacteristic
190#1797C2×C5911yescharacteristic
191#1749C2×C5911yescharacteristic
192#1280C2×C5912yes—
193#1280C2×C5912yes—
194C2×C59—22no—
195C2×C59—22no—
196C2×C59#146411yescharacteristic
197C2×C59#146511yescharacteristic
198C2×C59#146811yescharacteristic
199C2×C59#147311yescharacteristic
200C2×C59#198511yescharacteristic
201C2×C59#199611yescharacteristic
202C2×C59#199811yescharacteristic
203C22×C4⋊C4C4×C5911yescharacteristic
204C22×C4⋊C4C4×C5911yescharacteristic
205C22×C42C22×C5911yescharacteristic
206C2×C4⋊C8—21no—
207C2×C22⋊C8C22×C5912yes—
208C2×C22⋊C8C22×C5912yes—
209C2×#97—21no—
210#387—21no—
211#387—21no—
212#387—21no—
213#387—21no—
214C2×#95C4×C5911yescharacteristic
215C2×#95C4×C5911yescharacteristic
216C2×#95C22×C5911yescharacteristic
217C2×#95C22×C5911yescharacteristic
218#336—21no—
219#336—21no—
220C59#988111yescharacteristic, direct product factor, Sylow
221C23×C4C2×C4×C5911yescharacteristic
222C23×C4C2×C4×C5911yescharacteristic
223C23×C4C2×C4×C5911yescharacteristic
224C23×C4C2×C4×C5911yescharacteristic
225C23×C4C2×C4×C5911yescharacteristic
226C23×C4C2×C4×C5911yescharacteristic
227C23×C4C23×C5911yescharacteristic
228C22×C8—22no—
229C22×C8—22no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—22no—
233C2×C4⋊C4—22no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—42no—
237C2×C42—42no—
238C2×C42D4×C5911yescharacteristic
239C2×C42D4×C5911yescharacteristic
240C2×C42D4×C5911yescharacteristic
241C2×C42D4×C5911yescharacteristic
242C4⋊C8—42no—
243C22⋊C8—22no—
244C22⋊C8—24no—
245C22⋊C8Q8×C5914yes—
246#97—42no—
247#95—21no—
248#95—21no—
249#95—21no—
250#95—21no—
251#95—21no—
252#95—21no—
253#95—21no—
254#95—21no—
255C24C22×C4×C5911yescharacteristic
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—22no—
263C22×C4—22no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4C22⋊C4×C5911yescharacteristic
282C22×C4C22⋊C4×C5911yescharacteristic
283C22×C4C22⋊C4×C5911yescharacteristic
284C22×C4C22⋊C4×C5911yescharacteristic
285C22×C4M16×C5912yes—
286C22×C4M16×C5912yes—
287C22×C4C2×D4×C5911yescharacteristic
288C22×C4C2×D4×C5911yescharacteristic
289C22×C4C2×Q8×C5912yes—
290C22×C4#41×C5912yes—
291C2×C8—24no—
292C2×C8—42no—
293C2×C8—42no—
294C2×C8—42no—
295C2×C8—42no—
296C2×C8—42no—
297C4⋊C4—24no—
298C4⋊C4—24no—
299C4⋊C4—42no—
300C4⋊C4—42no—
301C42—22no—
302C42—22no—
303C42—41no—
304C42—41no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23C2×C22⋊C4×C5911yescharacteristic
310C23C4×Q8×C5912yes—
311C23C2×M16×C5911yescharacteristic
312C23C2×M16×C5911yescharacteristic
313C23#131×C5912yes—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—44no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—82no—
351C2×C4—82no—
352C2×C4#99×C5912yes—
353C2×C4C22⋊Q8×C5912yes—
354C2×C4#124×C5911yescharacteristic
355C2×C4C4⋊Q8×C5911yescharacteristic
356C8—44no—
357C8—82no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—22no—
363C22—22no—
364C22—22no—
365C22—22no—
366C22C59×#39111yescharacteristic
367C22C59×#40711yescharacteristic
368C22C59×#40811yescharacteristic
369C22C2×#99×C5911yescharacteristic
370C22C59×#41011yescharacteristic
371C22C59×#41311yescharacteristic
372C22C59×#41311yescharacteristic
373C22C59×#44612yes—
374C22C59×#44612yes—
375C4—22no—
376C4—22no—
377C4—21no—
378C4—21no—
379C4—42no—
380C4—41no—
381C4—41no—
382C4—42no—
383C4—41no—
384C4—81no—
385C4—81no—
386C2—22no—
387C2—22no—
388C2C59×#146411yescharacteristic
389C2C59×#146511yescharacteristic
390C2C59×#146811yescharacteristic
391C2C59×#147311yescharacteristic
392C2C59×#198511yescharacteristic
393C2C59×#199611yescharacteristic
394C2C59×#199811yescharacteristic
subgroupG/H
center, socleC23×C59C2×C22⋊C4
commutatorC24C22×C4×C59
Frattini, cosocleC23×C4C23×C59
prime radicalC24×C59C22×C4
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C59 ◁ C22×C42×C59 ◁ G

Complements

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

NH ≅ G/Ntype
160. #9881C59direct (N × H)
220. C59#9881direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C59×#3872
C59×#17972
C59×#17492
C59×#12802
#988159