Finite Group Databasebeta

← C59×#8876 #28420985

Subgroups — C59×#8876 #28420985

Order 15104.

380 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#2992C211yesmaximal, characteristic
2C59×#1843C211yesmaximal, characteristic, complemented
3C59×#1573C211yesmaximal, characteristic, complemented
4C59×#1500C211yesmaximal, characteristic
5C59×#1483C211yesmaximal, characteristic
6C59×#1300C211yesmaximal, characteristic, complemented
7C59×#1283C211yesmaximal, characteristic, complemented
8C59×#529C2211yescharacteristic
9C59×#446—21no—
10C59×#435—21no—
11C59×#435—21no—
12C8×D4×C59—21no—
13C59×#433—21no—
14C59×#432C2211yescharacteristic
15C59×#431C2211yescharacteristic
16C59×#424—21no—
17C2×C4⋊C8×C59—21no—
18C2×C4⋊C8×C59—21no—
19C2×C4⋊C8×C59C2211yescharacteristic
20C2×C4⋊C8×C59C2211yescharacteristic
21C4×M16×C59C2211yescharacteristic
22C59×#376C2211yescharacteristic
23C59×#335—21no—
24C59×#334—21no—
25C59×#328C411yescharacteristic
26C59×#328C411yescharacteristic
27C59×#327C411yescharacteristic
28C59×#327C411yescharacteristic
29C59×Q8⋊C8—21no—
30C59×D4⋊C8—21no—
31C2×M16×C59—21no—
32C2×M16×C59—21no—
33C22×C8×C59—21no—
34C22×C8×C59—21no—
35C22×C8×C59D411yescharacteristic
36C22×C8×C59D411yescharacteristic
37#126×C59—21no—
38#125×C59Q811yescharacteristic
39#124×C59Q811yescharacteristic
40#123×C59—21no—
41C22⋊Q8×C59C2×C411yescharacteristic
42#121×C59C2×C411yescharacteristic
43C4×Q8×C59D411yescharacteristic
44C4×D4×C59—21no—
45C4×D4×C59D411yescharacteristic
46#117×C59—21no—
47C2×C42×C59—21no—
48C2×C42×C59C2311yescharacteristic
49C4⋊C8×C59—21no—
50C4⋊C8×C59—21no—
51C4⋊C8×C59—21no—
52C4⋊C8×C59—21no—
53C4⋊C8×C59—21no—
54C4⋊C8×C59—21no—
55C4⋊C8×C59—21no—
56C4⋊C8×C59—42no—
57C4⋊C8×C59—42no—
58C4⋊C8×C59D411yescharacteristic
59C4⋊C8×C59D411yescharacteristic
60C22⋊C8×C59—21no—
61C22⋊C8×C59—21no—
62C22⋊C8×C59—21no—
63C22⋊C8×C59C2×C411yescharacteristic
64C22⋊C8×C59C2×C411yescharacteristic
65#97×C59—21no—
66#97×C59—21no—
67#97×C59—21no—
68C4×C8×C59—21no—
69C4×C8×C59—21no—
70C4×C8×C59—21no—
71#95×C59—21no—
72#95×C59C2×C411yescharacteristic
73#95×C59C2×C411yescharacteristic
74C2×Q8×C59C4⋊C411yescharacteristic
75C2×D4×C59—21no—
76C2×D4×C59C4⋊C411yescharacteristic
77C22×C4×C59—21no—
78C22×C4×C59—21no—
79C22×C4×C59—21no—
80C22×C4×C59C22×C411yescharacteristic
81C22×C4×C59C2×D411yescharacteristic
82C22×C4×C59#4111yescharacteristic
83M16×C59—22no—
84M16×C59—41no—
85M16×C59—81no—
86C2×C8×C59—21no—
87C2×C8×C59—21no—
88C2×C8×C59—21no—
89C2×C8×C59—21no—
90C2×C8×C59—21no—
91C2×C8×C59—21no—
92C2×C8×C59—41no—
93C2×C8×C59—41no—
94C2×C8×C59—41no—
95C2×C8×C59—41no—
96C2×C8×C59—41no—
97C2×C8×C59—41no—
98C2×C8×C59—81no—
99C4⋊C4×C59—21no—
100C4⋊C4×C59—21no—
101C4⋊C4×C59—21no—
102C4⋊C4×C59—21no—
103C4⋊C4×C59C4⋊C411yescharacteristic
104C4⋊C4×C59C4⋊C411yescharacteristic
105C22⋊C4×C59—21no—
106C22⋊C4×C59—21no—
107C22⋊C4×C59—21no—
108C22⋊C4×C59—21no—
109C22⋊C4×C59—21no—
110C42×C59—22no—
111C42×C59—22no—
112C42×C59—21no—
113C42×C59C2×D411yescharacteristic
114C42×C59C2×D411yescharacteristic
115C42×C59C2×Q811yescharacteristic
116C42×C59#4111yescharacteristic
117C23×C59—21no—
118C23×C59C4×D411yescharacteristic
119Q8×C59—41no—
120D4×C59—41no—
121D4×C59—41no—
122D4×C59—41no—
123C2×C4×C59—21no—
124C2×C4×C59—21no—
125C2×C4×C59—21no—
126C2×C4×C59—21no—
127C2×C4×C59—22no—
128C2×C4×C59—22no—
129C2×C4×C59—21no—
130C2×C4×C59—21no—
131C2×C4×C59—21no—
132C2×C4×C59—41no—
133C2×C4×C59—41no—
134C2×C4×C59—41no—
135C2×C4×C59—41no—
136C2×C4×C59—41no—
137C2×C4×C59—41no—
138C2×C4×C59—41no—
139C2×C4×C59C2×C4⋊C411yescharacteristic
140C2×C4×C59C4×D411yescharacteristic
141C2×C4×C59#12011yescharacteristic
142C2×C4×C59C22⋊Q811yescharacteristic
143C2×C4×C59C22⋊Q811yescharacteristic
144C2×C4×C59#12311yescharacteristic
145C8×C59—41no—
146C8×C59—41no—
147C8×C59—42no—
148C8×C59—41no—
149C8×C59—41no—
150C8×C59—41no—
151C8×C59—41no—
152C8×C59—81no—
153#8876C5911yesmaximal, characteristic, direct product factor, Sylow
154C22×C59—21no—
155C22×C59—21no—
156C22×C59—41no—
157C22×C59—41no—
158C22×C59—41no—
159C22×C59#38511yescharacteristic
160C22×C59#44311yescharacteristic
161C22×C59#44411yescharacteristic
162C4×C59—21no—
163C4×C59—21no—
164C4×C59—21no—
165C4×C59—21no—
166C4×C59—21no—
167C4×C59—42no—
168C4×C59—42no—
169C4×C59—41no—
170C4×C59—41no—
171C4×C59—41no—
172C4×C59#45311yescharacteristic
173C4×C59#45611yescharacteristic
174#2992C2×C5911yescharacteristic
175#1843C2×C5911yescharacteristic, complemented
176#1573C2×C5911yescharacteristic, complemented
177#1500C2×C5911yescharacteristic
178#1483C2×C5911yescharacteristic
179#1300C2×C5911yescharacteristic, complemented
180#1283C2×C5911yescharacteristic, complemented
181C2×C59—21no—
182C2×C59—21no—
183C2×C59—81no—
184C2×C59#185911yescharacteristic
185C2×C59#186611yescharacteristic
186C2×C59#186811yescharacteristic
187#529C22×C5911yescharacteristic
188#446—21no—
189#435—21no—
190#435—21no—
191C8×D4—21no—
192#433—21no—
193#432C22×C5911yescharacteristic
194#431C22×C5911yescharacteristic
195#424—21no—
196C2×C4⋊C8—21no—
197C2×C4⋊C8—21no—
198C2×C4⋊C8C22×C5911yescharacteristic
199C2×C4⋊C8C22×C5911yescharacteristic
200C4×M16C22×C5911yescharacteristic
201#376C22×C5911yescharacteristic
202#335—21no—
203#334—21no—
204#328C4×C5911yescharacteristic
205#328C4×C5911yescharacteristic
206#327C4×C5911yescharacteristic
207#327C4×C5911yescharacteristic
208Q8⋊C8—21no—
209D4⋊C8—21no—
210C59#887611yescharacteristic, direct product factor, Sylow
211C2×M16—21no—
212C2×M16—21no—
213C22×C8—21no—
214C22×C8—21no—
215C22×C8D4×C5911yescharacteristic
216C22×C8D4×C5911yescharacteristic
217#126—21no—
218#125Q8×C5911yescharacteristic
219#124Q8×C5911yescharacteristic
220#123—21no—
221C22⋊Q8C2×C4×C5911yescharacteristic
222#121C2×C4×C5911yescharacteristic
223C4×Q8D4×C5911yescharacteristic
224C4×D4—21no—
225C4×D4D4×C5911yescharacteristic
226#117—21no—
227C2×C42—21no—
228C2×C42C23×C5911yescharacteristic
229C4⋊C8—21no—
230C4⋊C8—21no—
231C4⋊C8—21no—
232C4⋊C8—21no—
233C4⋊C8—21no—
234C4⋊C8—21no—
235C4⋊C8—21no—
236C4⋊C8—42no—
237C4⋊C8—42no—
238C4⋊C8D4×C5911yescharacteristic
239C4⋊C8D4×C5911yescharacteristic
240C22⋊C8—21no—
241C22⋊C8—21no—
242C22⋊C8—21no—
243C22⋊C8C2×C4×C5911yescharacteristic
244C22⋊C8C2×C4×C5911yescharacteristic
245#97—21no—
246#97—21no—
247#97—21no—
248C4×C8—21no—
249C4×C8—21no—
250C4×C8—21no—
251#95—21no—
252#95C2×C4×C5911yescharacteristic
253#95C2×C4×C5911yescharacteristic
254C2×Q8C4⋊C4×C5911yescharacteristic
255C2×D4—21no—
256C2×D4C4⋊C4×C5911yescharacteristic
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4C22×C4×C5911yescharacteristic
261C22×C4C2×D4×C5911yescharacteristic
262C22×C4#41×C5911yescharacteristic
263M16—22no—
264M16—41no—
265M16—81no—
266C2×C8—21no—
267C2×C8—21no—
268C2×C8—21no—
269C2×C8—21no—
270C2×C8—21no—
271C2×C8—21no—
272C2×C8—41no—
273C2×C8—41no—
274C2×C8—41no—
275C2×C8—41no—
276C2×C8—41no—
277C2×C8—41no—
278C2×C8—81no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4C4⋊C4×C5911yescharacteristic
284C4⋊C4C4⋊C4×C5911yescharacteristic
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—21no—
290C42—22no—
291C42—22no—
292C42—21no—
293C42C2×D4×C5911yescharacteristic
294C42C2×D4×C5911yescharacteristic
295C42C2×Q8×C5911yescharacteristic
296C42#41×C5911yescharacteristic
297C23—21no—
298C23C4×D4×C5911yescharacteristic
299Q8—41no—
300D4—41no—
301D4—41no—
302D4—41no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4C2×C4⋊C4×C5911yescharacteristic
320C2×C4C4×D4×C5911yescharacteristic
321C2×C4#120×C5911yescharacteristic
322C2×C4C22⋊Q8×C5911yescharacteristic
323C2×C4C22⋊Q8×C5911yescharacteristic
324C2×C4#123×C5911yescharacteristic
325C8—41no—
326C8—41no—
327C8—42no—
328C8—41no—
329C8—41no—
330C8—41no—
331C8—41no—
332C8—81no—
333C22—21no—
334C22—21no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22C59×#38511yescharacteristic
339C22C59×#44311yescharacteristic
340C22C59×#44411yescharacteristic
341C4—21no—
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—42no—
347C4—42no—
348C4—41no—
349C4—41no—
350C4—41no—
351C4C59×#45311yescharacteristic
352C4C59×#45611yescharacteristic
353C2—21no—
354C2—21no—
355C2—81no—
356C2C59×#185911yescharacteristic
357C2C59×#186611yescharacteristic
358C2C59×#186811yescharacteristic
subgroupG/H
centerC2×C4×C59#120
commutatorC22×C4C22×C4×C59
Frattini, cosocleC2×C42C23×C59
socleC22×C59#385
prime radical#121×C59C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C59 ◁ C2×C42×C59 ◁ G

Complements

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

NH ≅ G/Ntype
2. C59×#1843C2semidirect
3. C59×#1573C2semidirect
6. C59×#1300C2semidirect
7. C59×#1283C2semidirect
153. #8876C59direct (N × H)
175. #1843C2×C59semidirect
176. #1573C2×C59semidirect
179. #1300C2×C59semidirect
180. #1283C2×C59semidirect
210. C59#8876direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#29922
C59×#18432
C59×#15732
C59×#15002
C59×#14832
C59×#13002
C59×#12832
#887659