Finite Group Databasebeta

← C59×#7732 #28419841

Subgroups — C59×#7732 #28419841

Order 15104.

420 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#2860C211yesmaximal, characteristic
2C59×#1831C211yesmaximal, characteristic, complemented
3C59×#1831C211yesmaximal, characteristic, complemented
4C59×#1271C212yesmaximal, complemented
5C59×#1270C212yesmaximal
6C2×#126×C59—21no—
7C2×C4⋊C8×C59—21no—
8C2×C4⋊C8×C59—21no—
9C59×#390C411yescharacteristic
10C59×#390C411yescharacteristic
11C59×#390C2211yescharacteristic
12C59×#389C411yescharacteristic
13C59×#389C411yescharacteristic
14C59×#389C2211yescharacteristic
15C59×#388—21no—
16C59×#388—21no—
17C59×#388—21no—
18C43×C59C2211yescharacteristic
19C59×#336—21no—
20C59×#336—21no—
21C59×#336C2212yes—
22C59×#336C2212yes—
23C22×D4×C59C2×C411yescharacteristic
24C22×C8×C59—22no—
25C22×C8×C59—22no—
26#126×C59—42no—
27#126×C59—42no—
28C2×C4⋊C4×C59—21no—
29C2×C4⋊C4×C59—21no—
30C2×C4⋊C4×C59—21no—
31C2×C4⋊C4×C59C2×C411yescharacteristic
32C2×C4⋊C4×C59C2×C411yescharacteristic
33C2×C4⋊C4×C59C2×C411yescharacteristic
34C2×C22⋊C4×C59—21no—
35C2×C22⋊C4×C59—21no—
36C2×C22⋊C4×C59—21no—
37C2×C22⋊C4×C59—21no—
38C2×C22⋊C4×C59—21no—
39C2×C22⋊C4×C59—21no—
40C2×C42×C59C2×C411yescharacteristic
41C2×C42×C59C2×C411yescharacteristic
42C2×C42×C59D411yescharacteristic
43C2×C42×C59D411yescharacteristic
44C2×C42×C59D411yescharacteristic
45C2×C42×C59D411yescharacteristic
46C2×C42×C59C2311yescharacteristic
47C4⋊C8×C59—42no—
48C4⋊C8×C59—42no—
49#95×C59—21no—
50#95×C59—21no—
51#95×C59—21no—
52C24×C59—21no—
53C2×D4×C59—22no—
54C2×D4×C59—41no—
55C2×D4×C59—41no—
56C22×C4×C59—21no—
57C22×C4×C59—21no—
58C22×C4×C59—21no—
59C22×C4×C59C22⋊C411yescharacteristic
60C22×C4×C59C22⋊C411yescharacteristic
61C22×C4×C59C22⋊C411yescharacteristic
62C22×C4×C59C22⋊C411yescharacteristic
63C22×C4×C59C22×C411yescharacteristic
64C22×C4×C59C2×D411yescharacteristic
65C22×C4×C59C2×D411yescharacteristic
66C2×C8×C59—42no—
67C2×C8×C59—42no—
68C2×C8×C59—42no—
69C2×C8×C59—42no—
70C2×C8×C59—42no—
71C2×C8×C59—42no—
72C4⋊C4×C59—22no—
73C4⋊C4×C59—41no—
74C4⋊C4×C59—41no—
75C4⋊C4×C59—42no—
76C4⋊C4×C59—42no—
77C4⋊C4×C59—41no—
78C4⋊C4×C59—41no—
79C22⋊C4×C59—42no—
80C22⋊C4×C59—42no—
81C22⋊C4×C59—42no—
82C22⋊C4×C59—42no—
83C22⋊C4×C59—41no—
84C22⋊C4×C59—41no—
85C22⋊C4×C59—41no—
86C22⋊C4×C59—41no—
87C42×C59—22no—
88C42×C59—21no—
89C42×C59—21no—
90C42×C59—41no—
91C42×C59—41no—
92C42×C59—41no—
93C42×C59—41no—
94C42×C59D812yes—
95C42×C59SD1612yes—
96C23×C59—41no—
97C23×C59—41no—
98C23×C59—41no—
99C23×C59—41no—
100C23×C59—41no—
101C23×C59—41no—
102C23×C59—41no—
103C23×C59C2×C22⋊C411yescharacteristic
104D4×C59—82no—
105C2×C4×C59—21no—
106C2×C4×C59—21no—
107C2×C4×C59—21no—
108C2×C4×C59—21no—
109C2×C4×C59—21no—
110C2×C4×C59—21no—
111C2×C4×C59—21no—
112C2×C4×C59—21no—
113C2×C4×C59—21no—
114C2×C4×C59—21no—
115C2×C4×C59—21no—
116C2×C4×C59—21no—
117C2×C4×C59—21no—
118C2×C4×C59—21no—
119C2×C4×C59—21no—
120C2×C4×C59—21no—
121C2×C4×C59—41no—
122C2×C4×C59—41no—
123C2×C4×C59—41no—
124C2×C4×C59—41no—
125C2×C4×C59—41no—
126C2×C4×C59—41no—
127C2×C4×C59—41no—
128C2×C4×C59—41no—
129C2×C4×C59—41no—
130C2×C4×C59#10212yes—
131C2×C4×C59#10212yes—
132C2×C4×C59#13112yes—
133C2×C4×C59C2×D811yescharacteristic
134C2×C4×C59C2×SD1611yescharacteristic
135C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C59#13711yescharacteristic
137C8×C59—82no—
138C8×C59—82no—
139#7732C5911yesmaximal, characteristic, direct product factor, Sylow
140C22×C59—81no—
141C22×C59—81no—
142C22×C59—81no—
143C22×C59—81no—
144C22×C59—81no—
145C22×C59—81no—
146C22×C59—81no—
147C22×C59#40811yescharacteristic
148C22×C59#41011yescharacteristic
149C22×C59#41311yescharacteristic
150C22×C59C2×#10211yescharacteristic
151C22×C59#41711yescharacteristic
152C22×C59#42111yescharacteristic
153C22×C59#42111yescharacteristic
154C4×C59—22no—
155C4×C59—22no—
156C4×C59—22no—
157C4×C59—21no—
158C4×C59—21no—
159C4×C59—21no—
160C4×C59—21no—
161C4×C59—41no—
162C4×C59—41no—
163C4×C59—81no—
164C4×C59—81no—
165C4×C59—81no—
166#2860C2×C5911yescharacteristic
167#1831C2×C5911yescharacteristic, complemented
168#1831C2×C5911yescharacteristic, complemented
169#1271C2×C5912yescomplemented
170#1270C2×C5912yes—
171C2×C59—161no—
172C2×C59#147311yescharacteristic
173C2×C59#148011yescharacteristic
174C2×C59#149511yescharacteristic
175C2×C59#151211yescharacteristic
176C2×C59#151711yescharacteristic
177C2×C59#153511yescharacteristic
178C2×C59#154711yescharacteristic
179C2×#126—21no—
180C2×C4⋊C8—21no—
181C2×C4⋊C8—21no—
182#390C4×C5911yescharacteristic
183#390C4×C5911yescharacteristic
184#390C22×C5911yescharacteristic
185#389C4×C5911yescharacteristic
186#389C4×C5911yescharacteristic
187#389C22×C5911yescharacteristic
188#388—21no—
189#388—21no—
190#388—21no—
191C43C22×C5911yescharacteristic
192#336—21no—
193#336—21no—
194#336C22×C5912yes—
195#336C22×C5912yes—
196C59#773211yescharacteristic, direct product factor, Sylow
197C22×D4C2×C4×C5911yescharacteristic
198C22×C8—22no—
199C22×C8—22no—
200#126—42no—
201#126—42no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4C2×C4×C5911yescharacteristic
206C2×C4⋊C4C2×C4×C5911yescharacteristic
207C2×C4⋊C4C2×C4×C5911yescharacteristic
208C2×C22⋊C4—21no—
209C2×C22⋊C4—21no—
210C2×C22⋊C4—21no—
211C2×C22⋊C4—21no—
212C2×C22⋊C4—21no—
213C2×C22⋊C4—21no—
214C2×C42C2×C4×C5911yescharacteristic
215C2×C42C2×C4×C5911yescharacteristic
216C2×C42D4×C5911yescharacteristic
217C2×C42D4×C5911yescharacteristic
218C2×C42D4×C5911yescharacteristic
219C2×C42D4×C5911yescharacteristic
220C2×C42C23×C5911yescharacteristic
221C4⋊C8—42no—
222C4⋊C8—42no—
223#95—21no—
224#95—21no—
225#95—21no—
226C24—21no—
227C2×D4—22no—
228C2×D4—41no—
229C2×D4—41no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4C22⋊C4×C5911yescharacteristic
234C22×C4C22⋊C4×C5911yescharacteristic
235C22×C4C22⋊C4×C5911yescharacteristic
236C22×C4C22⋊C4×C5911yescharacteristic
237C22×C4C22×C4×C5911yescharacteristic
238C22×C4C2×D4×C5911yescharacteristic
239C22×C4C2×D4×C5911yescharacteristic
240C2×C8—42no—
241C2×C8—42no—
242C2×C8—42no—
243C2×C8—42no—
244C2×C8—42no—
245C2×C8—42no—
246C4⋊C4—22no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—42no—
250C4⋊C4—42no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C22⋊C4—42no—
254C22⋊C4—42no—
255C22⋊C4—42no—
256C22⋊C4—42no—
257C22⋊C4—41no—
258C22⋊C4—41no—
259C22⋊C4—41no—
260C22⋊C4—41no—
261C42—22no—
262C42—21no—
263C42—21no—
264C42—41no—
265C42—41no—
266C42—41no—
267C42—41no—
268C42D8×C5912yes—
269C42SD16×C5912yes—
270C23—41no—
271C23—41no—
272C23—41no—
273C23—41no—
274C23—41no—
275C23—41no—
276C23—41no—
277C23C2×C22⋊C4×C5911yescharacteristic
278D4—82no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4#102×C5912yes—
305C2×C4#102×C5912yes—
306C2×C4#131×C5912yes—
307C2×C4C2×D8×C5911yescharacteristic
308C2×C4C2×SD16×C5911yescharacteristic
309C2×C4AGL(1,ℤ/8)×C5911yescharacteristic
310C2×C4#137×C5911yescharacteristic
311C8—82no—
312C8—82no—
313C22—81no—
314C22—81no—
315C22—81no—
316C22—81no—
317C22—81no—
318C22—81no—
319C22—81no—
320C22C59×#40811yescharacteristic
321C22C59×#41011yescharacteristic
322C22C59×#41311yescharacteristic
323C22C2×#102×C5911yescharacteristic
324C22C59×#41711yescharacteristic
325C22C59×#42111yescharacteristic
326C22C59×#42111yescharacteristic
327C4—22no—
328C4—22no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—21no—
333C4—22no—
334C4—41no—
335C4—41no—
336C4—81no—
337C4—81no—
338C4—81no—
339C2—161no—
340C2C59×#147311yescharacteristic
341C2C59×#148011yescharacteristic
342C2C59×#149511yescharacteristic
343C2C59×#151211yescharacteristic
344C2C59×#151711yescharacteristic
345C2C59×#153511yescharacteristic
346C2C59×#154711yescharacteristic
subgroupG/H
center, socleC23×C59C2×C22⋊C4
commutatorC22×C4C22×C4×C59
Frattini, cosocleC2×C42C23×C59
prime radicalC22×D4×C59C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C59 ◁ C43×C59 ◁ G

Complements

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

NH ≅ G/Ntype
2. C59×#1831C2semidirect
3. C59×#1831C2semidirect
4. C59×#1271C2semidirect
139. #7732C59direct (N × H)
167. #1831C2×C59semidirect
168. #1831C2×C59semidirect
169. #1271C2×C59semidirect
196. C59#7732direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#28602
C59×#18312
C59×#12712
C59×#12702
#773259